work and energysection 1 © houghton mifflin harcourt publishing company preview section 1 workwork...

Work and Energy Section 1

© Houghton Mifflin Harcourt Publishing Company

Preview

Section 1 Work

Section 2 Energy

Section 3 Conservation of Energy

Section 4 Power



What do you think?

• List five examples of things you have done in the last year that you would consider work.

• Based on these examples, how do you define work?



Work

• In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force.

• W = Fd• What are the SI units for work?

– Force units (N) distance units (m)– N•m are also called joules (J).

• How much work is 1 joule?– Lift an apple weighing about 1 N from the floor to the

desk, a distance of about 1 m.



Work

• Pushing this car is work because F and d are in the same direction.

• Why aren’t the following tasks considered work?– A student holds a heavy chair at

arm’s length for several minutes.– A student carries a bucket of water

along a horizontal path while walking at a constant velocity.



Work• How would you calculate the

work in this case?– What is the component of F in

the direction of d?• F cos

– If the angle is 90°, what is the component of F in the direction of d?

• F cos 90° = 0

– If the angle is 0°, what is the component of F in the direction of d?

• F cos 0° = F



Work



Work is a Scalar

• Work can be positive or negative but does not have a direction.

• What is the angle between F and d in each case?



Classroom Practice Problem

• A 20.0 kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase?

• Answer: 5.9 x 102 J or 590 J



Now what do you think?

• Based on the physics definition, list five examples of things you have done in the last year that you would consider work.



What do you think?

• You have no doubt heard the term kinetic energy.– What is it? – What factors affect the kinetic energy of an object and

in what way?

• You have no doubt heard the term potential energy.– What is it? – What factors affect the potential energy of an object

and in what way?



netW F x ma x

Kinetic Energy

Since

then

or

2 2 2f iv v a x 2 2

( )2

f inet

v vW m

2 21 1

2 2net f iW mv mv



Kinetic Energy

• What are the SI units for KE?– kg•m2/s2 or N•m or J



Work and Kinetic Energy

• KE is the work an object can do if the speed changes.

• Wnet is positive if the speed increases.



Classroom Practice Problems

• A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy?– Answer: 3.00 x 102 J or 300 J

• Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed?– Answer: 1.32 x 102 J or 132 J



Potential Energy

• Energy associated with an object’s potential to move due to an interaction with its environment– A book held above the desk– An arrow ready to be released from the bow

• Some types of PE are listed below.– Gravitational– Elastic– Electromagnetic



Gravitational Potential Energy

• What are the SI units?– kg•m2/s2 or N•m or J

• The height (h) depends on the “zero level” chosen where PEg = 0.



Elastic Potential Energy

• The energy available for use in deformed elastic objects– Rubber bands, springs in trampolines, pole-vault poles, muscles

• For springs, the distance compressed or stretched = x



Click below to watch the Visual Concept.

Visual Concept

Spring Constant(k)



Elastic Potential Energy

• The spring constant (k) depends on the stiffness of the spring.– Stiffer springs have higher k values.– Measured in N/m

• Force in newtons needed to stretch a spring 1.0 meters

• What are the SI Units for PEelastic?




• When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.– What is the gravitational potential energy associated

with the mass relative to the table?• Answer: 9.81 J

– What is the spring’s elastic potential energy if the spring constant is 400.0 N/m?

• Answer: 2.00 J




• What is kinetic energy? – What factors affect the kinetic energy of an object and

in what way?– How are work and kinetic energy related?

• What is potential energy?– What factors affect the gravitational potential energy of

an object and in what way?– What factors affect the elastic potential energy of an

object and in what way?



What do you think?

• Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed?– Explain your reasoning.

• Would your answer change if the slide were not frictionless? If so, how?



What do you think?

• What is meant when scientists say a quantity is conserved?

• Describe examples of quantities that are conserved.– Are they always conserved? If not, why?



Mechanical Energy (ME)

• ME = KE + PEg + PEelastic

– Does not include the many other types of energy, such as thermal energy, chemical potential energy, and others

• ME is not a new form of energy.– Just a combination of KE and PE




• Suppose a 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance.– Calculate the PE and the KE at the instant the book is

released.• Answer: PE = 19.6 J, KE = 0 J

– Calculate the KE and PE when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.)

• Answer: PE = 9.81 J, KE = 9.81 J

– Calculate the PE and the KE just as the book reaches the floor.

• Answer: PE = 0 J, KE = 19.6 J



Table of Values for the Falling Bookh (m) PE(J) KE(J) ME(J)

0 19.6 0 19.6

0.5 14.7 4.9 19.6

1.0 9.8 9.8 19.6

1.5 4.9 14.7 19.6

2.0 0 19.6 19.6



Conservation of Mechanical Energy

• The sum of KE and PE remains constant.• One type of energy changes into another type.

– For the falling book, the PE of the book changed into KE as it fell.

– As a ball rolls up a hill, KE is changed into PE.



Click below to watch the Visual Concept.

Visual Concept

Conservation of Mechanical Energy



Conservation of Energy

• Acceleration does not have to be constant.• ME is not conserved if friction is present.

– If friction is negligible, conservation of ME is reasonably accurate.

• A pendulum as it swings back and forth a few times

• Consider a child going down a slide with friction.– What happens to the ME as he slides down?

• Answer: It is not conserved but, instead, becomes less and less.

– What happens to the “lost” energy?• Answer: It is converted into nonmechanical energy (thermal

energy).




• A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0 102 N/m.– What is the elastic potential energy of the slingshot

before release?– What is the kinetic energy of the ball right after the

slingshot is released?– What is the ball’s speed at the instant it leaves the

slingshot?– How high does the ball rise if it is shot directly

upward?




• Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed?– Explain your reasoning.

• Would your answer change if the slide were not frictionless? If so, how?




• What is meant when scientists say a quantity is “conserved”?

• Describe examples of quantities that are conserved.– Are they always conserved? If not, why?



What do you think?

• Two cars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? – What does power mean?– What units are used to measure power?



Power

• The rate of energy transfer– Energy used or work done per second



Power

• SI units for power are J/s.– Called watts (W)– Equivalent to kg•m2/s3

• Horsepower (hp) is a unit used in the Avoirdupois system.– 1.00 hp = 746 W

Section 4Work and Energy


Watts

• These bulbs all consume different amounts of power.

• A 100 watt bulb consumes 100 joules of energy every second.




• Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min.– Calculate the power delivered by the horses.– How much work is done by the two horses?

• Answers: 1.0 x 103 W and 6.0 x 105 J




• Two cars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? – What does power mean?– What units are used to measure power?

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