work, energy, power, and society...

CH

AP

TE

R

5

KEY CONCEPTS

After completing this chapter you will

be able to

• describe and defi ne qualitatively

and quantitatively the scientifi c

concepts of work, energy, power,

and the law of conservation of

energy

• solve problems involving work,

energy, power, and the law of

conservation of energy

• distinguish qualitatively and

quantitatively between kinetic

energy and potential energy,

especially gravitational

potential energy

• describe various forms of energy

and their common uses

• distinguish between renewable

and non-renewable energy

resources

• design and conduct

investigations involving

work, energy, and energy

transformations

• make research-informed

decisions about the wise use

of energy in everyday life

What Are Work, Energy, and Power, and How

Do They Affect Society and the Environment?

Snowboarding is a popular winter sport. When Shaun White won the gold medal in the men’s snowboarding half-pipe competition at the Vancouver 2010 Winter Olympics, he scaled 7.6 m high walls of snow, sometimes jumping 9 m above the top edge—a total height of over 16 m above the ground (the equivalent of a i ve-storey building)!

In the Olympic half-pipe competition, snowboarders slide down a 120 m long half-cylinder-shaped course (the half-pipe) in a crisscross fashion, soaring over the top edges on each cross. While in the air, they perform amazing somersaults and twists. Competitors are judged on the height of their jumps (getting air), the dii culty of their twists and l ips, the steadiness of their landings, and their overall form.

Snowboarders alternately speed up and slow down as they crisscross the half-pipe. h ey speed up when they slide down one side and slow down when they climb the other side and soar into the air. h e faster they descend on one side, the higher they will be able to leap into the air on the other side. Higher jumps allow the athletes to perform more spectacular acro-batics. Snowboarders do everything they can to increase their speed on their descents.

Half-pipe snowboarders have to be very i t. h ey need to have strong mus-cles and a good sense of balance to perform the l ips and twists that judges and the public expect to see. In this chapter, you will explore some of the physics ideas that help us understand the ups and downs of half-pipe snowboarding. h ese same ideas help us explain how roller coasters work, how waterfalls can be used to generate electricity, and why it is wiser to use compact l uorescent lamps than incandescent light bulbs.

Work, Energy, Power, and Society

Answer the following questions using your current knowledge.

You will have a chance to revisit these questions later, applying

concepts and skills from the chapter.

1. What is a force?

2. Provide an example of an energy transformation.

3. Why are fossil fuels non-renewable energy resources?

4. Which of the following uses more energy in 1 h of use:

a 100 W light bulb or a 50 W light bulb? Explain.

STARTING POINTS

220 Chapter 5 • Work, Energy, Power, and Society NEL

Mini Investigation

Pizza Pan Half-Pipe

Skills: Predicting, Performing, Observing, Analyzing, Evaluating, Communicating

In this activity, you will use a marble to model the motion of a

half-pipe snowboarder.

Equipment and Materials: 3–4 textbooks; small marble;

metric ruler; large sheet of paper; circular pizza pan

(30 cm diameter) with edge; tape

1. Stack 3–4 textbooks in a step-like fashion on a tabletop

so that part of the edge of each book is exposed.

2. Carefully cut a sheet of paper so that it fi ts inside the

bottom of a circular pizza pan.

3. Tape the paper into the bottom of the pan and place

pencil marks at the 4 o’clock and 6 o’clock positions.

4. Lean the top edge of the pan on the lowest book in the

stack. Tape the bottom edge of the pan at the 6 o’clock

position onto the tabletop so that it does not move.

5. Place a marble on the inside edge of the pan at the level

of the 4 o’clock pencil mark (this is the marble’s initial

position). Release the marble and let it roll along the inside

edge of the pan. Repeat this 2 or 3 times, noting the height

to which the marble rises on the other side. Place a pencil

mark at that point (this is the marble’s fi nal position).

6. Use a ruler to measure the vertical distance from the

tabletop to the marble’s initial and fi nal positions.

7. Remove the tape from the lower edge of the pan and

increase its slope by leaning the top edge against a

higher book. Tape the bottom of the pan to the table at

the 6 o’clock position.

8. Repeat Steps 5 and 6, releasing the marble from the

same initial position.

9. Explore the motion of the marble further by repeating

Steps 7 and 8 a few more times.

A. Describe any differences in the initial and fi nal positions

of the marble in each case. T/I C

B. Compare the results you obtained in Steps 5, 6, 8, and 9,

and try to provide reasons for any observed differences. T/I

SKILLSHANDBOOK

A2.1

introduction 221NEL

5.1 Work

It took a lot of work for Canadian Olympic weightliter Marilou Dozois-Prevost to lit a 76 kg barbell over her head at the 2008 Beijing Olympics (Figure 1). In weightliting, you do work by moving weights from the ground to a position above your head. To lit the weights, you apply an upward force that displaces (moves) the weights in the direction of the force. his form of work is called mechanical work. In science, mechanical work is done on an object when a force displaces the object in the direction of the force or a component of the force.

Work Done by a Constant Force

Mathematically, the mechanical work, W, done by a force on an object is the product of the magnitude of the force, F, and the magnitude of the displacement of the object, Dd:

W 5 FDd

his equation applies only to cases where the magnitude of the force is constant and where the force and the displacement are in the same direction. Since work is a product of the magnitude of the force and the magnitude of the displacement, the symbols for force and displacement in the equation W 5 FDd are written without the usual vector notations 1 F>, Dd

>

2 . Work is a scalar quantity; there is no direction associated with work.

he SI unit for work is the newton metre (N?m). he newton metre is called the joule (J) in honour of James Prescott Joule, an English physicist who investigated work, energy, and heat (1 N?m 5 1 J). Notice that we do not consider the amount of time the force acts on an object or the velocities or accelerations of the object in the calculation of work.

Work Done When Force and Displacement

Are in the Same Direction

he equation W 5 FDd may be used to calculate the amount of mechanical work done on an object when force and displacement are in the same direction. In the fol-lowing Tutorial, you will solve two Sample Problems involving mechanical work in which a force displaces an object in the same direction as the force.

mechanical work (W ) applying a force

on an object that displaces the object in

the direction of the force or a component

of the force

Figure 1 Olympic weightlifter Marilou

Dozois-Prevost did work on a barbell

while lifting it over her head.

Describing Work

When describing work, you should

always mention the object that does

the work and the object that the work

is done on.

LEARning TIP

NEL222 Chapter 5 • Work, Energy, Power, and Society

Tutorial 1 Using the Equation W 5 FDd to Calculate Work Done

In this Tutorial, you will use the equation W 5 FDd to calculate the amount of work done by a

force when the force and displacement are in the same direction.

Sample Problem 1

How much mechanical work does a store manager do on a

grocery cart if she applies a force with a magnitude of 25 N in

the forward direction and displaces the cart 3.5 m in the same

direction (Figure 2)?

We are given the force, Fa, and the cart’s displacement, Dd.

Since the force and displacement are in the same direction, we

may use the equation W 5FaDd to solve the problem.

Given: Fa 5 25 N; Dd 5 3.5 m

Required: W

Analysis: W 5 Fa Dd

3.5 m

25 N

Figure 2

Fv = Fa sin

Fh = Fa cos

θθ∆d

θ

Fa

Fg

Fv

Fh

F N

Work

Work has a different meaning in

science than it does in everyday life.

In science, work is done only when a

force displaces an object. If a force is

applied on an object, but the object

does not move, then no work is done.

For example, Marilou Dozois-Prevost

was applying a force on the barbell

while she was lifting it and while she

was holding it motionless over her

head. However, she did work on the

barbell (in the scientific sense) only

while she was lifting it, not while

holding it over her head as in Figure 1.

LEARning TIPWork Done When Force and Displacement

Are in Different Directions

In some cases, an object may experience a force in one direction while the object moves in a diferent direction. For example, this occurs when a person pulls on a suitcase with wheels and a handle (Figure 3(a)). he free-body diagram (FBD) for this situation is shown in Figure 3(b). In this case, the applied force is directed toward the person’s hips, while the suitcase rolls on the loor in the forward direction. he FBD shows all the forces acting on the suitcase, including the force of gravity (Fg), the normal force (FN), and the applied force resolved into horizontal (Fh) and vertical (Fv) components.

Figure 3 (a) A system diagram of a

trolley suitcase displaced to the right

(b) FBD of a trolley suitcase displaced

to the rightdisplacement

applied

force

θ(b)(a)

5.1 Work 223NEL

Sample Problem 2

Solution: W 5 Fa Dd

5 (25 N)(3.5 m)

5 88 N # m W 5 88 J

Statement: The store manager does 88 J of mechanical work on

the grocery cart.

A curler applies a force of 15.0 N on a curling stone and

accelerates the stone from rest to a speed of 8.00 m/s in 3.50 s.

Assuming that the ice surface is level and frictionless, how much

mechanical work does the curler do on the stone?

In this problem, we are given the force but not the stone’s

displacement. However, in Chapter 1, you learned that the

displacement of an accelerating object may be determined

using the equation Dd 5 av1 1 v2

2bDt if you know the initial

speed, v1, the final speed, v2, and the time interval, Dt, in which

the object’s change in speed occurs.

Given: Fa 5 15.0 N; v1 5 0 m/s; v2 5 8.00 m/s; Dt 5 3.50 s

Required: W

Analysis: Dd 5 av1 1 v2

2bDt ; W 5 FaDd

Solution: First, we calculate Dd using the v1, v2, and Dt values given.

Dd 5 av1 1 v2

2bDt

5 a0 1 8.00 m/s

2b 13.50 s2

Dd 5 14.0 m

We now substitute the values of Fa and Dd into the equation for

work and solve.

W 5 Fa Dd

5 (15.0 N)(14.0 m)

5 2.10 3 102 N # m W 5 2.10 3 102 J

Statement: The curler does 2.10 3 102 J of mechanical work on

the curling stone.

Practice

1. A 0.50 kg laboratory dynamics cart with an initial velocity of 3.0 m/s [right] accelerates for 2.0 s

at 1.2 m/s2 [right] when pulled by a string. Assume there is no friction acting on the cart. T/I

(a) Calculate the force exerted by the string on the cart. [ans: 0.60 N]

(b) Calculate the displacement of the cart. [ans: 8.4 m]

(c) Calculate the mechanical work done by the string on the cart. [ans: 5.0 J]

Tutorial 2 Using the Equation W 5 F (cos u)Dd to Calculate Work Done

In this Tutorial, you will analyze two cases in which objects experience a force in one direction and

a displacement in a different direction.

CASE 1: An objECT iS DiSPLACED bY A FoRCE THAT HAS A ComPonEnT in THE DiRECTion oF THE DiSPLACEmEnT

(We will assume that the force of friction is negligible.) he FBD also indicates that the applied force vector, F

>

a, makes an angle θ with the displacement vector, Dd>

.he magnitude of Fh is given by the equation

Fh 5 Fa cos u

Since the horizontal component, Fh, is the only force in the direction of the suit-case’s displacement, it is the only force that causes the suitcase to move along the loor. hus, the amount of mechanical work done by Fh on the suitcase may be calcu-lated using the equation W 5 Fa (cos u)Dd or, in general,

W 5 F (cos u)Dd

where W is the work done, F is the force, and cos u is the angle between the force and the displacement vector, Dd.

What about the vertical component of Fa? Fv does no work on the suitcase because the suitcase is not displaced in the direction of Fv. Since Fv is perpendicular to the suitcase’s displacement along the loor (u 5 90°), Fv does no work on the suitcase. his can be calculated using the work equation, W 5 Fa (cos u)Dd, where u 5 90°:

W 5 Fa (cos u)Dd

5 Fa (cos 90°)Dd

5 Fa (0)Dd, since cos 90° 5 0

W 5 0 J

his result illustrates an important principle of mechanical work. In general, the work done by a force is zero when the force’s direction is perpendicular to the object’s displacement; that is, when u 5 90°, cos 90° 5 0, and W 5 0 J.

Dot ProductsThe scalar product of two vectors is

commonly indicated by placing a dot

between the vector symbols (e.g.,

W 5 F> # Dd

>

) and unit symbols

(N.m). It is for this reason that a scalar

product is sometimes called a dot

product. A dot product may also be

represented by using scalar symbols

without the dot between them (as we

do in this book), W 5 FDd.

LEARning TIP

Sample Problem 1Calculate the mechanical work done by a custodian on a vacuum

cleaner if the custodian exerts an applied force of 50.0 N on the

vacuum hose and the hose makes a 30.0° angle with the floor. The

vacuum cleaner moves 3.00 m to the right on a level, flat surface.

The system diagram for this problem is shown in Figure 4.

30.0°

FN

Fa = 50.0 N

d = 3.00 m

Fg

Figure 4

In this problem, the system diagram shows that three forces

are acting on the vacuum cleaner: the force of gravity, F>

g; the

normal force, F>

N; and the applied force, F>

a. Only the magnitude

of the component of F>

a in the direction of the displacement

(Fa cos u) does work on the vacuum cleaner. The other two forces

(F>

N and F>

g) do no work on the vacuum cleaner because they are

perpendicular to the displacement.

Given: Fa 5 50.0 N; Dd 5 3.00 m; u 5 30.0°

Required: W

Analysis: W 5 Fa (cos u)Dd

Solution: W 5 Fa (cos u)Dd

5 (50.0 N)(cos 30.0°)(3.00 m)

5 1.30 3 102 N # m W 5 1.30 3 102 J

Statement: The custodian does 1.30 3 102 J of mechanical

work on the vacuum cleaner.


CASE 2: An objECT iS DiSPLACED, bUT THERE iS no FoRCE oR ComPonEnT oF A FoRCE in THE DiRECTion oF THE DiSPLACEmEnT

Practice

1. A person cutting a flat lawn pushes a lawnmower with a force of 125 N at an angle of 40.0°

below the horizontal for 12.0 m. Determine the mechanical work done by the person on the

lawnmower. T/I [ans: 1.15 kJ]

2. A father pulls a child on a toboggan along a flat surface with a rope angled at 35.0° above

the horizontal. The total mechanical work done by the father over a horizontal displacement

of 50.0 m is 2410 J. Determine the work done on the toboggan by the normal force and the

force of gravity, and explain your reasoning. T/I [ans: 0]

Sample Problem 2

Ranbir wears his backpack as he walks forward in a straight hallway. He walks at a constant

velocity of 0.8 m/s for a distance of 12 m. How much mechanical work does Ranbir do on his

backpack?

Consider the system diagram shown in Figure 5. Ranbir walks at constant velocity. Thus,

there is no acceleration in the direction of displacement and no applied force on the backpack in

that direction. The only applied force on the backpack is the force that Ranbir’s shoulders apply

on the backpack (F>

a) to oppose the force of gravity on the backpack (F>

g, the backpack’s weight).

However, neither the applied force nor the force of gravity does work on the backpack because

both forces are perpendicular to the displacement. Therefore, Ranbir does no mechanical work

at all on the backpack.

Work Done When a Force Fails to Displace an Object

In some cases, a force is applied on an object, but the object does not move: no displacement occurs. For example, when you stand on a solid loor, your body

applies a force on the loor equal to your weight (F>

a 5 F>

g), but the loor does not

move. Your body does no work on the loor because the loor is not displaced. In the following Tutorial, you will examine a situation in which a force is applied but no displacement occurs.

∆d

Fa

Fg

Figure 5

5.1 Work 225NEL

In the following Sample Problem, you will determine how much work is done when an

applied force does not cause displacement.

Sample Problem 1

How much mechanical work is done on a stationary car if a student pushing with a 300 N

force fails to displace the car?

Given: Fa 5 300 N; Dd 5 0 m

Required: W

Analysis: W 5 FDd

Solution: W 5 FDd

5 (300 N)(0 m)

W 5 0 J

Statement: No mechanical work is done by the student on the car.

Tutorial 3 Applied Force Causing no Displacement

Positive and Negative Work

In many cases, an object experiences several forces at the same time. For example, when Marilou Dozois-Prevost lited weights at the Beijing Olympics, she applied

a force, F>

a, on the barbell in the upward direction, while Earth applied a force of

gravity, F>

g, on the barbell in the opposite direction (Figure 6).In cases such as this, the total work done on the object is equal to the algebraic sum

of the work done by all of the forces acting on the object. We assume that the forces act in the same direction as the object’s displacement or in a direction opposite the object’s displacement (u 5 0° or u 5 180°). In the following Tutorial, you will calculate the total work done on an object when the object experiences forces in opposite directions.

Fa

Fg

Figure 6 Marilou Dozois-Prevost applied

a force on the barbell in the upward

direction, while Earth applied a force of

gravity in the downward direction.

Tutorial 4 Positive and negative Work

In the following Sample Problem, we will consider the total work done on an object when the

object experiences two forces: an applied force in the same direction as its displacement

and another force (a force of friction) in the opposite direction.

Sample Problem 1

A shopper pushes a shopping cart on a horizontal surface

with a horizontal applied force of 41.0 N for 11.0 m. The cart

experiences a force of friction of 35.0 N. Calculate the total

mechanical work done on the shopping cart.

In this problem, the applied force, F>

a, does work, Wa, on the

cart, and the force of friction, F>

f, does work, Wf, on the cart. While F>

a

acts in the same direction as the cart’s displacement, F>

f acts in the

opposite direction. Thus, we will use the equation W 5 F (cos u)Dd

to calculate work. We will solve this problem in three parts.

(a) Calculate the work done by the applied force using the

equation Wa 5 Fa(cos u)Dd.

(b) Calculate the work done by the force of friction using the

equation Wf 5 Ff (cos u)Dd.

(c) Determine the total, or net, work done on the cart, Wnet, by

calculating the sum of Wa and Wf .

Given: Fa 5 41.0 N; Dd 5 11.0 m; Ff 5 35.0 N

Required: Wa ; Wf ; Wnet

(a) mechanical work done by the applied force on the cart

Analysis: Wa 5 Fa (cos u)Dd

Solution: Since the force of friction acts in the same

direction as the displacement, u 5 0° here.

Wa 5 Fa (cos u)Dd

5 (41.0 N)(cos 0°)(11.0 m)

5 451 N # m Wa 5 451 J

In general, if a force fails to displace an object, then the force does no work on

the object. Another case in which no work is done occurs when an object moves on

a frictionless surface at constant velocity with no horizontal forces acting on it. For

example, an air hockey puck that travels 2 m at constant velocity on an air hockey table

experiences a displacement but no force (assuming no friction). In this case,

Fa 5 0 N and Dd 5 2 m

W 5 FaDd

5 (0 N)(2 m)

W 5 0 J

No work is done on the puck as it glides at constant velocity on the air hockey table.

Practice

1. There is no work done for each of the following examples. Explain why. K/U C

(a) A student leans against a brick wall of a large building.

(b) A space probe coasts at constant velocity toward a planet.

(c) A textbook is sitting on a shelf.


Graphing Work Done

he work done by a force on an object may be represented graphically by plotting the magnitude of the force, F, on the y-axis and the magnitude of the object’s position, d, on the x-axis. In such cases, we assume that the force acts in the same direction as the object’s displacement or in a direction opposite the object’s displacement (u 5 0° or u 5 180o). his is known as a force–position, or F–d, graph. Figure 7 shows an F–d graph for a constant force acting through a displacement Dd. he work done, W, is equal to the area under the F–d graph (the shaded rectangle) and is equal in value to the product FDd.

Positive and negative work may also be represented using an F–d graph. In Figure 8, positive work (work done when force and displacement are in the same direction) is represented by the blue rectangle above the d-axis. Negative work (work done when force and displacement are in opposite directions) is represented by the red rectangle below the d-axis.

Work Done by a Changing Force

he equation W 5 FDd or W 5 F(cos u)Dd can be used only to calculate the mechan-ical work done on an object when the force on the object is constant. However, in many cases, a force varies in magnitude during a displacement. For example, when a bus driver steadily depresses the accelerator pedal of a bus, the force the engine applied on the wheels increases uniformly. he force is not constant.

he work done on an object by a changing force that is in the same direction as the object’s displacement may be represented using an F–d graph. Figure 9 shows an F–d graph for a uniformly increasing force. As in the case of a constant force, the work done is equal to the area under the F–d graph. In this case, the work done, W, is equal in value to the product Fav Dd. Fav represents the average force applied to the object as it is displaced.

Statement: The applied force does 451 J of mechanical

work on the cart.

(b) mechanical work done by the force of friction on the cart

Analysis: Wf 5 Ff (cos u)Dd

Solution: Since the force of friction acts in the opposite

direction of the displacement, u 5 180° here.

Wf 5 Ff (cos u)Dd

5 (35.0 N)(cos 180°)(11.0 m)

Wf 5 2385 J

Statement: The force of friction does 2385 J of mechanical

work on the cart.

(c) net work done by the applied force and the force of friction

on the cart

Solution: Wnet 5 Wa 1 Wf

5 451 J 1 (2385 J)

Wnet 5 66 J

Statement: The net work done by the applied force and the

force of friction on the cart is 66 J.

Practice

1. Curtis pushes a bowl of cereal along a level counter a distance of 1.3 m. What is the net

work done on the bowl if Curtis pushes the bowl with a force of 4.5 N and the force of

friction on the bowl is 2.8 N? T/I [ans: 2.2 J]

2. A crane lifts a 450 kg beam 12 m straight up at a constant velocity. Calculate the

mechanical work done by the crane. T/I [ans: 53 kJ]

W = F∆d

d

F

∆dF

0

Figure 7 F–d graph for a constant force

acting through a displacement

negativeworkdone

d

positiveworkdone

–F

F

∆d

∆d

F

0

Figure 8 F–d graph representing

positive and negative work done

F

d

Fav

area = work done

= Fav ∆d

∆d

Figure 9 F–d graph representing a

uniformly increasing force

5.1 Work 227NEL

5.1 Summary

• Mechanicalworkisdonewhenaforcedisplacesanobjectinthedirectionofthe force or a component of the force.

• h eequationW 5 F(cos u)Dd may be used to calculate the amount of mechanical work done on an object.

– If the force on an object and the object’s displacement are in the same direction, then u 5 0°, cos u 5 1, the equation W 5 F(cos u)Dd becomes W 5 FDd, and the amount of work is a positive value.

– If the force on an object and the object’s displacement are perpendicular, then u 5 90°, cos u 5 0, and W 5 0 J (no work is done).

– If a force acts on an object in a direction opposite the object’s displacement, then u 5 180°, cos u 5 21, the equation W 5 F(cos u)Dd becomes W 5 (F∆d)(21), and the amount of work is a negative value.

• Whentheforceonanobjectandthedisplacementoftheobjectareparallel(in the same direction or opposite in direction), the work done on the object may be determined from an F–d graph by i nding the area between the graph and the position axis. h e work is positive if the area is above the position axis and negative if it is below the position axis.

• Whenaforcevariesinmagnitudeduringadisplacement,theworkdoneisequal to the product of the average force, Fav , and the displacement, Dd.

In this activity, you will determine the work done by a person lifting a book and a shoe.

Equipment and Materials: scale; textbook; tape measure or metre stick; desk; shoe

1. Use a scale to measure the mass of a textbook. Calculate the textbook’s weight in

newtons.

2. Use a tape measure or metre stick to measure the vertical distance from the fl oor to

the top of a desk.

3. Place the textbook on the fl oor beside the desk and lift it straight up to the top of the

desk at a constant speed.

4. Calculate the work you did on the book.

5. Obtain a clean shoe. Hold the shoe in your hand for a few seconds to get a feel for

its weight.

6. Predict the amount of work you would have to do on the shoe to lift the shoe straight

up from the fl oor to the top of the desk at constant speed.

7. Test your prediction by determining the weight of the shoe and then lifting the shoe

from the fl oor to the top of the desk and calculating the work done.

A. Compare the amount of work you did on the textbook to the amount of work you did

on the shoe. T/I

B. Evaluate the prediction you made in Step 6 on the basis of the results you obtained

in Step 7. T/I

C. Calculate the height above the fl oor to which you would have to lift the shoe to do

the same amount of work as you did on the textbook. T/I

Human Work

Mini Investigation

Skills: Predicting, Performing, Observing, Analyzing SKILLSHANDBOOK

A2.1


5.1 Questions

1. A 25.0 N applied force acts on a cart in the direction of the

motion. The cart moves 13.0 m. How much work is done by

the applied force? T/I

2. A tow truck pulls a car from rest onto a level road. The tow

truck exerts a horizontal force of 1500 N on the car. The

frictional force on the car is 810 N. Calculate the work done

by each of the following forces on the car as the car moves

forward 12 m: T/I

(a) the force of the tow truck on the car

(b) the force of friction

(c) the normal force

(d) the force of gravity

3. A child pulls a wagon by the handle along a flat sidewalk.

She exerts a force of 80.0 N at an angle of 30.0° above

the horizontal while she moves the wagon 12 m forward.

The force of friction on the wagon is 34 N. T/I

(a) Calculate the mechanical work done by the child on

the wagon.

(b) Calculate the total work done on the wagon.

4. A horizontal rope is used to pull a box forward across

a rough floor doing 250 J of work over a horizontal

displacement of 12 m at a constant velocity. T/I C

(a) Draw an FBD of the box.

(b) Calculate the tension in the rope.

(c) Calculate the force of friction and the work done by the

force of friction. Explain your reasoning.

5. A 62 kg person in an elevator is moving up at a constant

speed of 4.0 m/s for 5.0 s. T/I C

(a) Draw an FBD of the person in the elevator.

(b) Calculate the work done by the normal force on the person.

(c) Calculate the work done by the force of gravity on the

person.

(d) How would your answers change if the elevator were

moving down at 4.0 m/s for 5.0 s?

6. A force sensor pulls a cart horizontally from rest.

The position of the cart is recorded by a motion sensor.

The data were plotted on a graph as shown in Figure 10.

The applied force and the displacement are parallel. What

is the work done on the cart by the force sensor after a

displacement of 0.5 m? T/I

d (m)0.50.40.30.20.100

2

4

F (N)

Figure 10

7. A rope pulls a 2.0 kg bucket straight up, accelerating it

from rest at 2.2 m/s2 for 3.0 s. T/I

(a) Calculate the displacement of the bucket.

(b) Calculate the work done by each force acting on the

bucket.

(c) Calculate the total mechanical work done on the

bucket.

(d) Calculate the net force acting on the bucket and the

work done by the net force. Compare your answer

to the total mechanical work done on the bucket as

calculated in (c).

8. In your own words, explain if mechanical work is done in

each of the following cases: K/U C

(a) A heavy box sits on a rough horizontal counter in a

factory.

(b) An employee pulls on the box with a horizontal force

and nothing happens.

(c) The same employee goes behind the box and pushes

even harder, and the box begins to move. After a few

seconds, the box slides onto frictionless rollers and

the employee lets go, allowing the box to move with a

constant velocity.

9. The graph in Figure 11 shows the force acting on a

cart from a spring. The force from the spring is either in

the same direction as the cart’s displacement or in the

opposite direction. T/I C

d (m)43

AB

C210

5

F (N)

–5

Figure 11

(a) Calculate the work done in sections A, B, and C.

(b) Calculate the total work done.

(c) Explain why the work done in section C must be

negative.

10. Describe two ways to determine the total work done by one

object on another object. K/U C

11. Consider the equation W 5 F (cos u)Dd. K/U C

(a) Using the equation, explain why a force perpendicular

to the displacement does zero work.

(b) Using the equation, explain why a force opposite to the

displacement does negative work.

5.1 Work 229NEL

5.2 EnergyAs you learned in Section 5.1, mechanical work is done by applying forces on objects and displacing them. How are people, machines, and Earth able to do mechanical work? h e answer is energy: energy provides the ability to do work. Objects may pos-sess energy whether they are moving or at rest. In this section, we will focus on a form of energy possessed only by moving objects.

Kinetic Energy: The Energy of Moving Objects

A moving object has the ability to do work because it can apply a force to another object and displace it. h e energy possessed by moving objects is called kinetic energy (Ek) (from the Greek word kinema, meaning “motion”). For example, a moving hammer has kinetic energy because it has the ability to apply a force on a nail and push the nail into a piece of wood (Figure 1). h e faster the hammer moves, the greater its kinetic energy, and the greater the displacement of the nail. In general, objects with kinetic energy can do work on other objects.

Quantifying Kinetic Energy

Since kinetic energy is energy possessed by moving objects, consider a motor-cycle moving in a straight line on a roadway (Figure 2). h e motorcyclist and the motorcycle have a total mass, m. When the motorcyclist twists the motorcycle’s throttle, the motorcycle experiences a net force of magnitude, Fnet, that accelerates the motorcycle from an initial speed, vi, to a i nal speed, vf. h e acceleration occurs over a displacement of magnitude, Dd, in the same direction as the displacement. In this case, the engine does positive mechanical work on the motorcycle, since the displacement is in the same direction as the force. h e net force is the sum of the applied force produced by the engine, the normal force, the force of gravity, the force of friction between the wheels and the road, and the force of friction between the air and the vehicle (including the motorcyclist).

h e work equation may be used to describe the relationship between the total, or net, work done on the motorcycle, the magnitude of the net force and the displace-ment, and the angle between the applied force and the displacement:

Wnet 5 F net (cos u)Dd

Since the force and displacement are in the same direction, cos u 5 0° and W 5 Fnet Dd.Newton’s second law relates the magnitude of the net force to the motorcycle’s

mass and the magnitude of its resulting acceleration:

Fnet 5 ma

Substituting ma for Fnet in the work equation gives

Wnet 5 ma Dd

In Chapter 1, you learned that the following equation relates the i nal speed of an accelerating object to its initial speed and the magnitudes of its acceleration and displacement:

vf

2 5 vi

2 1 2aDd

Isolating aDd on the let side of this equation, we get

aDd 5vf

2 2 vi

2

2

Substituting vf

2 2 vi

2

2 for aDd in the equation Wnet 5 maDd, we get

Wnet 5 mavf

2 2 vi

2

2b or Wnet 5

mvf

2

22

mvi

2

2

energy the capacity to do work

kinetic energy (E k) energy possessed by

moving objects

∆d

Fa

Figure 1 A moving hammer can do

work on a nail because it has kinetic

energy.

Figure 2 Displacement of a motorcycle

accelerating on a fl at, level roadway

∆d

Fnet

Fnet

vi

vf


If we assume that the motorcycle accelerates from rest to v, then vi 5 0 m/s and vf 5 v:

Wnet 5mv

2

22 0

Wnet 5mv 2

2

he quantity mv2

2 is equal to the net amount of work done on the motorcycle

to cause it to reach a inal speed of v and also equals the amount of kinetic energy the motorcycle possesses as it travels at a speed of v. herefore, in general, an object of mass, m, travelling at a constant speed, v, has a kinetic energy, Ek, given by the equation

Kinetic energy is a scalar quantity: it has a magnitude given by the equation above, but it does not have a direction. If mass is measured in kilograms and speed

in metres per second, then Ek will have units of kg # m2

s2 . he unit kg # m2

s2 may be sim-pliied as follows:

kg # m2

s25 akg

# m

s2bm 5 N

# m

As you learned in Section 5.1,

1 N # m 5 1 J

herefore, both kinetic energy and mechanical work may be quantiied in units of joules, J. his indicates the close relationship between mechanical work and kinetic energy. We will use the kinetic energy equation in the following Tutorial.

Ek 5mv 2

2

Tutorial 1 Calculating the Kinetic Energy of a moving object

In this Tutorial, you will use the equation Ek 5mv 2

2 to calculate the kinetic energy of an object of

mass, m, moving at a constant speed, v.

Sample Problem 1

Calculate the kinetic energy of a 150 g baseball that is travelling

toward home plate at a constant speed of 35 m/s.

Given: m 5 150 g or 0.150 kg; v 5 35 m/s

Required: Ek, kinetic energy

Analysis: Ek 5mv 2

2

Solution: Ek 5mv 2

2

510.150 kg2 135 m/s2 2

2

Ek 5 92 J

Statement: The baseball has a kinetic energy of 92 J.

Practice

1. A 70.0 kg athlete is running at 12 m/s in the 100.0 m dash. What is the kinetic energy of the

athlete? T/I [ans: 5.0 kJ]

2. A dynamics cart has a kinetic energy of 4.2 J when moving across a floor at 5.0 m/s. What is

the mass of the cart? T/I [ans: 0.34 kg]

3. A 150 g bird goes into a dive, reaching a kinetic energy of 30.0 J. What is the speed of the

bird? T/I [ans: 20 m/s]

5.2 Energy 231NEL

The Relationship between Mechanical Work

and Kinetic Energy

You can observe the relationship between mechanical work and kinetic energy by

analyzing the mechanical work and kinetic energy equations. Since Ek 5mv2

2, the

equation Wnet 5mvf

2

22

mvi

2

2 may be written as Wnet 5 Ekf

2 Eki or Wnet 5 DEk,

where Ekf is the i nal kinetic energy and Eki

is the initial kinetic energy of the object. In words, this equation tells us that the total mechanical work, W, that increases the speed of an object is equal to the change in the object’s kinetic energy, Ekf

2 Eki. In

other words, work is a change in energy. h is relationship between kinetic energy and mechanical work is known as the work–energy principle.

work–energy principle the net amount

of mechanical work done on an object

equals the object’s change in kinetic

energy

Tutorial 2 Solving Problems Using the Work–Energy Principle

In the following Sample Problem, you will use the work–energy principle to determine the fi nal

speed of a hockey puck that is being pushed by a hockey stick.

Sample Problem 1

A 165 g hockey puck initially at rest is pushed by a hockey stick

on a slippery horizontal ice surface by a constant horizontal force

of magnitude 5.0 N (assume that the ice is frictionless), as shown

in Figure 3. What is the puck’s speed after it has moved 0.50 m?

vf

Fa

Fg

F N

∆d

Consider the diagram shown in Figure 3. In this problem, the

gravitational force and the normal force are equal in magnitude

and opposite in direction. Therefore, they cancel each other.

Since there is no friction, the magnitude of the net force on the

puck is equal to the magnitude of the applied force, F>

a, directed

horizontally. Since the net force is in the same direction as

the displacement, we may use the equation Wnet 5 Fnet Dd to

calculate the total work done on the puck. We may then use the

equation Wnet 5mvf

2

22

mvi

2

2 to calculate the puck’s fi nal speed, vf.

Given: m 5 0.165 kg; Fa 5 5.0 N; Dd 5 0.50 m; vi 5 0 m/s

Required: vf , the puck’s fi nal speed

Analysis: Wnet 5 Fnet Dd; Wnet 5mvf

2

22

mvi

2

2

Solution: Wnet 5 FaDd

5 15.0 N2 10.50 m2 5 2.5 N

# m

Wnet 5 2.5 J

Now that we have calculated the net work done on the puck, we

can use this value to fi nd the puck’s fi nal velocity.

Wnet 5mvf

2

22

mvi

2

2

Wnet 5mvf

2

22 0

vf

2 52Wnet

m

vf 5 Å2Wnet

m

5 Å 2 12.5 J20.165 kg

vf 5 5.5 m/s

Statement: The hockey puck’s fi nal speed is 5.5 m/s.

Practice

1. A 1300 kg car starts from rest at a stoplight and accelerates to a speed of 14 m/s over a

displacement of 82 m. T/I

(a) Calculate the net work done on the car. [ans: 130 kJ]

(b) Calculate the net force acting on the car. [ans: 1.6 3 103 N]

2. A 52 kg ice hockey player moving at 11 m/s slows down and stops over a displacement of

8.0 m. T/I C

(a) Calculate the net force on the skater. [ans: 390 N [backwards]]

(b) Give two reasons why you can predict that the net work on the skater must be negative.

Figure 3


Kinetic energy is the energy possessed by moving objects. he work–energy prin-ciple tells us that the change in an object’s kinetic energy is equal to the total amount of work done on that object. However, kinetic energy is not the only type of energy an object may have. Objects may possess another form of energy.

Gravitational Potential Energy: A Stored Type

of Energy

In a circus stunt, one acrobat stands on a platform at the top of a tower ready to jump onto one end of a seesaw. Another acrobat stands on the other end. When the acrobat on the tower steps of his platform, the force of gravity pulls him downward, and he accelerates toward the seesaw. Just before landing, the acrobat is moving very quickly and has a lot of kinetic energy. his kinetic energy allows the acrobat to do mechanical work on his end of the seesaw, displacing it downward. his downward motion causes the other acrobat to be thrown into the air (Figure 4).

When the acrobat was at the top of the tower, he was at rest and did not have kinetic energy. However, since he was positioned high above the ground, he had the ability to fall and gain kinetic energy that could do mechanical work. He was able to fall because of the force of gravity on him. he ability of an object to do work because of forces in its environment is called potential energy. Potential energy may be consid-ered a stored form of energy. he force acting on the acrobat as he fell is Earth’s gravi-tational force. herefore, we say that the acrobat had gravitational potential energy when he was above the ground because of his position. he acrobat’s gravitational potential energy started turning into kinetic energy as soon as he began to fall. A ski racer perched at the top of a ski hill, the water at the top of a waterfall, and a space shuttle orbiting Earth all have gravitational potential energy (Figure 5).

Figure 5 (a) A downhill skier, (b) the water at the top of Niagara Falls, and (c) the orbiting space

shuttle all have gravitational potential energy.

Quantifying Gravitational Potential Energy

Have you ever heard the expression “the higher you go, the harder you fall”? In physics, this means that objects can do more work on other objects if they fall from higher positions above a particular reference level, or the level to which an object may fall. Any level close to Earth’s surface may be used as a reference level. he selected reference level is assigned a gravitational potential energy value of 0 J, and levels above it have positive values (greater than 0 J). Levels below the reference level have negative values (less than 0 J).

Gravitational potential energy may be calculated using the equation Eg 5 mgh (where g 5 9.8 m/s2) only near Earth’s surface because the value of g changes as you move farther away from (or closer to) Earth’s centre. he value of g is about 9.8 m/s2 near Earth’s surface. However, the value steadily decreases to approximately 8.5 m/s2 at 400 km above Earth’s surface (height of a space shuttle orbit) and increases to about 10.8 m/s2 at a depth of 3000 km below the surface.

potential energy a form of energy an

object possesses because of its position in

relation to forces in its environment

gravitational potential energy energy

possessed by an object due to its position

relative to the surface of Earth

reference level a designated level to

which objects may fall; considered to have

a gravitational potential energy value of 0 J

Figure 4 The acrobat’s kinetic energy

does mechanical work on the seesaw,

causing the other acrobat to be

displaced into the air.

(a) (b) (c)

5.2 Energy 233NEL

Assume that a construction worker needs to drive a spike into the ground with a sledgehammer (Figure 6). To do this, the worker must i rst raise the hammer and then allow it to fall onto the spike. If we assume the top of the spike to be our refer-ence level, then the distance from the top of the spike to the hammer’s head is the height, h. h e weight of the hammer is given by the magnitude of F

>

g and is equal to mg, where m is the hammer’s mass and g is the magnitude of the gravitational force constant, 9.8 N/kg.

If the construction worker (CW) lit s the hammer straight up at constant speed, then he applies a force F

>

cw upward that is equal in magnitude to the weight of the hammer, mg. In lit ing the hammer, the worker is doing work given by Wcw 5 Fcw Ddsince the applied force and the displacement are in the same direction. h erefore, the work done by the construction worker on the hammer is Wcw 5 mgh since Fcw 5 mgand Dd 5 h. h is mechanical work serves to transfer energy from the construction worker to the hammer, increasing the hammer’s gravitational potential energy. h e change in the hammer’s gravitational potential energy is equal to the work done by the construction worker: Eg 5 mgh.

Note that the hammer is raised at constant speed (vi 5 vf). h e construction worker does work on the hammer, but the force of gravity also does work on the hammer, equal to Wg 5 Fg(cos 180°)Dd, or Wg 5 mgh(21).

In general, the gravitational potential energy of an object of mass, m, lit ed to a height, h, above a reference level is given by the following equation:

Eg 5 mgh

h e SI unit for gravitational potential energy is the newton metre, or the joule—the same SI unit used for kinetic energy and all other forms of energy. As with kinetic energy and work, gravitational potential energy is a scalar quantity.

Tutorial 3 Determining gravitational Potiential Energy

In this Tutorial, we will determine the gravitational potential energy of a person on a

drop tower amusement park ride. In a drop tower ride, people sit in gondola seats

that are lifted to the top of a vertical structure and then dropped to the ground. Special

brakes are used to slow the gondolas down just before they reach the ground.

Sample Problem 1

What is the gravitational potential energy of a 48 kg student at

the top of a 110 m high drop tower ride relative to the ground?

In this Sample Problem, the student’s mass and height

above ground (the reference level) are given. Therefore, we may

use the gravitational potential energy equation, Eg 5 mgh, to

calculate the student’s gravitational potential energy.

Given: m 5 48 kg; h 5 110 m; g 5 9.8 N/kg

Required: Eg, gravitational potential energy

Analysis: Eg 5 mgh

Solution: Eg 5 mgh

5 (48 kg)a9.8 N

kgb (110 m)

5 5.23104 N # m Eg 5 5.2 3 104 J or 52 kJ

Statement: The student has 52 kJ of gravitational potential

energy at the top of the ride relative to the ground.

Practice

1. A 58 kg person walks down the fl ight of stairs shown in Figure 7. Use the ground as

the reference level. T/I

(a) Calculate the person’s gravitational potential energy at the top of the stairs, on the

landing, and at ground level. [ans: 3400 J, 1700 J, 0 J]

(b) What happens to gravitational potential energy as you go down a fl ight of stairs?

What happens to gravitational potential energy as you climb a fl ight of stairs?

top

landing

ground

3.0 m

6.0 m

Figure 7

h

Fa

Fg

reference level

Figure 6 A construction worker uses a

sledgehammer.


Mechanical Energy

Objects may possess kinetic energy only, gravitational potential energy only, or a combination of kinetic energy and gravitational potential energy relative to a partic-ular reference level. For example, a hockey puck sliding on a l at ice surface at ground level has kinetic energy but no gravitational potential energy. An acorn hanging on a tree branch has gravitational potential energy but no kinetic energy. A parachutist descending to the ground has kinetic energy and gravitational potential energy.

h e sum of an object’s kinetic energy and gravitational potential energy is called mechanical energy. h erefore, if a sliding hockey puck has 10 J of kinetic energy and no gravitational potential energy, then it has 10 J of mechanical energy. If a descending parachutist has 5 kJ of kinetic energy and 250 kJ of gravitational potential energy, then the parachutist has 255 kJ of mechanical energy.

mechanical energy the sum of kinetic

energy and gravitational potential energy

Conservation of Energy (p. 257)

In this investigation, you will explore

what happens to the gravitational

potential energy, kinetic energy, and

total mechanical energy of a cart as

it rolls down a ramp.

investigation 5.2.15.2 Summary

• Energyisthecapacity(ability)todowork.• Kineticenergyisenergypossessedbymovingobjects.h ekineticenergyof

an object with mass, m, and speed, v, is given by Ek 5mv2

2.

• h etotalwork,Wnet, done on an object results in a change in the object’s kinetic energy: Wnet 5 Ekf

2 Eki, where Ekf

and Eki represent the i nal and

initial kinetic energy of the object, respectively. In other words, Wnet 5 DEk.

• Gravitationalpotentialenergyispossessedbyanobjectbasedonitspositionrelative to a reference level, which is ot en the ground. Eg 5 mgh, where h is the height above the chosen reference level.

• Mechanicalenergyisthesumofkineticenergyandgravitationalpotentialenergy.

5.2 Energy 235NEL

5.2 Questions

1. A bobsleigh with four people on board has a total mass

of 610 kg. How fast is the sleigh moving if it has a kinetic

energy of 40.0 kJ? T/I

2. A 0.160 kg hockey puck starts from rest and reaches a

speed of 22 m/s when a hockey stick pushes on it for

1.2 m during a shot. T/I

(a) What is the fi nal kinetic energy of the puck?

(b) Determine the average net force on the puck using two

different methods.

3. A large slide is shown in Figure 8. A person with a mass

of 42 kg starts from rest on the slide at position A and

then slides down to positions B, C, and D. Complete the

following using the ground as the reference level: T/I

16.0 m

A

D

h

B

h

C

Figure 8

(a) Calculate the gravitational potential energy of the

person at position A.

(b) The person has a gravitational potential energy of

4500 J at position B. How high above the ground is the

person at position B?

(c) The person loses 4900 J of gravitational potential

energy when she moves from A to C. How high is the

person at C?

(d) What is the person’s gravitational potential energy at

ground level at D?

4. Forty 2.0 kg blocks 20.0 cm thick are used to make a

retaining wall in a backyard. Each row of the wall will contain

10 blocks. You may assume that the fi rst block is placed at

the reference level. How much gravitational potential energy

is stored in the wall when the blocks are set in place? T/I

5. You throw a basketball straight up into the air. Describe

what happens to the kinetic energy and gravitational

potential energy of the ball as it moves up and back down

until it hits the fl oor. K/U C

6. Using the terms work, kinetic energy, and gravitational

potential energy, describe what happens to people in a drop

tower ride as they are slowly pulled to the top, released, and

then safely slowed down at the bottom. K/U C

5.3 Types of Energy and the Law of Conservation of EnergyYou use mechanical energy (a combination of kinetic energy and gravitational poten-tial energy) to do mechanical work every day. Is mechanical energy the only type of energy? In fact, there are many types of energy in the universe, all of which involve kinetic energy, potential energy, or both. Diferent types of energy have diferent names. Table 1 describes some diferent types of energy.

Table 1 Types of Energy

Type of energy

Form (kinetic,

potential, or

both)

Description

Application/Example

mechanical energy potential and

kinetic

energy possessed by

objects that are primarily

affected by the force

of gravity and frictional

forces

gravitational energy potential energy possessed by

objects that are affected

by the force of gravity;

applies to all objects on

Earth (and the universe)

radiant energy

(also known as

light, light energy,

or electromagnetic

radiation)

potential and

kinetic

energy possessed by

oscillating electric and

magnetic fields

electrical energy

(static electricity)

potential energy possessed by

accumulated static

charges

electrical energy

(current electricity)

potential and

kinetic

energy possessed by

flowing charges (you will

learn more about this in

Chapter 11)

thermal energy

(sometimes

incorrectly called

heat energy)

potential and

kinetic

energy possessed by

randomly moving atoms

and molecules (you will


Chapter 6)

sound energy potential and

kinetic

energy possessed by

large groups of oscillating

atoms and molecules

thermal energy the total quantity of

kinetic and potential energy possessed by

the atoms or molecules of a substance


Table 1 (continued)

nuclear energy

(also known as

atomic energy)

potential energy possessed by

protons and neutrons in

atomic nuclei (you will


Chapter 7)

elastic energy (also

known as spring

energy)

potential energy possessed

by materials that are

stretched, compressed, or

twisted and tend to return

to their original shape

chemical energy

(also known as

bond energy, fuel

energy, food energy,

molecular energy,

and internal energy)

potential energy associated with

bonds in molecules

nuclear energy potential energy of

protons and neutrons in atomic nuclei

Energy Transformations

he conversion of energy is called an energy transformation: the change of one form or type of energy into another. For example, photosynthesis is a process involving energy transformations in a plant. In photosynthesis, plants transform radiant energy into the chemical energy stored in food molecules (food energy) such as glucose (a sugar) and starch. In the process, some of the radiant energy is also transformed into thermal energy. Animals, including humans, eat plants and transform the chemical energy in the plants into chemical energy in their muscles. Muscles then transform this chemical energy into the kinetic energy of moving limbs, which do work on objects in the environment.

Technological systems also transform energy from one form into another. For example, an electric light bulb transforms electrical energy into radiant energy (light) and thermal energy (Figure 1). he internal combustion engine transforms the chemical energy in fuels such as gasoline and diesel into the kinetic energy of moving cars, motorcycles, trains, buses, and boats (Figure 2). In all of these processes, a lot of thermal energy is also produced and emitted into the environment.

The Law of Conservation of Energy

People oten wonder how much energy there is in the universe and whether we will eventually run out of energy. Scientists have studied energy and energy transforma-tions and have arrived at some important generalizations. For example, they noticed that when one form of energy is transformed into another form (or forms) of energy, the quantity of one form is reduced by the same amount that the quantity of the other form (or forms) is increased. his suggests that, in an energy transformation, the total amount of energy does not change but remains constant. For example, a light bulb may transform 100 J of electrical energy into 5 J of radiant energy and 95 J of thermal energy. he total amount of energy has not changed:

100 J of electrical energy 5 95 J of thermal energy 1 5 J of radiant energy

100 J of energy 5 100 J of energy

energy transformation the change of

one type of energy into another

Figure 1 A light bulb transforms

electrical energy into radiant energy

and thermal energy.

Figure 2 A gasoline engine transforms

the chemical energy in gasoline into

kinetic energy, thermal energy, and

sound energy.

5.3 Types of Energy and the Law of Conservation of Energy 237NEL

5 m

5 m

10 m

Eg

= 3.2 kJ

Ek

= 3.2 kJ

Em

= 6.4 kJ

Figure 4 Phase 2: at the halfway point

his generalization, known as the law of conservation of energy, is stated as follows:

Quantifying Energy Transformations

Evidence of the law of conservation of energy is all around us, but to notice it, you need to take measurements and perform simple calculations. Let us see how the law is demonstrated when a 65.0 kg diver performs a handstand dive from a 10.0 m high diving platform into the water below.

Let us analyze the dive in terms of the diver’s potential energy, Eg, kinetic energy, Ek, and total mechanical energy, Em, which is the sum of Eg and Ek. We will calcu-late these values for three phases of the dive occurring at three distinct moments in time: the phase before the diver leaves the platform, the phase when the diver has travelled half the distance to the water’s surface, and the phase when the diver’s ingers reach the water’s surface. We will assume that the water’s surface is the refer-ence level, where Eg 5 0 J.

Phase 1: Before the Dive

he diver begins the dive in a handstand position on the platform of the diving tower (Figure 3). Since he is motionless, the diver’s kinetic energy is equal to zero (Ek 5 0 kJ), and his gravitational potential energy is calculated as follows:

Eg 5 mgh

5 165 kg2 a9.8 N

kgb 110.0 m2

Eg 5 6.4 3 103 J or 6.4 kJ (two extra digits carried)

At this point in the dive, the diver’s kinetic energy is equal to 0 J and his potential energy is equal to 6.4 kJ. he diver’s total mechanical energy is equal to 6.4 kJ, the sum of his gravitational potential energy and his kinetic energy:

Em 5 Eg 1 Ek

5 6.4 kJ 1 0 kJ

Em 5 6.4 kJ

Phase 2: At the Halfway Point

When the diver leaves the platform, he will accelerate toward the water at 9.8 m/s2 (assuming negligible friction with the air). At the halfway point, the diver is 5.0 m above the water’s surface (Figure 4). At this point in the dive, the diver’s gravitational potential energy may be calculated as follows:

Eg 5 mgh

5 165 kg2 a9.8 N

kgb 15.0 m2

Eg 5 3.2 3 103 J or 3.2 kJ

At the halfway point, the diver’s kinetic energy may be calculated using the

equation Ek 5mv2

2. his equation requires us to determine the diver’s speed, v, at

the halfway point in the dive.

Law of Conservation of Energy

The total amount of energy in the universe is conserved. There is a certain total amount of

energy in the universe, and this total never changes. New energy cannot be created out of

nothing, and existing energy cannot disappear; the energy that exists can only be changed

from one form into another. When an energy transformation occurs, no energy is lost.

law of conservation of energy energy

is neither created nor destroyed; when

energy is transformed from one form into

another, no energy is lost

10 m

Eg

= 6.4 kJ

Ek

= 0 kJ

Em

= 6.4 kJ

Figure 3 Phase 1: before the dive


Since the diver accelerates as he descends, we may use the equation vf

2 5 vi

2 1 2aDd for this purpose. Since vf in the equation vf

2 5 vi

2 1 2aDd and v in the equation

Ek 5mv2

2 both represent the diver’s speed at this point in the dive, we will use the

symbol v (not vf) to represent the diver’s speed. hus,

v

2 5 vi

2 1 2aDd

v 5 "vi 1 2aDd

5 "2aDd since vi 5 0 m/s

5 "2 19.8 m/s22 15.0 m2 v 5 9.899 m/s 1two extra digits carried2

Substituting v 5 9.899 m/s into the equation Ek 5mv2

2 gives

Ek 5mv 2

2

5165 kg2 19.899 m/s2 2

2

Ek 5 3.2 3 103 J or 3.2 kJ

At the halfway point, the diver’s total mechanical energy is

Eg 5 Eg 1 Ek

5 3.2 kJ + 3.2 kJ

Em 5 6.4 kJ

he total mechanical energy is the same at this point in the dive as it was before the dive.

Phase 3: At the Water’s Surface

When the diver reaches the surface of the water, his height above the water is 0 m (Figure 5). hus, Eg 5 0 J since Eg 5 mgh and h 5 0 m. By this point, the diver has been accelerating for the full distance between the platform and the water. His kinetic energy is calculated as in Phase 2:

vf 5 "vi 1 2aDd

5 "2aDd, since vi 5 0 m/s

5 "2 19.8 m/s22 110.0 m2 vf 5 14 m/s

Ek 5mv 2

2

5165 kg2 114 m/s2 2

2

Ek 5 6.4 kJ

At the water’s surface, the diver’s total mechanical energy is

Em 5 Eg 1 Ek

5 0 kJ 1 6.4 kJ

Em 5 6.4 kJ

he total mechanical energy is the same at this point in the dive as it was just before the dive and at the halfway point. You can assume that the diver possesses the same total mechanical energy throughout the dive. You can check this assumption by performing similar calculations at diferent phases of the dive.

10 mE

g = 0 kJ

Ek

= 6.4 kJ

Em

= 6.4 kJ

Figure 5 Phase 3: at the water’s

surface


he example of the diver illustrates the law of conservation of energy by showing that while the diver’s gravitational potential energy was transformed into kinetic energy throughout the dive, his total mechanical energy did not change—it was conserved. he law of conservation of energy is an important fundamental law of nature that can help us solve many problems in everyday life.

A 1.1 kg camera slips out of a photographer’s hands while he

is taking a photograph. The camera falls 1.4 m to the ground

below.

(a) What is the camera’s gravitational potential energy relative

to the ground when it is in the photographer’s hands?

(b) Using the law of conservation of energy, determine the

camera’s kinetic energy at the instant it hits the ground.

(c) Use the camera’s kinetic energy to determine its speed at

the instant it hits the ground.

Solution

(a) Given: m 5 1.1 kg; h 5 1.4 m

Required: Eg, gravitational potential energy

Analysis: Eg 5 mgh

Solution: Eg 5 mgh

5 11.1 kg2 a9.8 N

kgb 11.4 m2

5 15 N # m Eg 5 15 J

Statement: The camera has 15 J of gravitational

potential energy relative to the ground when it is in the

photographer’s hands.

(b) We know that the camera has 0 J of kinetic energy when

it is in the photographer’s hands since it is not moving

at that time. Using the mechanical energy equation,

Em 5 Eg 1 Ek, we may show that the camera has 15 J

of total mechanical energy, Em, at this time since

Em 5 Eg 1 Ek

5 15 J 1 0 J

Em 5 15 J

According to the law of conservation of energy, the camera

will have the same total mechanical energy for its entire

fall. However, as the camera falls, its gravitational potential

energy is transformed into kinetic energy. The camera will

continuously lose gravitational potential energy as it gains

kinetic energy. At the instant it hits the ground, the camera

will have only kinetic energy since it is now at the reference

level (h 5 0) and its gravitational potential energy is zero.

We may use the mechanical energy equation, Em 5 Eg 1 Ek,

to calculate the camera’s kinetic energy at the instant it hits

the ground:

Em 5 Eg 1 Ek

Ek 5 Em 2 Eg

5 15 J 2 0 J

Ek 5 15 J

The camera has 15 J of kinetic energy when it hits the ground.

(c) Since we know the camera’s mass, m, and the kinetic

energy, Ek, it has when it hits the ground, we may use

the kinetic energy equation, Ek 5mv 2

2, to determine the

camera’s speed, v, when it hits the ground.

Given: Ek 5 15 J; m 5 1.1 kg

Required: v , speed

Analysis: Ek 5mv 2

2

Solution: Ek 5mv 2

2

v 5 Å2Ek

m

5 Å2 115 J21.1 kg

v 5 5.2 m/s

Statement: The camera has a speed of 5.2 m/s when it hits

the ground.

The camera’s speed may also be calculated using the kinematic

equations used earlier in this section. Try this approach to check

the calculation performed here.

The law of conservation of energy may be used to solve problems involving energy

transformations. In the following Sample Problem, we will analyze the energy transformations

that occur when an object (a camera in this case) falls to the ground.

Sample Problem 1

Tutorial 1 Applying the Law of Conservation of Energy


5.3 Summary

• Energyexistsinmanyforms.• Inanenergytransformation,energychangesfromoneformintoanother.• h elawofconservationofenergystatesthatwhenenergyischangedfrom

one form into another, no energy is lost.

• Whenusingthelawofconservationofenergytosolveproblems,youmayi nd the total mechanical energy, Em, at one point in the motion of the object and then equate it to the total mechanical energy at another point. h e total mechanical energy is Em 5 Eg 1 Ek.

Practice

1. A 0.20 kg ball is thrown straight up from the edge of a 30.0 m tall building at a velocity of

22.0 m/s. The ball moves up to the maximum height and then falls to the ground at the base

of the building. Use the law of conservation of energy to answer the following questions,

assuming that the reference level for gravitational potential energy is ground level. T/I

(a) What is the total energy of the ball at the start when it had a velocity of 22.0 m/s? [ans: 110 J]

(b) What is the velocity of the ball at the maximum height? What is the maximum height of the ball? [ans: 0 m/s [up], 55 m]

(c) What is the velocity of the ball when it hits the ground? [ans: 33 m/s [down]]

5.3 Questions

1. Describe the energy transformations occurring in each of

the following situations: K/U

(a) A ball falls from the top of a building.

(b) An archer pulls a bow back and releases the arrow.

(c) A fi rework explodes.

(d) An incandescent light bulb comes on.

(e) A gasoline lawnmower cuts the lawn.

2. A golf ball of mass 45.9 g is launched from a height of

8.0 m above the level of the green at a speed of 20.0 m/s.

At the maximum height above the green, the ball is moving

at 12 m/s. Assume there is no air resistance acting on the

ball. Calculate the following for the golf ball: T/I

(a) the total mechanical energy at the start (assume the

level of the green to be the reference level)

(b) the maximum height of the ball above the green

(c) the speed of the ball when it strikes the green

3. Many roller coasters have loops where carts roll on a

track that curves sharply up into the air. At the top, the

people are upside down (and usually screaming). For

safety reasons, many of these roller coasters must have a

minimum speed at the top of the loop. In the roller coaster

shown in Figure 6, the cart must have a minimum speed

of 10.0 m/s at the top of the loop to make it around safely.

Assuming that the roller coaster starts from rest at the top

of the fi rst hill and there is no friction on the roller coaster,

what is the minimum height of the fi rst hill? T/I

ground level

16 mh

Figure 6

4. A net force acts on an object initially at rest, giving it an

acceleration, a, while moving it a distance, Dd, forward

across a horizontal surface. T/I C

(a) Use kinematics equations to show that v 2 5 2aDd .

(b) The fi nal total mechanical energy is Ek 5mv 2

2.

Substitute the equation for the fi nal velocity into the

equation for the fi nal kinetic energy and simplify. What

does this new equation prove?


5.4 Effi ciency, Energy Sources, and Energy ConservationElectric light bulbs were invented over 150 years ago. Today, billions of light bulbs (lamps) illuminate vast areas of Earth at night (Figure 1). Light bulbs transform elec-trical energy into radiant energy and thermal energy.

95 %

waste thermal

energy out

5 %

useful radiant

energy out

100 %

electrical

energy in

Figure 2 Incandescent light bulbs

transform a very small percentage

of the electrical energy supplied into

radiant energy. Therefore, incandescent

bulbs produce a lot of thermal energy

waste.

Tutorial 1 Using the Efi ciency Equation

The effi ciency equation may be used to calculate the effi ciency of transforming one form of energy

into another, or the effi ciency with which work changes an object’s gravitational potential energy

or kinetic energy. In the fi rst Sample Problem of this Tutorial, you will calculate the effi ciency of

transforming one form of energy into another. In the second Sample Problem, you will calculate the

effi ciency with which a machine transforms mechanical work into gravitational potential energy.

Sample Problem 1

Figure 1 Large areas of Earth are illuminated by incandescent light bulbs at night.

A fi refl y’s body transforms chemical energy in food into

radiant energy that appears as a greenish glow in its abdomen

(Figure 3 on the next page). Firefl ies use this glow to attract

mates or prey. What is a fi refl y’s effi ciency if its body transforms

4.13 J of chemical energy into 3.63 J of radiant energy?

Since we are given the amounts of energy used and

produced, we may use the effi ciency equation to calculate the

effi ciency with which the fi refl y’s body transforms chemical

energy into radiant energy.

Have you ever noticed how hot incandescent light bulbs get? Typical incandescent bulbs transform only about 5 % of the electrical energy delivered to the bulbs into radiant energy. h e other 95 % of the electrical energy is transformed into thermal energy (Figure 2). We say that incandescent light bulbs are 5 % ei cient at converting electrical energy (the supplied energy) into radiant energy (the desired energy). Since we use light bulbs for illumination, not heating, the thermal energy produced is con-sidered to be waste energy or lost energy.

Effi ciency

Effi ciency is the ratio of the amount of useful energy produced (energy output, or Eout) to the amount of energy used (energy input, or Ein), expressed as a percentage. Ei ciency is calculated as follows:

efficiency 5Eout

Ein

3 100 %

effi ciency the amount of useful energy

produced in an energy transformation

expressed as a percentage of the total

amount of energy used


Figure 3 A firefly can transform chemical energy into

radiant energy.

Given: Ein 5 4.13 J (chemical); Eout 5 3.63 J (radiant)

Required: efficiency

Analysis: efficiency 5Eout

Ein

3 100 %

Solution: efficiency 5Eout

Ein

3 100 %

53.63 kJ

4.13 kJ3 100 %

efficiency 5 88 %

Statement: The firefly’s body transforms chemical energy into

radiant energy with 88 % efficiency.

Sample Problem 2

What is the efficiency of a rope-and-pulley system if a painter

uses 1.93 kJ of mechanical energy to pull on the rope and lift a

20.0 kg paint barrel at constant speed to a height of 7.5 m above

the ground (Figure 4)?

m = 20.0 kg

7.5 m

Em

= 1.93 kJ

In this question, the input energy is the energy the painter

uses to pull on the rope. You are not given the output energy,

so you cannot use the efficiency equation right away. As the

painter pulls on the rope, the paint barrel moves higher and gains

gravitational potential energy. The painter’s mechanical energy

is transformed into gravitational potential energy. Therefore,

Eg is the output energy, Eout. We may calculate the barrel’s

gravitational potential energy when it is 7.5 m above the ground

by using the equation Eg 5 mgh.

Given: Ein 5 1.93 kJ or 1.93 3 103 J; m 5 20.0 kg; h 5 7.5 m;

g 5 9.8 N/kg

Required: Eg, Eout, efficiency

Analysis: Eg 5 mgh and efficiency 5Eout

Ein

3 100 %

Solution: Eg 5 mgh

5 120.0 kg2a9.8 N

kgb 17.5 m2

5 1.470 3 103 J (two extra digits carried)

Eout 5 1.470 kJ (two extra digits carried)

efficiency 5Eout

Ein

3 100 %

51.470 kJ

1.93 kJ3 100 %

efficiency 5 76 %

Statement: The efficiency of the rope-and-pulley system

is 76 %.

Figure 4 What is the efficiency of this rope-and-pulley system?

Practice

1. A forklift uses 5200 J of energy to lift a 50.0 kg mass to a height of 4.0 m at a constant

speed. What is the efficiency of the forklift? T/I [ans: 38 %]

2. A tow truck attaches a cable to a car stuck in a muddy ditch. The 1250 kg car is pulled up

an embankment to a height of 1.8 m at a constant speed. The cable exerts a force of 5500 N

over a distance of 12.6 m to pull the car out of the ditch. K/U T/I

(a) What is the amount of useful energy produced? [ans: 22 kJ]

(b) What amount of energy is used to pull the car from the ditch? [ans: 69 kJ]

(c) Calculate the percent efficiency. Why is the efficiency less than 100 %? [ans: 32 %]

5.4 Eficiency, Energy Sources, and Energy Conservation 243NEL

Improving the Efficiency of Energy Transformations

Incandescent light bulbs are wasteful because they produce more thermal energy than radiant energy. Light bulbs are more eicient when they transform a greater amount of electrical energy into radiant energy. his is achieved, for example, in luorescent lamps and compact luorescent lamps (CFLs).

A CFL is a more compact version of the long luorescent tube lamps commonly used in large spaces such as oice buildings and schools (Figure 5). Fluorescent lamps may transform up to 25 % of the supplied electrical energy into radiant energy. his is a signiicant improvement in eiciency over incandescent light bulbs. Although luorescent lamps typically cost more than incandescent bulbs to purchase, they may provide the same amount of illumination at a lower overall cost because they use less electrical energy to produce the same amount of radiant energy. However, luorescent lamps contain mercury, a poisonous element, which may pollute the environment when the lamps are not disposed of properly. Table 1 describes the energy transfor-mation eiciency of a number of diferent devices and processes.

Table 1 Energy Transformation Efficiencies of Various Devices and Processes

Device or process

Energy

transformation

Major waste

output energy

Transformation

efficiency Considerations

gasoline-powered

vehicle

chemical (in

gasoline) → kinetic

(vehicle motion)

thermal 8–15 % • produces carbon dioxide, which contributes to

climate change

• creates air pollution

electric vehicle electrical → kinetic

(vehicle motion)

thermal 24–45 % • currently more expensive to purchase than gasoline-

powered vehicles

• more efficient than a gasoline vehicle but uses heavy

batteries that must be constructed and discarded in

special ways to help limit environmental contamination

bicycle kinetic (pedal) →

kinetic (bicycle

motion)

thermal 90 % • most efficient self-powered vehicle

• limited to transporting one or two individuals

• use is weather dependent

• road safety issues

loudspeakers electrical → sound thermal 1 % • efficiency appears to be low, but useful output energy

is more than enough to produce audible sound

• most of the electrical input is transformed into

thermal energy

electric heater electrical →

thermal

radiant 98 % • very efficient transformer of electrical energy into

thermal energy

hydroelectric

power plant

kinetic (moving

water) → electrical

thermal 80 % • efficient method of generating electricity

• damming rivers may flood land and disrupt ecosystems

nuclear power plant nuclear →

electrical

thermal 30–40 % • relatively efficient for generating electricity

• produces radioactive waste

solar cell radiant → electrical thermal 20–40 % • relatively efficient for generating electricity

photosynthesis radiant → chemical thermal 5 % • although it appears inefficient, it is the only process

that transforms radiant energy into chemical energy in

organisms

• directly or indirectly responsible for maintaining

virtually all life on Earth

animal muscles

(including human

muscles)

chemical (in food)

→ kinetic (muscle

movement)

thermal 20 % • although it appears to be relatively inefficient, this

energy-transforming process provides all the energy

animals use to perform work

Figure 5 Fluorescent lamps are more

efficient at producing radiant energy

than are incandescent lamps.


All the devices and processes in Table 1 transform energy with less than 100 % eiciency. his is a general result: no device or process is 100 % eicient. Another general result is that thermal energy is the most common form of waste energy. Of course, when thermal energy is the desired form of energy output (as in a heater), it is not considered to be waste energy. A primary goal of scientists and engineers is to improve the eiciency of devices and processes that transform energy.

Sources of Energy

We obtain energy from a variety of sources. For example, animals obtain chemical energy from food. his energy originates as radiant energy from the Sun (solar energy), which is captured and transformed into chemical energy by plants in the process of photosynthesis.

Energy-rich substances such as crude oil and natural gas are commonly called energy resources. Some energy resources are considered non-renewable, while others are renewable. A non-renewable energy resource is an energy-rich substance that cannot be replenished as it is used in energy-transforming processes. Fuels such as coal, oil, and natural gas are common non-renewable energy resources. A renewable energy

resource is an energy-rich substance with an unlimited supply or a supply that can be replenished as the substance is used in energy-transforming processes. Radiant energy from the Sun is an example of a renewable energy resource.

Non-renewable Energy Resources

Non-renewable energy resources are the most widely used sources of energy. Most automobiles, trains, motorized boats, and airplanes use non-renewable sources of energy. he most common are fossil fuels.

FOSSIL FUELS

Today, most automobile engines use the chemical energy in fuels such as gasoline and diesel. hese fuels are called fossil fuels because they are the decayed and com-pressed remains of prehistoric plants and animals that lived between 100 million and 600 million years ago. Like today’s plants, ancient plants transformed solar energy into chemical energy through photosynthesis. Ater the plants died, their bodies decomposed to form chemical mixtures such as crude oil. Today, we pump crude oil from underground deposits and separate, or reine, it into a variety of useful sub-stances, including gasoline and diesel fuels.

Other commonly used fossil fuels are coal and natural gas. Unlike gasoline and diesel, which are liquids at room temperature, natural gas is a gas that is mainly com-posed of a compound called methane. Natural gas is used as a fuel in furnaces (for heating), stoves (for cooking), and automobiles (for transportation) (Figure 6).

Fossil fuels are non-renewable energy resources because it takes millions of years for them to form. Once we use up the limited supply of these fuels, we will no longer have them as a source of energy. Of course, we will run out of fossil fuels and other non-renewable energy resources faster if we waste them or if we use devices that transform their energy ineiciently.

NUCLEAR ENERGY

Nuclear energy is a form of potential energy produced by interactions in the nucleus of atoms (atomic nuclei). Nuclear energy is released and transformed into other forms of energy when the nuclei of large, unstable atoms such as uranium decompose into smaller, more stable nuclei. Nuclear energy is also released when the nuclei of small atoms such as hydrogen combine to form larger nuclei. he decomposition of large, unstable nuclei is called nuclear fission, which takes place in power plants and radioactive elements. he combination of smaller nuclei to form larger nuclei is called nuclear fusion, which is the power source of the Sun.

energy resource energy-rich substance

non-renewable energy resource a sub-

stance that cannot be replenished as it is

used in energy-transforming processes

renewable energy resource a substance

with an unlimited supply or a supply that

can be replenished as the substance is

used in energy-transforming processes

fossil fuel fuel produced by the decayed

and compressed remains of plants that

lived hundreds of millions of years ago

nuclear fission the decomposition of

large, unstable nuclei into smaller, more

stable nuclei

nuclear fusion a nuclear reaction in

which the nuclei of two atoms fuse

together to form a larger nucleus

Figure 6 The burner of a natural gas

stove


In Canada, nuclear energy is produced mostly by the ission of uranium in large nuclear power plants (Figure 7). In this process, nuclear energy is transformed into thermal energy, which heats water and turns it into steam. he high-pressure steam passes through pipes and turns the blades of a turbine, which is connected to an elec-tricity generator (Figure 8). he electricity generator produces current electricity that is distributed through a large network of wires called the power grid. Currently, nuclear power plants produce approximately 52 % of Ontario’s supply of electrical energy. You will learn more about nuclear energy in Chapter 7.

turbine building

condenser

(steam is condensed

and returned to

steam generator)

steam in closed system

drives turbine

steam generator

heavy water in closed

system carries heat

from reactor

fuel-loading

machine

reactor

turbine

water from lake

cools steam

(not connected to

other water systems)

generator

reactor building

Figure 8 Basic operations of a nuclear

power plant

Figure 7 The Pickering Nuclear power

plant in Pickering, Ontario

Renewable Energy Resources

Renewable energy resources are virtually inexhaustible. Some renewable energy resources have been used as sources of energy for a long time, while others have been discovered more recently. he radiant energy of the Sun, the kinetic energy of moving water (waves and waterfalls), and the kinetic energy of moving air (wind) are some of the renewable energy resources that humans have used over time.

SOLAR ENERGY

A common renewable energy resource is radiant energy from the Sun, or solar energy. Scientists have estimated that the Sun will continue to emit radiant energy for the next 5 billion years. his is such a long time that we consider the supply of radiant energy to be unlimited and, therefore, renewable.

Solar energy may be transformed into thermal energy for heating or into elec-trical energy to run electrical devices and appliances. Passive solar design is designing homes and buildings to take direct advantage of the Sun’s radiant energy for heating. Alternatively, the Sun’s radiant energy may be transformed into electrical energy using a device called a photovoltaic cell. he electrical energy produced by photovol-taic cells may be used immediately to run electrical appliances or may be stored in batteries for future use.

Passive Solar Design

In the northern hemisphere, the Sun appears to move from east to west in the southern part of the sky. However, the Sun appears to reach a much higher altitude in the middle of the day during the warmer summer months than it does during the colder winter months. Architects and designers may take advantage of the seasonal changes in the Sun’s apparent position in the sky when they design buildings.

solar energy radiant energy from the Sun

passive solar design building design that

uses the Sun’s radiant energy directly for

heating

photovoltaic cell a device that

transforms radiant energy into electrical

energy


For example, they may place windows and eaves on the south-facing side of a building so that the rays of the Sun shine directly through the windows in the winter but not in the summer (Figure 9). h is design will help the building’s interior spaces warm up in the winter and remain cooler in the summer.

Additional passive solar design elements that architects may use include

• orientingbuildingssothattheyhaveonewallfacingtheSun• placingmorewindowsorlargerwindowsonthesunnysideofa

building

• placingtalldeciduoustreesonthesunnysideofabuildingsotheSun’srays are blocked in the summer when the trees are covered in leaves but not in the winter when the leaves have fallen of the trees

Photovoltaic Cells

When solar energy interacts with certain solids, such as modii ed forms of silicon, the radiant energy may be transformed into electrical energy in the form of an electric current. h is is the energy transformation that occurs in a photovoltaic cell. When the source of radiant energy is the Sun, the photovoltaic cell is sometimes called a solar cell (Figure 10).

Photovoltaic cells may be placed on the roofs of houses and other buildings or on the surfaces of devices such as outdoor light i xtures and parking meters (Figure 11). Since photovoltaic cells rely on a constant supply of solar energy to operate, they are usually connected to batteries, which store excess electrical energy produced on bright, sunny days for use at night or on cloudy days.

Figure 9 Passive solar design helps reduce the

need for furnaces and air conditioners.

angle of the Sun’s

rays in summer

angle of the Sun’s

rays in winter

S N

overhanging eave

window

radiant energyfrom the Sun

glassmetalcontacts

current

currentmodified silicon

Figure 10 Radiant energy is

transformed into electrical energy

(electric current) in a photovoltaic cell.

Figure 11 A parking meter uses electrical

energy produced by a solar cell.

HYDROELECTRICITY

h e kinetic energy of rushing water is transformed into electrical energy (elec-tric current) in a hydroelectric power plant. Electrical energy produced in this way is called hydroelectricity or, simply, hydro. Hydroelectricity is considered a renewable energy resource because the water cycle ensures that there is always a supply of water with high potential energy in the power plant’s reservoir (Figure 12). In the water cycle, solar energy causes water in lakes and rivers to evaporate and rise into the upper atmosphere, where the vapour cools, con-denses, and falls as precipitation. As water in the reservoir falls through the penstock, it gains kinetic energy and strikes the blades of a fan-like turbine at the lower end. h e turbine is connected to an electricity generator, which produces electric current. Hydroelectric power plants produce more electrical energy than any other renewable energy resource in the world.

hydroelectricity electricity produced by

transforming the kinetic energy of rushing

water into electrical energy

reservoir

intakepenstock

turbine

generator

powerhouse

long-distance power lines

river

Figure 12 Operations of a typical hydroelectric

power plant

5.4 Efi ciency, Energy Sources, and Energy Conservation 247NEL

Table 2 Additional Renewable Energy Resources

Renewable

energy resource Description Considerations

geothermal • Earth possesses a virtually

unlimited supply of thermal

energy deep underground.

• Geothermal energy may be used

directly for heating and cooling

or be transformed into electrical

energy.

• accessible only in certain areas

• in some locations, deep holes

need to be drilled into the ground

to reach pockets of thermal

energy

wind • Wind strikes the blades of a

fan-like turbine, which turns

an electricity generator that

generates electrical energy.

• can be used only in windy

locations

• turbines generate electricity only

when wind is blowing

• turbines are noisy, and the blades

may strike birds and other wildlife

tidal • As tides rise and fall, the moving

water strikes the blades of a

turbine, which turns a generator.

The generator generates

electrical energy.

• Tidal turbines are similar to wind

turbines and are placed in bodies

of water where significant tidal

movements occur.

• turbines only work during tidal

movements

• may disrupt aquatic ecosystems

biofuels • Biofuels are solid, liquid, and

gaseous fuels derived from the

bodies of living or dead plants

and animals.

• Biofuels can include wood,

biological waste, and gases such

as methane produced during the

decomposition of plant matter.

• Solid biofuel may be called

biomass and gaseous biofuel

may be called biogas.

• burning the fuels may produce

air pollutants, including carbon

dioxide, which is linked to

climate change

Although renewable energy resources are replaceable or unlimited in supply, non-renewable energy resources such as coal, oil, and natural gas continue to be the most widely used sources of energy in the world today. Much of this is because most of today’s electric power plants, engines, heating systems, and appliances are designed to transform the chemical energy in fossil fuels into other forms of energy. he large-scale, global use of fossil fuels and fossil fuel–using devices keeps prices

relatively low.

“Conserving Energy” and “The

Law of Conservation of Energy”

When we say “conserve energy”

or “energy conservation,” we are

referring to ways in which people

may avoid wasting energy. However,

the law of conservation of energy

refers to the idea that the total

amount of energy is conserved when

one form of energy is transformed

into another form of energy.

LEARning TIP

A number of other renewable energy resources, in addition to solar energy and hydroelectricity, may help us reduce pollution and meet our energy needs. Table 2 describes additional renewable energy resources.

To learn more about becoming an

energy operations manager or power

systems engineer,

CAREER LINK

go To nELSon SCiEnCE


To learn more about ways you can

conserve energy,

WEb LINK


Conserving Energy

Energy may be conserved by designing, producing, and using machines, appliances, and devices that transform energy more eiciently. Energy may also be conserved by

• turninglightsofwhennotrequired• switchingofelectricaldevicesinsteadofleavingthemonstandbymode• takingshortshowersinsteadofbathsifpossible• runningdishwashersandclotheswashersonlywhentheyarefull• hangingclothestodry• usingfanstoreducetheneedforairconditioning• usingpublictransitandcarpoolingwhenpossible

5.4 Questions

1. In a race, a 54 kg athlete runs from rest to a speed of

11 m/s on a flat surface. The athlete’s body has an

efficiency of 85 % during the run. How much input energy

did the athlete provide? T/I

2. Athletes who compete in downhill skiing try to lose as little

energy as possible. A skier starts from rest at the top of a

65 m hill and skis to the bottom as fast as possible. When

she arrives at the bottom, she has a speed of 23 m/s. T/I

(a) Calculate the efficiency of the skier.

(b) Explain why the mass of the skier is not required when

calculating the efficiency.

3. A golf club with 65 J of kinetic energy strikes a

stationary golf ball with a mass of 46 g. The energy

transfer is only 20 % efficient. Calculate the initial speed

of the golf ball. T/I

4. Describe one advantage and one disadvantage in using

(a) non-renewable energy resources

(b) renewable energy resources K/U A

5. Compare nuclear power plants with hydroelectric power

plants in terms of efficiency, method of generating

electricity, energy transformations, and environmental

impact. K/U C A

6. An article on the Internet claims, “Fossil fuels are actually

a renewable energy resource since decaying plant and

animal matter is making new oil, natural gas, and coal all

the time.” Discuss the validity of this statement. C A

7. In this section, two different methods of using solar energy

were described: passive solar design and photovoltaic cells.

Explain the difference between passive solar design and

photovoltaic cells. K/U

5.4 Summary

• heequationtocalculatetheeiciencyofanenergytransformationis

efficiency 5Eout

Ein

3 100 %, where Eout is the useful energy output and Ein is

the energy input.

• Noenergy-transformingdeviceis100%eicient.Typicallythewasteenergyis in the form of thermal energy.

• Non-renewableenergyresourcesareenergy-richsubstancesthatcannotbereplenished when they are used up in the energy transformation process.

• Renewableenergyresourcesareenergy-richsubstanceswithanunlimitedsupply or a supply that can be replenished.

• herearemanywaystoconserveenergy.

UNIT TASK BOOKMARK

You can apply what you have learned

about efficiency and energy resources

to the Unit Task on p. 360.


5.5

Tutorial 1 Calculating Power

In this Tutorial, we will use the equation P 5DE

Dt to solve both of the following Sample Problems,

although we may use the equation P 5Wnet

Dt as well since Wnet 5 DE.

Sample Problem 1

How much power does a swimmer produce if she transforms

2.4 kJ of chemical energy (in food) into kinetic energy and

thermal energy in 12.5 s?

Solution

Since this question gives the values for the energy transformation

and the time interval, we may use the equation P 5DE

Dt to

calculate the power.

Given: DE 5 2.4 kJ or 2.4 3 103 J; Dt 5 12.5 s

Required: P

Analysis: P 5DE

Dt

Solution: P 5DE

Dt

52.4 3 103 J

12.5 s

5 190 J/s

P 5 190 W

Statement: The swimmer’s power is 190 W.

power (P) the rate of transforming

energy or doing work

Power

It takes time to change one form of energy into another. he rate at which energy is transformed depends on certain factors. For example, your muscles transform the chemical energy in food into kinetic energy (motion) and thermal energy much faster if you run up a set of stairs than if you walk slowly up the same set of stairs. Your body feels warmer and more tired the faster you climb the stairs.

You may also analyze this situation in terms of the work your body does in climbing to the top of the stairs. Whether you run or walk up a set of stairs, your body applies the same force against gravity and travels the same vertical distance. Your body does the same amount of work in each case. However, your body does the work faster when you run and slower when you walk. In other words, the rate at which work is done depends on how fast you move.

Physicists use the word power (P ) to describe the rate at which energy is trans-formed, or the rate at which work is done. Your body produces more power when you run up a set of stairs than when you climb up slowly. We may describe power mathematically as follows:

P 5DE

Dt or P 5

Wnet

Dt

Energy, work, and time are scalar quantities, so power is also a scalar quantity (it has no direction associated with it). Since energy and work are measured in joules and time is measured in seconds, power is measured in joules per second (J/s). In the SI system, the unit for power is called the watt (W) in honour of James Watt, a Scottish engineer who invented the irst practical steam engine. One watt is equal to 1 J/s.

Earlier in this chapter, you learned that work involves the transfer, or transforma-

tion, of energy. For example, if a golf club does 100 J of work on a golf ball in 0.1 s,

then the club transfers 100 J of energy to the golf ball in 0.1 s. he golf ball’s energy

changes by 100 J in 0.1 s. hus, the work done by the club on the golf ball is equal

to the change in energy, or Wnet 5 DE. We may calculate the golf club’s power using

the equation P 5Wnet

Dt or the equation P 5

DE

Dt. Both equations yield the same result

because Wnet 5 DE. In Tutorial 1, you will solve problems involving power.

Power and the Work–Energy

Principle

Although we developed the

work–energy principle (Wnet 5 DE) in

terms of changes in an object’s kinetic

energy, the principle also applies

when an object’s potential energy

changes.

LEARning TIP

Student Power (p. 258)

In this investigation, you will explore

your own personal power and work

done using different types of fitness

equipment. You will design your own

procedure using fitness equipment of

your choice.

investigation 5.5.1


A 64 kg student climbs from the ground fl oor to the second

fl oor of his school in 5.5 s. The second fl oor is 3.7 m above

the ground fl oor. What is the student’s power?

Solution

The fi rst two phrases in this problem describe a situation in

which a student travels from a lower fl oor to a higher fl oor of

his school. This means that the student’s gravitational potential

energy increases from a value of zero at the ground fl oor (the

reference level) to a value given by the equation Eg 5 mgh at the

second fl oor. Thus, the value of Eg is equal to the change in the

student’s energy, DE, which may be substituted into the equation

P 5DE

Dt to calculate the student’s power.

Given: m 5 64 kg; g 5 9.8 N/kg; h 5 3.7 m; Dt 5 5.5 s

Required: P

Analysis: Eg 5 mgh ; P 5DE

Dt

Solution: Eg 5 mgh

5 164 kg2 a9.8 N

kgb 13.7 m2

Eg 5 2.321 3 103 J (two extra digits carried)

DE 5 2.321 3 103 J

P 5 DE

Dt

52.321 3 103 J

5.5 s

5 4.2 3 102 J/s

P 5 4.2 3 102 W

Statement: The student’s power is 4.2 3 102 W.

Sample Problem 2

Practice

1. How long would it take a motor with 0.50 kW of power to do 1200 J of work? T/I [ans: 2.4 s]

2. A mountain climber with a mass of 55 kg starts from a height of 850 m above sea level at

9 in the morning and reaches a height of 2400 m by noon. What is the climber’s average

power? T/I [ans: 77 W]

3. A 60.0 kg person accelerates from rest to 12 m/s in 6.0 s. What is the person’s power? T/I

[ans: 720 W]

Human Power

Mini Investigation

Skills: Performing, Observing, Analyzing SKILLSHANDBOOK

A6.2

In this activity, you will compare the power of a student walking

slowly and walking quickly up a fl ight of stairs.

Equipment and Materials: bathroom scale; metric tape

measure or metre stick; staircase; stopwatch

1. Use a scale to measure your partner’s mass. Calculate your

partner’s weight in newtons.

2. Use a tape measure or metre stick to measure the height of

a staircase. You may do this by measuring the height of one

step and multiplying this by the total number of steps.

3. Use a stopwatch to measure the time it takes your partner

to walk up the stairs slowly at constant speed. Repeat this

three times and average the results.

Exercise caution when walking up the stairs. Never run.

4. Measure the time it takes your partner to walk up the stairs

more quickly at constant speed. Repeat this three times and

average the results.

A. Calculate the average power produced by walking up the

stairs slowly. T/I

B. Calculate the average power produced by walking up the

stairs more quickly. T/I

C. Was your partner’s power greater when walking up the

stairs quickly or slowly? Explain your observations. T/I

D. Compare your partner’s power in walking up the stairs slowly

and walking up the stairs quickly to the power of a 100 W light

bulb. Which process produces the most power: walking up the

stairs slowly, walking up the stairs more quickly, or using the

light bulb? Explain why you think this is the case. T/I

5.5 Power 251NEL

he electric elevator motor in Tutorial 2 transformed 290 kJ of electrical energy into gravitational potential energy in 16 s—a power of 18 kW. his is a common result for the power ratings of electrical devices: the ratings tend to be in the hun-dreds or thousands of watts. Table 1 lists the power ratings of some typical household appliances.

Energy Ratings and the Cost of Electricity

Companies that provide electrical energy to consumers use electricity meters to measure the total amount of electrical energy used (Figure 2 on the next page). his amount depends on the number of electrical devices being used, the power rating of each device, and the total amount of time each device is used. It is common for elec-tricity meters to measure the electrical energy used in units of kilowatt hours (kWh).

Tutorial 2 Calculating the Power of an Electrical Device

In this Tutorial, we will determine the power of an electrical device.

Sample Problem 1

What is the power of an electric elevator motor if it uses 2.9 3 105 J

of electrical energy to lift an elevator car 12 m in 16 s?

Solution

In this problem, the elevator motor transforms 2.9 3 105 J

of electrical energy into the elevator car’s gravitational

potential energy when it is 12 m above the ground. Therefore,

DE 5 2.9 3 105 J and Dt 5 16 s.

Given: DE 5 2.9 3 105 J; Dt 5 16 s

Required: P

Analysis: P 5DE

Dt

Solution: P 5DE

Dt

52.9 3 105 J

16 s

5 1.8 3 104 J/s

5 1.8 3 104 W

P 5 18 kW

Statement: The elevator motor’s power is 18 kW.

Practice

1. The Pickering Nuclear power plant has a power rating of 3100 MW. How much energy can the

generating station produce in one day? (Answer in MJ.) T/I [ans: 2.7 3 108 MJ]

Figure 1 (a) A toaster and (b) an electric guitar transform electrical energy.

(a)

(b)

Electrical Power

Electrical devices transform electrical energy into other forms of energy. For example, the hot, glowing elements of a toaster transform electrical energy into thermal energy and radiant energy, and an electric guitar transforms electrical energy into sound energy and thermal energy (Figure 1).

Like other energy-transforming devices, electrical devices may transform energy quickly or slowly. When they transform energy more quickly, they are more powerful, and when they transform energy more slowly, they are less powerful. he maximum power of an electrical device or appliance is sometimes referred to as the device’s power rating. he power rating of an electrical device may be calculated using the equation

P 5DE

Dt. Rearranging this equation yields the equation ∆E 5 PDt, which may be

used to calculate the amount of energy transformed by a device. In the following Tutorial, you will calculate the power of an electrical device.

Table 1 Power Ratings of Appliances

Appliance Power rating (W)

laptop computer 20–75

vacuum cleaner 200–700

microwave oven 600–1500

dishwasher 1200–1500

refrigerator 100–500

stove 6000–10 000


he use of the kilowatt hour for measuring a change in energy (energy used) becomes apparent when we analyze the equation DE 5 PDt. When power, P, is measured in kilowatts, kW, and the time interval, Dt, is measured in hours, h, the product PDt pro-duces the unit kilowatt hours, kWh. he energy used (transformed) by an electrical appliance, DE, is sometimes called the energy consumption rating, or energy rating, of the appliance. hus, the energy rating is commonly measured in kilowatt hours. In the following Tutorial, we will determine the energy rating of a common household appliance and the cost of operating the appliance.

Tutorial 3 Determining the Energy Rating of a Device

In this Tutorial, we will use the equation P 5DE

Dt to calculate the energy rating and the cost

of operating an electrical device with a particular power rating for a given amount of time.

Sample Problem 1

What is the cost of operating a 25 W light bulb 4.0 h a day for 6.0 days if the price of

electrical energy is 5¢/kWh?

Solution

We will solve this problem in two parts. In part (a), we will calculate the amount of energy

the light bulb will use (transform) in 6 days of operation (4 h per day). Then, in part (b), we

will use the amount of electrical energy transformed to calculate the cost of the electrical

energy. Note that the amount of electrical energy transformed must be calculated in kilowatt

hours, not joules, since the electricity provider charges per kilowatt hour, not per joule.

Therefore, we convert the units first.

Given: P 5 25 W or 0.025 kW; Dt 5 6.0 da4.0 h

db 5 24 h; price of electrical

energy 5 5¢/kWh

Required: DE, energy used (transformed); cost

Analysis: P 5DE

DtSolution:

(a) P 5DE

Dt

DE 5 PDt

5 (0.025 kW)(24 h)

DE 5 0.60 kWh

(b) cost 5 10.60 kWh2 a 5¢

kWhb

cost 5 3¢

Statement: It costs 3¢ to operate a 25 W light bulb for 24 h.

Practice

1. Twenty incandescent light bulbs are turned on for 12 h a day for an entire year

to light up a store. Each bulb has a power rating of 100.0 W. The average cost of

electricity is 6.0¢/kWh. T/I

(a) Determine the total amount of energy used by all the bulbs in the year.

[ans: 8800 kWh]

(b) Calculate the cost of lighting the store for the year. [ans: $530]

(c) How much money could be saved by using CFLs instead of the incandescent

bulbs if each CFL has a power rating of 23 W? [ans: $400]

Figure 2 Electricity meters measure the amount of electrical energy used.

5.5 Power 253NEL

he Canadian government requires all manufacturers of electrical appliances to place an EnerGuide label on all electrical appliances sold in Canada (Figure 3). he EnerGuide label shows the annual energy rating for an appliance in kilowatt hours. he consumer may use this value and the price of electrical energy to determine the average annual cost of operating the appliance. Consumers are encouraged to pur-chase appliances that have the lowest energy consumption rating possible. his will allow them to consume less electrical energy and save money.

5.5 Summary

• Poweristherateoftransformingenergyortherateofdoingwork.

he equations for power are P 5Wnet

Dt or P 5

DE

Dt.

• Powerisascalarquantitymeasuredinwatts(1W5 1 J/s).

• Electricaldevicestransformelectricalenergyintootherformsofenergy, and the power rating of these devices can be determined using the equations for power.

• heelectricalenergyusedbyanelectricaldevicecanbefoundusingtheequation DE 5 PDt.

5.5 Questions

1. A 54 kg person climbs a set of stairs at a constant speed

from the first floor to the fourth floor in 32 s. The change in

height from one floor to the next is 3.4 m. T/I

(a) Calculate the gravitational potential energy at the top of

the climb relative to the first floor.

(b) Calculate the power of the person for the climb.

(c) If a lighter person climbed the stairs in the same

time, would this person’s power be higher or lower?

Explain.

2. A 65 kg student climbs 5.0 m up a rope in gym class at a

constant speed of 1.4 m/s. T/I

(a) Determine the time it takes the student to climb up the

rope, and then determine the student’s power.

(b) Determine the student’s power without finding the time

it takes the student to climb up the rope. Explain your

reasoning.

3. A student uses a pulley to lift a mass into the air. K/U C

(a) Assume the mass is lifted at a constant speed. Describe

one way you could determine the power of the student

when she is lifting the mass.

(b) Assume the mass started from rest at ground level and

accelerated upward with a constant acceleration. What

types of energy will the object have while it is being

pulled up by the student? How would you determine the

student’s power in this case?

4. A family of five is planning to install solar panels on the roof

of their home to help reduce the cost of electricity and save

energy to help the environment. The family plans to install

10 panels, each with a power rating of 600 W. On average,

a solar panel can produce electricity for 4.5 h daily. T/I

(a) How much solar energy will the solar panels transform

into electrical energy each day?

(b) Assume the average cost of electricity is 5.5¢/kWh.

How much money will the family save in a year on their

electrical energy bill?

(c) Each person in the family uses electrical energy at

an average rate of 2 kWh per day. Will they still need

to buy electricity from an electrical energy supplier?

Explain your reasoning.

5. Show that 1 kWh 5 3.6 MJ. C

Figure 3 EnerGuide label on a typical household refrigerator


• Researching• Performing• Observing• Analyzing

• Evaluating• Communicating• Identifying

Alternatives

SKILLS MENU

Explore Applications of Renewable Energy Sources5.6

Going Off the Grid

Families and individuals are becoming more concerned with the rising cost of energy and the use of energy resources that harm the environment. More and more Canadians are considering alternative sources of energy. Brownouts, which are short-term reductions in the supply of electricity, are becoming more common in the summer. When the demand for electricity peaks, power companies are unable to keep up with the demand. Governments are planning to construct new nuclear power plants to meet the rising demand for electricity.

Most buildings in Canada are connected to a large electricity distribution system called the electrical power grid. hese grids are managed by large utility companies. Most families rely on these networks to supply their electrical energy needs. hey may not be aware of alternative sources of energy.

The Application

David Jamal, a Grade 11 student, lives with his mother, father, brother, and two sis-ters in a mid-sized, detached, suburban home on the outskirts of Sudbury, Ontario (Figure 1). he Jamals have been discussing their family’s energy consumption and have made several changes to reduce energy use as much as possible. Some of the changes are the installation of a programmable thermostat, a drain water heat-recovery system, ceiling fans, and CFLs (Figure 2). he ceiling fans help keep rooms cool during warm summer nights. In the winter, the programmable thermostat turns the furnace down when everyone is out and back up again just before everyone gets home.

hese devices have reduced the Jamals’ heating and air conditioning costs quite a bit, but their monthly electricity bills are still very high. he cost of electricity also seems to increase every year. he family has decided to try a bigger change—they are going to reduce their reliance on the power grid by generating their own electricity!

brownout reduced supply of electricity

caused by system damage or excess

demand

electrical power grid a large electricity

distribution system composed of a

network of electrical power plants and

electricity distribution towers and cables

Ater learning about renewable energy resources such as solar energy, wind energy, and geothermal energy at school and on the Internet, David convinced his parents to speak to a renewable energy consultant and explore the possibility of installing solar panels on the roof of their home or a wind turbine in their backyard, or both. David’s parents have agreed with this idea and have decided to look into the matter further.

Figure 1 The Jamal family’s home Figure 2 Ceiling fan with CFLs

NEL 5.6 Explore Applications of Renewable Energy Sources 255

You and your group members will assume the role of renewable energy consul-tants. You have been hired to advise the Jamal family of its renewable energy options. You will take into consideration the Jamal family’s situation and the location of their home. You will explain how residential photovoltaic and wind turbine systems work and how they can be installed in homes like the Jamals’. You will also advise the Jamals of costs associated with installing solar panels and wind turbines. Finally, you will identify government programs that provide incentives to residents who install

renewable energy systems.

Your Goal

To advise the Jamal family on how they may generate their own electricity from a renewable energy source

Research

Conduct library or Internet research about renewable energy sources and of-the-grid electrical energy generation, especially through the use of solar panels and wind turbines. Be sure to research the costs associated with each method of generating

energy.

Summarize

Use the following questions to summarize your recommendations to the Jamal family:

• WhataresomeofthebeneitsanddrawbacksoftheJamals’currentenergysystems? What are some of the beneits and drawbacks of generating their own electricity?

• Howdoresidentialphotovoltaicandwindturbinesystemswork?• WhatdotheJamalshavetodotostartgeneratingtheirownelectricity?• Whichrenewableenergy-generatingsystemswouldbethemostcost-efective

for the Jamals to implement in their home, taking into consideration the costs associated with installation and maintenance?

• Howmuchcouldthefamilyreducetheirelectricitybillsbygeneratingtheirown electricity?

Communicate

Give your renewable energy consulting irm a name and present your advice to the Jamal family in the form of a renewable energy plan. You may present the plan ver-bally, in writing, or in the form of a multimedia presentation to the class or a smaller group of your classmates.


Plan for Action

Plan a media campaign you may use to inform students and

the residents in your school community of off-the-grid electrical

energy generation and other renewable energy options.

Compare these renewable energy sources to non-renewable

sources used in Ontario (fossil fuels, for example). Be sure

to research the affordability of each option and inform your

audience of the most cost-effective choices. You may prepare

sample community or school newspaper articles, posters,

pamphlets, T-shirt logos, or radio and TV announcements to

share your findings with your school community.

To learn more about renewable

energy sources and off-the-grid

energy generation,

WEb LINK


UNIT TASK BOOKMARK

You can apply what you have learned

about renewable energy sources to the

Unit Task on page 360.

To learn more about becoming a

renewable energy consultant or

sustainable energy researcher,

CAREER LINK



Conservation of Energy

In this investigation, you will explore what happens to the gravitational potential energy, kinetic energy, and total mechanical energy of a cart as it rolls down a ramp.

Testable Question

What are the relationships between• gravitationalpotentialenergyandposition• kineticenergyandposition• totalmechanicalenergyandposition

for a laboratory cart rolling down a ramp?

Hypothesis/Prediction

Make hypotheses based on the Testable Question. Your hypotheses should include predictions and reasons for your predictions.

Variables

Read the Testable Question, Experimental Design, and Procedure, and identify the manipulated variables, responding variables, and controlled variables in this experiment.

Experimental Design

In this experiment, you will place a motion sensor at the top of a ramp and use the sensor’s sot ware to sketch a position–time graph of a laboratory cart as it rolls down the ramp. You will use one position near the end of the relevant data as the i nal position or reference point. You will use other positions to i nd the height and speed of the cart. You will then use these data to calculate the gravitational potential energy, kinetic energy, and total mechanical energy of the cart. Finally, you will look for patterns in these data to complete the experiment.

Equipment and Materials

• eyeprotection• ramp• 3–4textbooksorwoodblocks• metrestick• motionsensor• laboratorycart

Procedure SKILLS

HANDBOOKA2.2

1. Prop up one end of a ramp using textbooks or wood blocks. Use a metre stick to measure the length of the ramp (L) and the height of the ramp (H) as shown in Figure 1.

2. Place the motion sensor at the top of the ramp, directed toward the bottom. Release the cart from a position near the motion sensor. Obtain the position–time graph of the cart as it rolls down the ramp away from the motion sensor.

3. Choose one point on the position–time graph near the end of the run. h e position coordinate for this

point will represent the i nal position d>

2 and the reference point that will be used to determine the height of the cart (h 5 0 at the reference point). h is point will not change throughout the experiment.

4. To i nd the height of any other position above the reference point, examine Figure 1. h e ramp itself forms a larger triangle and the displacement of the cart down the ramp forms a smaller, similar triangle. Using these similar triangles, we have

h

Dd5

H

L

h 5 Dd aH

Lb

h is equation will be used to calculate the height, h, of the cart on the ramp.

H

L

h

cart at position ∆d1

motion sensor

cart at position ∆d2

d2

∆d

d1

Figure 1

SKILLS MENU

• Questioning• Researching • Hypothesizing• Predicting

• Planning• Controlling

Variables

• Performing

• Observing • Analyzing• Evaluating• Communicating

investigation 5.2.1 CONTROLLED EXPERIMENT

CHAPTER 5 Investigations

NEL Chapter 5 investigations 257

5. To determine the speed at any point on the position–time graph, use the slope tool in the program for the motion sensor.

6. Starting with a point near the start of the run,

determine the position, d>

1, and the speed, v, at this point. Use these values to complete the irst row of Table 1.

7. Use other positions from the graph to complete the next three rows in Table 1. hese positions should get gradually closer to the inal position.

Table 1 Data for Conservation of Energy Investigation

Initial

position

Variable

d>

2 d>

1 Dd 5 d>

2 2 d>

1 h v Eg Ek E m

1

2

3

4

Analyze and Evaluate

(a) What variables were measured and manipulated in this investigation? What relationships, based on the Testable Question, were tested?

(b) Calculate the cart’s gravitational potential energy, Eg, kinetic energy, Ek, and total mechanical energy, Em,

for each initial position in Table 1. T/I

(c) Answer the Testable Question. T/I

(d) What efect does friction have on the diferent types of energy in this experiment? Use an FBD and the

concept of work to explain your reasoning. T/I C

(e) What are some possible sources of error? T/I

(f) Evaluate your hypotheses. How did your hypotheses

compare to the results of the experiment? T/I

(g) What energy changes take place in this experiment? What evidence have you found that almost no energy

is lost in this experiment? T/I

(h) Why is it essential to keep the inal position, d>

2, ixed for the entire investigation when testing conservation

of energy? T/I

(i) In your own words, explain how to determine the height of the cart above the inal position using the

position–time graph. T/I C

Apply and Extend

(j) Imagine doing the experiment again with one change: starting the cart at the bottom and launching it up the sensor. You may assume the cart does not hit the sensor. How would the initial speed up the ramp compare to the inal speed down the ramp at the

same position? Explain your reasoning. T/I

SKILLS MENU

• Questioning• Researching• Hypothesizing• Predicting

• Planning• Controlling

Variables

• Performing

• Observing • Analyzing• Evaluating• Communicating

investigation 5.5.1 OBSERVATIONAL STUDY

Student Power

In this investigation, you will explore your own personal power using different types of fitness equipment. To calculate your power, you will first determine how much work you have done while performing different exercises.

You must measure your own work and power while performing exercises for brief and long periods of time. he brief activity can last for 10 s and the long activity will last for 2 min. he activities should involve two types of itness equipment—one that uses mainly arm muscles and another that uses mainly leg muscles. Keep safety in mind when selecting exercises. Perform exercises at a comfortable level rather than pushing yourself to ind maximum power.

You should never use any fitness equipment without being

instructed on how to use it safely. Always get your teacher’s

approval before using any equipment. Notify your teacher of

any health problems that may prevent you from completing

this activity safely. Be careful when lifting weights and avoid

fast movements.

Purpose

To determine how the power of your legs compares to the power of your arms for diferent exercises, and to observe how the amount of work changes as the duration of an exercise increases


Equipment and Materials

• itnessequipment• stopwatch• metrestick• bathroomscale

Procedure SKILLS

HANDBOOKA2.4

1. Choose a piece of i tness equipment that can be used to exercise your arms. h e exercise you perform should involve lit ing weights.

2. Prepare a table in your notebook similar to Table 1 below. Record the mass you will be lit ing in the table. To calculate the force, use the equation Fg 5 mg.

3. Before performing the activity, measure the distance for the motion of your arms when lit ing the mass once. h e long exercise might involve lit ing a lighter mass, but it should be the same exercise.

4. Complete each exercise, recording any necessary information. Calculate the total work done by multiplying the force by the distance and the number of repetitions. Use the work and time to calculate the power. Make sure you take a break at er each activity. You can accomplish this by alternating turns among group members.

5. Choose a piece of i tness equipment you can use to exercise your legs. Your exercise should involve lit ing weights with your legs. h e weight could be external, such as in a leg press, or even your own body if you are using a stair climber.

6. Repeat Step 3 using the new piece of equipment (using your legs instead of your arms).

7. Complete each exercise, recording any necessary information. Calculate the total work done by multiplying the force by the distance and the number of repetitions. Use the work and time to calculate the power. Make sure you take a break at er each activity.

Analyze and Evaluate

(a) How does the amount of work done by your arms in the brief exercises compare with the work done in the long exercises? How does the power compare under the same circumstances? Explain why the powers are

dif erent. T/I

(b) How does the amount of work done by your legs in the brief exercises compare with the work done in the long exercises? How does the power compare under the same circumstances? Explain why the powers are

dif erent. T/I

(c) How does the power of your legs compare to the power

of your arms? Explain why they are dif erent. T/I

Apply and Extend

(d) People ot en i nd that a workout gets easier over time. Describe two changes that can be made to increase the work done and the power required for each

exercise to make it more challenging. T/I

A

(e) Many strength-training exercises are brief, while cardiorespiratory exercises take much longer. Use what you have learned in this activity to explain why

this is true. C A

(f) Explain why both the work done and the power are important things to consider when designing a new

workout routine. T/I

A

Table 1 Observations

Type of exercise Mass (kg) Force (N) Distance (m) Number of repetitions Time (s) Work (J) Power (W)

arms (brief)

arms (long)

legs (brief)

legs (long)

NEL Chapter 5 investigations 259

CHAPTER 5 SUMMARY

B.Sc.

M.B.A.

industrial engineer

power systems engineer

M.Sc.college/university

professor

sustainable

energy researcher

sustainable energy

and building technologist

power engineering

technologist

Ph.D.

B.Eng.12U Physics

11U Physics

OSSD

renewable energy

consultant

energy operations

manager

college diploma

Summary Questions

1. Create a study guide based on the Key Concepts on page 220. For each point, create three or four subpoints that provide further information, relevant examples, explanatory diagrams, or general equations.

2. Look back at the Starting Points questions on page 220. Answer these questions using what you have learned in this chapter. Compare your latest answers to those that you wrote at the beginning of the chapter. Note how your answers have changed.

mechanical work (W ) (p. 222)

energy (p. 230)

kinetic energy (Ek) (p. 230)

work–energy principle (p. 232)

potential energy (p. 233)

gravitational potential energy

(p. 233)

reference level (p. 233)

mechanical energy (p. 235)

thermal energy (p. 236)

nuclear energy (p. 237)

energy transformation (p. 237)

law of conservation of energy

(p. 238)

effi ciency (p. 242)

energy resource (p. 245)

non-renewable energy resource

(p. 245)

renewable energy resource

(p. 245)

fossil fuel (p. 245)

nuclear fi ssion (p. 245)

nuclear fusion (p. 245)

solar energy (p. 246)

passive solar design (p. 246)

photovoltaic cell (p. 246)

hydroelectricity (p. 247)

power (P ) (p. 250)

brownout (p. 255)

electrical power grid (p. 255)

Vocabulary

CAREER PATHWAYS

Grade 11 Physics can lead to a wide range of careers. Some require a college diploma

or a B.Sc. degree. Others require specialized or postgraduate degrees. This graphic

organizer shows a few pathways to careers related to topics covered in this chapter.

1. Select an interesting career that relates to Work, Energy, Power, and Society.

Research the educational pathway you would need to follow to pursue this career.

2. What is involved in becoming an energy consultant? Research at least two pathways

that could lead to this career, and prepare a brief report of your fi ndings.

SKILLSHANDBOOK

A7



CHAPTER 5 SELF-QUIZK/U

Knowledge/Understanding T/I Thinking/Investigation C

Communication A Application

For each question, select the best answer from the four

alternatives.

1. he SI unit for work is the joule. What is one joule equivalent to in SI units? (5.1) K/U

(a) 1 m/s2

(b) 1 N # m

(c) 1kg # m

s2

(d) 1kg

m # s2

2. A farmer lits a 216 N bale of hay onto the bed of a wagon that is 2.00 m above the ground. How much work is done on the bale of hay? (5.1) T/I

(a) 132 J

(b) 232 J

(c) 432 J

(d) 832 J

3. What is the kinetic energy of a 2.0 3 103 kg car travelling at a speed of 20.0 m/s? (5.2) T/I

(a) 2.0 3 105 J

(b) 4.0 3 105 J

(c) 4.0 3 106 J

(d) 8.0 3 106 J

4. A physics book is sitting on an overhead shelf and a biology book is sitting on a table at waist level. Which of the following statements about this situation is correct? (5.2) K/U

(a) he physics book has less potential energy than the biology book.

(b) he physics book has more potential energy than the biology book.

(c) he physics book has more kinetic energy than the biology book.

(d) Both books have the same amount of kinetic energy and potential energy.

5. What is the basis of thermal energy? (5.3) K/U

(a) the random motion of atoms and molecules

(b) the accumulation of static charges on a surface

(c) the interaction of protons and neutrons in atoms

(d) the stretching and twisting of molecules

6. An apple hanging from a tree has no initial kinetic energy (Eki

) and a certain amount of initial potential energy (Egi

). he stem of the apple breaks, and the apple falls to the ground. When the apple has fallen halfway to the ground, how do its inal kinetic energy (Ekf

) and inal potential energy (Egf) compare to Egi

? (5.3) K/U

(a) Egi , Ekf

1 Egf

(b) Egi 5 Ekf

2 Egf

(c) Egi 5 Eki

1 Egf

(d) Eki2 Egf

7. Which energy transformation takes place during photosynthesis? (5.4) K/U

(a) nuclear energy to radiant energy

(b) radiant energy to chemical energy

(c) chemical energy to thermal energy

(d) thermal energy to chemical energy

8. Which energy source is renewable? (5.4) K/U

(a) coal

(b) biofuel

(c) natural gas

(d) nuclear power

Indicate whether each statement is true or false. If you think

the statement is false, rewrite it to make it true.

9. Work equals mass times acceleration. (5.1) K/U

10. When a force acts on an object in a direction diferent from the direction of displacement, work can be calculated if the angle between the force and displacement vectors is known. (5.1) K/U

11. he kinetic energy of an object can be increased or decreased by doing work on it. (5.2) K/U

12. A bicycle moving at 5 m/s at sea level has more potential energy than a motionless bicycle at the top of a mountain. (5.2) K/U

13. he law of conservation of energy does not apply to electrical motors that are less than 100 % eicient. (5.3) K/U

14. Washing half loads of laundry instead of full loads conserves energy. (5.4) K/U

15. A motor that does 500 J of work in 1 s has the same power as a motor that does 500 J of work in 2 s. (5.5) K/U


To do an online self-quiz,

NEL Chapter 5 Self-Quiz 261

CHAPTER 5 REVIEWK/U

Knowledge/Understanding T/I Thinking/Investigation C

Communication A Application

Knowledge

Select the best answer from the four alternatives.

1. Which equation correctly describes the mechanical work done on an object? (5.1) K/U

(a) Wnet 5DE

DT

(b) Wnet 5Eout

Ein

3 100 %

(c) Wnet 5 vi2 1 2aDd

(d) Wnet 5 Fnet 1cos u2Dd

2. Which form of energy is wind energy? (5.3) K/U

(a) chemical

(b) electrical

(c) kinetic

(d) thermal

3. Into which two forms of energy is the electrical energy that powers a light bulb transformed? (5.3) K/U

(a) radiant energy and thermal energy

(b) thermal energy and chemical energy

(c) chemical energy and elastic energy

(d) elastic energy and kinetic energy

4. Which type of energy is commonly a by-product of any kind of energy transformation? (5.4) K/U

(a) radiant energy

(b) thermal energy

(c) chemical energy

(d) elastic energy

5. Which sequence of processes is correctly ordered from least eicient to most eicient in terms of energy transformations? (5.4) K/U

(a) generation of electricity with a hydroelectric power plant, photosynthesis, riding a bicycle, generation of electricity with a nuclear power plant

(b) generation of electricity with a nuclear power plant, riding a bicycle, photosynthesis, generation of electricity with a hydroelectric power plant

(c) photosynthesis, generation of electricity with a nuclear power plant, generation of electricity with a hydroelectric power plant, riding a bicycle

(d) riding a bicycle, generation of electricity with a hydroelectric power plant, generation of electricity with a nuclear power plant, photosynthesis

Indicate whether each statement is true or false. If you think

the statement is false, rewrite it to make it true.

6. Mechanical work is calculated by multiplying the magnitude of a force by the amount of time it is applied. (5.1) K/U

7. Energy can be deined as the ability to do work. (5.2) K/U

8. Gravitational energy is a form of kinetic energy. (5.3) K/U

9. Energy, work, and time are scalar quantities, but power is a vector quantity. (5.5) K/U

Match each term on the left with the most appropriate

description on the right.

10. (a) biofuel (i) may interfere with bird light paths

(b) geothermal energy (ii) harnesses the energy of moving water

(c) tidal generation (iii) may produce air pollutants when burned

(d) wind turbines (iv) available in unlimited supply deep underground (5.4) K/U

Write a short answer to each question.

11. Describe the relationship among displacement, work, and force. (5.1) K/U C

12. A 2000 kg rock rolls down a hillside at 40 m/s and crashes into a large tree, where it comes to rest. he tree does not move. How much work was done on the tree by the rock? Explain your answer. (5.1) T/I C

13. Explain how thermal energy is related to kinetic energy. (5.2) K/U

14. A skydiver with a mass of 60.0 kg reaches a terminal velocity of 40.0 m/s and continues to fall at that velocity until she opens her parachute. What is the kinetic energy of the skydiver as she falls at terminal velocity? (5.2) T/I

15. What do the terms m, g, and h in the equation Eg 5 mgh stand for? (5.2) K/U

16. Describe the main energy transformations that occur when an apple falls from a tree. (5.3) C K/U


17. What are the two types of electrical energy? (5.3) K/U

18. What methods may architects use to take advantage of the Sun’s radiant energy for heating a building? (5.4) K/U

19. In your own words, deine eiciency as it applies to a device designed to perform an energy transformation. (5.4) K/U

20. Which nuclear process do conventional nuclear power plants take advantage of to produce electricity? (5.4) K/U

21. Why are fossil fuels called fossil fuels? (5.4) K/U

22. What unit is commonly used when measuring the energy rating of an electrical appliance? (5.5) K/U

23. Explain the diference between energy and power. (5.5) K/U

Understanding

24. (a) Describe a situation in which pushing a wheelbarrow illed with soil does no work.

(b) Describe two diferent situations in which pushing a wheelbarrow full of soil does work. (5.1) K/U

25. A boy is mowing a lawn with a push mower. he handle of the mower makes a 30° angle with the ground. Explain how you would determine the horizontal component of the applied force if you know the total force exerted by the boy on the mower handle. (5.1) K/U

26. A 2100 kg car starts from rest and accelerates at a rate of 2.6 m/s2 for 4.0 s. Assume that the force acting to accelerate the car is acting in the same direction as its motion. How much work has the car done? (5.1) T/I

27. A roller coaster drops from the initial high point and continues to rise and fall as it follows the track up and down. Explain how transformations between kinetic and potential energy are related to the rising and falling of the roller coaster. (5.2, 5.3) K/U

28. A force does positive work on a moving object. (5.2) K/U A

(a) How is the velocity of the object afected?

(b) How is the energy of the object afected?

29. A 1900 kg car slows down from a speed of 25.0 m/s to a speed of 15.0 m/s in 6.25 s. How much work was done on the car? (5.2) T/I

30. A 68 kg rock climber who is 320 m above the ground descends down a rope at 1.5 m/s. Using the ground as a reference point, determine the total mechanical energy of the rock climber at this point. (5.2) T/I

31. A 2600 kg truck travelling at 72 km/h slams on the brakes and skids to a stop. he frictional force from the road is 8200 N. Use the relationship between kinetic energy and mechanical work to determine the distance it takes for the truck to stop. (5.2) T/I

32. Describe two energy transformations taking place at a hydroelectric power plant. Specify the energy types before and ater each transformation. (5.3) K/U

33. Describe the energy transformations occurring in each of the following situations. (5.3) K/U C

(a) Grass is growing.

(b) A vibrating guitar string is heard around the room.

(c) A stuntman falls and lands safely on a trampoline.

(d) he black asphalt on a driveway gets warm in the hot sun.

34. A bungee jumper has a mass of 73 kg and falls a distance of 120 m before the bungee catches and sends the jumper upward. Use the law of conservation of energy to calculate the speed of the jumper just before the bungee catches. (5.3) T/I

35. Compact luorescent light bulbs are more eicient than incandescent bulbs. (5.4) K/U

(a) Describe the energy transformations taking place in a light bulb.

(b) Explain the diference in eiciency of the two types of bulbs in terms of energy transformations.

36. (a) Deine the term renewable energy resource and give an example.

(b) Deine the term non-renewable energy resource and give an example. (5.4) K/U

37. A roller coaster descends 55 m from the top of the irst high point to the irst low point in the track. he roller coaster converts gravitational potential energy to kinetic energy with an eiciency of 50.0 %. What is the velocity of the roller coaster at the bottom of the irst low point? (5.4) T/I

38. A compact luorescent bulb is 17.0 % eicient. (5.4) T/I

(a) How much energy input would be required for the bulb to produce 252 J of light energy?

(b) What type of energy is the waste output and how much would be created?

39. A car’s engine is only 12 % eicient at converting chemical energy in gasoline into mechanical energy. If it takes 18 000 N of force to keep the car moving at a constant speed of 21 m/s, how much chemical energy would be needed to move the car a distance of 450 m at this speed? (5.4) T/I

Chapter 5 Review 263NEL

40. Copy and complete Table 1 in your notebook. (5.4) K/U

Table 1 Energy Sources

Energy source

Renewable or

non-renewable?

biofuel

coal

geothermal

hydroelectric

natural gas

nuclear

oil

solar

wind

wood

41. Explain how each of the following renewable energy sources is used to generate electricity or other forms of usable energy. Describe all the energy transformations involved, including the energy form before and ater each transformation. For each energy source, explain why it is considered renewable in terms of the original source of the energy. (5.4) K/U

(a) hydroelectric

(b) tidal

(c) geothermal

(d) wind

42. How many watts of power does a man with a weight of 600.0 N have when he climbs a light of stairs 3.0 m high in 5.0 s? (5.5) T/I

43. A girl pushes a merry-go-round with a force of 120 N for a distance of 6.0 m. If she does this in 2.0 s, how much power does she have? (5.5) T/I

44. A baseball player puts a baseball on a batting tee. he baseball bat is able to deliver 4.0 3 105 W of power and is in contact with the ball for 0.70 ms and a distance of 1.4 cm. he mass of the ball is 145 g. What is the net force applied to the ball and what is its average acceleration? (5.5) T/I

Analysis and Application

45. Give an example of a force that causes displacement but does no work. (5.1) K/U

46. In this chapter you learned that many activities that people think of as work are not classiied as work by scientists. (5.1) K/U C A

(a) Describe two physical activities that are considered to be work in a workplace situation but are not work in the scientiic sense. hese should be activities for which people are paid. Explain in terms of the directions of force and displacement why they are not work.

(b) Describe two physical activities that are classiied as work in both the everyday sense and the scientiic sense. hese should be activities for which people might be paid. Explain your classiication in terms of the directions of force and displacement.

47. A man is loading boxes onto a shelf that is 2.2 m high. It took 98 N of force to lit a 10.0 kg box at a constant speed onto the shelf. (5.1) T/I

(a) How much work was done by the man liting the box?

(b) How much work was done by gravity?

(c) What was the net work done on the box?

(d) Is it possible to determine the net work done on the box in this problem without knowing the mass of or the force exerted by the man? Explain.

48. A weightliter lits a 155 kg weight with 1910 N of force overhead to a height of 2.80 m. he weight then falls back down to the ground. Determine the net force acting on the weight for both the lit and the drop and create an F-d graph for this situation. (5.1) T/I C

49. A boy drops a 0.50 kg rock of of a 22 m high bridge into a river below. (5.2, 5.3) T/I

(a) Using the river as a reference point, what is the initial potential energy of the rock?

(b) What is the kinetic energy of the rock just before it hits the water?

(c) What is the inal speed of the rock just before it hits the water?

50. A 1800 kg trick airplane is 450 m in the air. At this point the plane takes a dive with an initial speed of 42 m/s and accelerates to 64 m/s, dropping a total distance of 120 m. (5.2, 5.3) T/I

(a) Using the ground as a reference point, calculate the potential energy of the plane at the beginning and the end of the dive.

(b) What is the kinetic energy of the plane at the beginning and at the end of the dive?

(c) What is the total work done on the plane during its dive?


51. A car travels at a constant velocity of 60.0 km/h on a level highway for a distance of 10.0 km. he car accelerates briely to 70.0 km/h to pass another car and then returns to 60.0 km/h as it ascends a hill. he car accelerates to 65 km/h as it descends the other side of the hill, even though the driver has taken her foot of the accelerator. (5.1, 5.2, 5.3) T/I A

(a) Identify the times when the car’s engine was doing work on the car. Explain your answers.

(b) Describe the energy transformations taking place when the engine was doing work.

(c) Describe the energy transformations when the engine was not doing work.

52. In this chapter you learned that solar cells are only relatively eicient at transforming radiant energy into electrical energy. Green plants are even less eicient at converting radiant energy to chemical energy. (5.4) C A

(a) Explain why low eiciency in these processes is less of a concern than it is in the processes that convert chemical energy in fossil fuels to useful forms of energy.

(b) Both biofuels and fossil fuels store chemical energy that originally came to Earth as sunlight. If the original source is the same, why are biofuels classiied as a renewable energy resource and fossil fuels as a non-renewable energy resource?

53. A man is pushing an 11 kg lawn mower against a frictional force of 86 N for 22 m. (5.4) T/I

(a) What is the minimal force that the man needs to push with in order to keep the lawnmower moving?

(b) Calculate the minimum amount of energy required for the man to push the lawnmower the required distance.

(c) If the man uses 2180 J of energy to push the mower at a constant speed what is his eiciency?

54. Traditional farmhouses oten have covered, open porches along the sides of the house (Figure 1). (5.4) K/U A

Figure 1

(a) Explain why this is a useful passive solar design.

(b) Explain why planting deciduous trees around a house is a better passive solar design than planting coniferous trees.

55. Two students perform an experiment to study the eiciency of an energy conversion and test the law of conservation of energy. For an energy conversion device, they choose a playground slide. hey take measurements as diferent students slide down the slide. hey use a speed gun to measure the inal speed of the sliders at the bottom of the slide. hey measure the height diference between the top and bottom of the slide to be 3.0 m. (5.4, 5.5) K/U T/I C A

(a) Derive the equation for the eiciency of transformation of potential energy into kinetic energy. Explain why the mass of the sliders is not needed.

(b) If the speed of a slider at the bottom of the slide is 5.0 m/s, what is the eiciency of the energy transformation?

(c) Describe one factor that contributes to loss of eiciency.

(d) Identify a type of energy that potential energy was converted to (do not use “kinetic energy” in your answer).

(e) Write a word equation using types of energy that expresses the law of conservation of energy for this energy transformation.

(f) Was the law of conservation of energy violated? Explain.

56. Describe three ways to conserve electrical energy by making small changes to your daily habits. (5.4) K/U C

57. An incandescent bulb is only 5.0 % eicient. How much waste thermal energy is produced by a 100.0 W bulb in 1.0 h? (5.4, 5.5) T/I

58. he transformation eiciency of a nuclear power plant is more than twice that of a gasoline-powered vehicle. (5.4) K/U C

(a) Describe the energy transformations that take place in a nuclear power plant when it is generating electricity.

(b) Describe two disadvantages of using nuclear power as a source of electrical energy.

59. A microwave oven operates at 1275 W. Assume electricity costs 5/kWh. (5.5) T/I A

(a) What is the cost of heating a cup of soup in a microwave for 2 min?

(b) Describe two possible “hidden” costs of heating the cup of soup in the microwave.


60. he hand-cranked radio is a fairly recent innovation. hese radios draw power from a battery that is charged by turning a hand crank (Figure 2). People buy them so that they will have a source of information during natural disasters that result in loss of electrical power. Describe all the energy transformations that take place in a hand-cranked radio, beginning with the original source of energy and continuing step-by-step to the type of energy emitted by the radio. (5.3) K/U C A

Figure 2

61. he Sun is the original source of most of the energy we use on Earth. his is true not only of renewable energy sources, but also non-renewable sources. (5.4) C A

(a) Identify two renewable sources of energy for which the Sun is the original source of energy. Explain how the energy is transferred from the Sun to the sources you chose.

(b) Identify a renewable source of energy for which the Sun is not the original source of energy.

(c) Identify two non-renewable sources of energy for which the Sun is the original source of energy. Explain how the energy is transferred from the Sun to the sources you chose.

(d) Explain how two forms of energy can both have the Sun as their source, and yet one is classiied as renewable and the other non-renewable.

62. Deine and describe each of the following sources of renewable energy. For each source, describe the type of region in Canada where it would most easily be produced. (5.4) K/U C

(a) biofuels

(b) geothermal

(c) tidal

(d) wind

63. A 610 kg racehorse is able to accelerate from rest to a speed of 14 m/s in only 1.1 s. (5.5) T/I

(a) Assume that the acceleration of the racehorse is constant. What is the distance required by the horse to reach this speed?

(b) What is the minimum amount of energy required by the horse to reach this speed?

(c) How much power does the horse have during acceleration?

64. A cyclist is competing in a race and decides to pass some fellow cyclists who are getting tired. he initial speed of the cyclist is 21 km/h and he has 3.0 3 102 W of power. If the bicycle is able to convert 92 % of the input energy into kinetic energy, how fast will the cyclist be travelling ater 4.0 s? he combined mass of the cyclist and the bicycle is 78 kg. (5.3, 5.4) T/I

Evaluation

65. Use what you have learned about energy sources to discuss which changes Ontario could make in order to reduce its use of some energy sources while increasing its use of other energy sources. Answer the questions below. (5.4) K/U A

(a) Explain which non-renewable sources should be phased out and replaced with other sources.

(b) For those sources you would phase out, justify your choice in terms of availability, cost, or environmental concerns.

(c) For the alternative sources you propose, explain why they should be favoured in terms of availability, cost, or environmental concerns.

(d) Explain your reasoning for not including the alternative sources that you did not propose.

66. he use of solar, or photovoltaic, cells is a well-known method of transforming sunlight into useful electrical energy. Evaluate the generation of electricity using photovoltaic cells. (5.4) K/U A

(a) Describe two advantages and two disadvantages of using photovoltaic cells.

(b) Describe any hidden costs you can think of that may arise from the production, transportation, or transmission of the energy.

(c) Compare the suitability of using photovoltaic cells for generating electrical energy in Canada to that of other regions of North America.

Reflect on Your Learning

67. What did you learn in this chapter that you found most surprising? Explain. C

68. (a) What questions do you still have about work, power, and energy?

(b) What methods can you use to ind answers to your questions? K/U C A


69. Has the information you have learned in this chapter changed your opinion about any environmental issues related to energy? Explain. C A

70. In this chapter you learned that potential energy is the ability of an object to do work because of forces in the environment. We commonly consider objects to have gravitational potential energy because of the work gained or lost due to their change in height. here were other types of energy mentioned that can also be considered a form of potential energy. In your own words describe how the following types of energy can be considered potential energy and give an example of each. C A

(a) thermal energy

(b) nuclear energy

(c) chemical energy

Research go To nELSon SCiEnCE

71. Canada has extensive deposits of oil sands (Figure 3). Oil sands can be processed to yield petroleum, and it has been suggested as an alternative to North America’s dwindling reserves of crude oil. Research the potential of oil sands as an energy resource. Write a few paragraphs discussing its advantages and disadvantages in terms of cost, practicality, and environmental impact. T/I C

Figure 3

72. Canada is second only to China in the production of hydroelectric power. Canada is one of the few countries that generate the majority of their electrical energy from hydroelectricity. Research hydroelectricity in Canada, and write a short report that addresses the advantages and disadvantages of using this resource. Discuss the beneits and hazards of expanding Canadian hydroelectric power. T/I C

73. No energy conversion device is 100 % eicient. Some energy always escapes as waste heat. his heat does not disappear, but it is lost because it cannot be converted to useful work. Many strategies designed to conserve energy in the home are based on preventing heat from escaping. Research the causes of heat loss in appliances and home heating systems. Pay special attention to newer technologies and improvements in building materials that prevent heat loss from homes. Create a news report summarizing your indings. Be sure to explain heat loss in terms of the law of conservation of energy. T/I C A

74. Animals such as glow-worms and irelies have long been known to convert chemical energy into light (Figure 4). Write a page on bioluminescence describing how it works and what animals use it for. How eicient are these methods at converting chemical energy into light? Are there any applications that humans have adapted from bioluminescence? C

Figure 4 Some organisms like these insect larvae called

glow-worms can transform the chemical energy in food into

radiant energy.

75. For most sources, stored energy is easily converted into some form of usable energy. Chemical energy is easily combusted to create kinetic energy, the kinetic energy of rivers is used to turn turbines to create electrical energy, and electrical energy is easily converted into light and heat for our homes. However, the converse is not true. Any excess energy that is generated is not easily converted back into a form that can be stored for later use. Research diferent types of devices that are used to store excess energy and write a page describing how they work and any problems they might have with eiciency or functionality. C


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