ENERGYPHY1121

This Week

We introduce the concept of ENERGY. Last WebAssign before the exam is

posted. Read Chapter 7 “Energy”

Next Class Week (After Break) Monday – We will spend the entire session working on problems

for the chapters we have covered since the last examination. (Send Requests) Chapters 6 and 7 in the textbook The Pythagorean Scale

(Measured Tones – Pages 1-9) Class Notes Beats and Intervals (Also Review p289-291, 324-5 in textbook) Pressure (Text pages 214-218) Review all WebAssigns on these topics.

Enjoy your break!!! Wednesday – EXAMINATION #2EXAMINATION #2 Friday – Onward and Upward

There are many different kinds of energy .. many listed in the papers recently. Chemical (Burning coal, oil, wood) Wind Thermal Nuclear Energy of Motion Energy related to position (Potential Energy) Sound

This topic has been politicized during the last year. We will avoid the politics. Maybe.

Let’s begin with the definition of WORK

The man applies a constant force F. He pushes the cart over a distance d. The force is in the DIRECTION of the motion. (Important –

later) There is NO friction The amount of work that he does is defineddefined as

Work done = Force x Distance through which the force acts W=F x d

F

Distance “d”

Example – A man pushes a 100 kg cart with a force of 50 N over a distance of 10 m. How much work did he do?

m-N 500 m 10 x 50N Work

m 10 distance

50

NForce

The units of work are Newton-Metersalso called a JOULEJOULE

Observation

When the pusher stops pushing the object, it continues to move.

It therefore has acquired some energy of motion from the work that the pusher did.

We call this energy of motion, KINETIC ENERGY

We define Kinetic Energy as 2

2

1mvKE

Notice … Push a mass m through a distance “x” with a force F:

20

2

20

2

20

2

20

2

2

1

2

1

2

2

2

mvmvFx

xm

Fvv

axvv

axvvmaF

f

f

f

f

20

2

2

1

2

1mvmvFx f

2

2

1 KE

ENERGY KINETIC

mv

DEFINE

In the absence of friction, he work done by an external force on a mass is

Equal to the change in its Kinetic Energy.

A First Equation

Energy of Motion

Like momentum, kinetic energy depends on the mass and the motion of the object. But the kinetic energy KE of an object has its own equation.

Details of the Equation

Energy of Motion

The factor of ½ makes the kinetic energy compatible with other forms of energy, which we will study later.

Notice that the kinetic energy of an object increases with the square of its speedsquare of its speed. This means that if an object has twice the

speed, it has 4× the kinetic energy; if it has 3× the speed, it has 9× the kinetic energy; and so on.

Units of Energy

Energy of Motion

The units for kinetic energy, and therefore for all types of energy, are kilograms multiplied by (meters per second) squared (kg · m2/s2). This energy unit is called a joule (J).

Kinetic energy differs from momentum in that it is not a vector quantity. An object has the same kinetic energy regardless of

its direction as long as its speed does not change. A typical textbook dropped from a height of 10

centimeters (about 4 inches) hits the floor with a kinetic energy of about 1 J.

Doing the Math

Energy of Motion

The kinetic energy of a 70-kilogram (154-pound) person running at a speed of 8 meters per second is:

KE = ½mv 2

= ½(70 kg)(8 m/s)2

= (35 kg)(64 m2/s2) = 2240 J

Conservation of Kinetic Energy

The search for invariants of motion often involved collisions. In fact, early in their development, the concepts of momentum and kinetic energy were often confused.

Things became much clearer when these two were recognized as distinct quantities. We have already seen that momentum is

conserved during collisions. Under certain, more restrictive conditions, kinetic energy is also conserved.

Remember, there are other forms of energy than kinetic energy!

At the Moment of Impact

Conservation of Kinetic Energy

Consider the collision of a billiard ball with a hard wall. Obviously, the kinetic energy of the ball is not constant. At the instant the ball reverses its direction, its

speed is zero, and therefore its kinetic energy is zero.

As we will see, even if we include the kinetic energy of the wall and Earth, the kinetic energy of the system is not conserved.

Outcomes & Averages

Conservation of Kinetic Energy

However, if we don’t concern ourselves with the details of what happens during the collision and look only at the kinetic energy before the collision and after the collision, we find that the kinetic energy is nearly conserved.

During the collision the ball and the wall distort, resulting in internal frictional forces that reduce the kinetic energy slightly. Let’s assume we have “perfect” materials and can ignore

these frictional effects. In this case the kinetic energy of the ball after it leaves

the wall equals its kinetic energy before it hit the wall. Collisions in which kinetic energy is conserved are known as

elastic collisions. Many atomic and subatomic collisions are perfectly

elastic.

Final Notes

Conservation of Kinetic Energy

Collisions in which kinetic energy is lost are known as inelastic collisions. The loss in kinetic energy shows up as other forms of

energy, primarily in the form of heat, which we will discuss in Chapter 13.

Collisions in which the objects move away with a common velocity are never elastic.

The outcomes of collisions are determined by the conservation of momentum and the extent to which kinetic energy is conserved. We know that the collisions of billiard balls are not perfectly

elastic because we hear them collide. (Sound is a form of energy and therefore carries off some of the energy.)

Is kinetic energy conserved here?

In the previous slide

All of the kinetic energy was lost. It crunched the metal It created heat (thermal energy) It destroyed the tires

Momentum WAS conserved

Cars are not conserved!

A Better Statement of Conservation of Energy

More Better

There is still another form of “mechanical energy” that we haven’t discussed yet. This is called “potential energy”

If we include this form of energy, a “more better” statement of conservation of energy would be: The total mechanical energy BEFORE a collision

(or interaction) is equal to the total FINAL mechanical energy after the collision + any losses to friction, chemical explosions, etc.

This can also work in reverse.

Forces That Do No Work

The meaning of work in physics is different from the common usage of the word. Commonly, people talk about “playing” when they

throw a ball and “working” when they study physics. The physics definition of work is quite precise

—work occurs when the product of the force and the distance is nonzero. When you throw a ball, you are actually doing work

on the ball; its kinetic energy is increased because you apply a force through a distance.

Although you may move pages and pencils as you study physics, the amount of work is quite small.

Pushing At An Angle

Forces That Do No Work

Often, a force is neither parallel nor perpendicular to the displacement of an object. Because force is a vector, we can think of it as having two components, one that is parallel and one that is perpendicular to the motion as illustrated in Figure 7-4. The parallel component does work, but the perpendicular one does not do any work.

Any force can be replaced by two perpendicular component forces.

Only the component along the direction of motion does work on the

box.

Mass held high and released ….

Mass held at some height.Not moving.

No Kinetic Energy

Before it hits the ground it is now moving.It has Kinetic Energy.Where did it come from??

Originally, the mass was on the ground (our reference level for y=0)

Force Required

To Raise item to

Height “h”

F

mg

h

The work done to raisethe block to the height h

is theFORCE x Distance =(mg)x(h)

This is the amount of energyThat is stored by virtue of itsPosition above the ground.

We call this the potential energy

PE = mgh

Another Example

Energy winds upStored in t he spring!

Some important points

When doing potential energy problems, always identify the “zero” or reference position (height) of energy.

Remember that Potential energy, Kinetic Energy and all energies are SCALARS!

Momentum, of course, is a VECTOR.

Reference LevelAll Kinetic

Energy

All Potential Energy

Both types ofEnergy

The Pendulum

How Fast??

The wind turbine doesn’t actually store energy.

It can only generate a certain amount of energy per minute (or hr or sec).

Therefore we can only use this energy at a certain rate (or, send it along the grid for someone else to use.

Power

In previous chapters we discussed how various quantities change with time. For example, speed is the change of position with time, and acceleration is the change of velocity with time.

The change of energy with time is called power. Power P is equal to the amount of energy converted

from one form to another (ΔE ) divided by the time (Δt ) during which this conversion takes place:

Power is measured in units of joules per second, a metric unit known as a watt (W). One watt of power would raise a 1-kg mass (with a weight of 10 newtons) a height of 0.1 meter each second.

Some Different Units of Measurement

Power

The English unit for electric power is the watt, but a different English unit is used for mechanical power. A horsepower is defined as 550 foot-pounds per

second. This definition was proposed by the

Scottish inventor James Watt because he found that an average strong horse could produce 550 foot-pounds of work during an entire working day. One horsepower is equal to 746 watts.

Human Power

A human can generate 1500 watts (2 horsepower) for very short periods of time, such as in weightlifting.

The maximum average human power for an 8-hour day is more like 75 watts (0.1 horsepower).

Each person in a room generates thermal energy equivalent to that of a 75-watt light bulb. That’s one of the reasons why crowded rooms warm up!

Working It Out

Power

A compact car traveling at 27 m/s (60 mph) on a level highway experiences a frictional force of about 300 N due to the air resistance and the friction of the tires with the road.

Therefore, the car must obtain enough energy by burning gasoline to compensate for the work done by the frictional forces each second:

This means that the power needed is 8100 W, or 8.1 kW. This is equivalent to a little less than 11 horsepower.

Paying for it!

Working It Out

Power

How much electric energy does a motor running at 1000 W for 8 h require?

ΔE = P Δt = (1000 W)(8 h) = 8000 Wh

This is usually written as 8 kilowatt-hours (kWh). Although this doesn’t look like an energy unit, it is—(energy/time) × time = energy.

The energy used by the motor in 1 h is

ΔE = P Δt = (1000 W)(1 h) = (1000 J/s)(3600 s)= 3,600,000 J

In other words, 1 kWh = 3.6 million J.

Conceptual Question

Power

Question: How much energy is required to leave a 75-watt yard light on for 8 hours?

Answer: ΔE = PΔt

= (75 watts)(8 hours) = 600 watt-hours = 0.6 kWh.