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Chapter 7 Energy

• Work

• Power

• Mechanical Energy– Potential Energy– Kinetic Energy– Work-Energy Theorem

• Conservation of Energy

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Work• When we lift a load against Earth’s gravity, work

is done. – The heavier the load or the higher we lift the load, the

more work is done.– Two things enter the picture whenever work is done:

• (1) application of a force, and• (2) the movement of something by that force.

• Thus, in the simplest case, where the force is constant and the motion takes place in a straight line in the direction of the force, we define the work done on an object as:

Work = force distanceUnit of work = N m = joule (J)

Work is done in lifting the barbell. If the weight lifter were taller, he would have to expend proportionally more energy to press the barbell over his head.

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Definition of work involves both a force and a distance.

He may expend energy when he pushes on the wall, but if it doesn’t move, no work is performed on the wall.

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Power

• Why are we more tired after running upstairs in a few seconds than after walking upstairs in a few minutes?

• To understand this difference, we need to talk about a measure of how fast the work is done - power:

Power = work done / time interval, or how fast the work is done

Unit of power = J / s = watt

Other units commonly used: horsepower, kilowatts, etc.

The three main engines of a space shuttle can develop 33,000 MW of power when fuel is burned at the enormous rate of 3400 kg/s. This is like emptying an average-size swimming pool in 20 s.

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Power of an automobile engine

Power = work done / time interval• An engine of great power can do work rapidly.• What does it mean that one engine is twice as

powerful as another?– It means that it can do the same amount of work in half

the time or twice the work in the same amount of time.

• For example, a more powerful engine can get an automobile up to a given speed in less time than a less powerful engine can.

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Energy• When work is done by an archer in drawing a

bow, the bent bow has the ability to do work on the arrow; When work is done to wind a spring mechanism, the spring acquires the ability to do work on various gears to run a clock, ring a bell, etc.

• In each case, something has been acquired. This “something” given to the object enables the object to do work. What is this “something”?

• This “something” that enables an object to do work is energy!

Unit of energy = joule (J)

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Energy appears in many forms

• For now, we focus on mechanical energy– (I) Potential energy: the form of energy due to the

relative position of interacting bodies

– (II) Kinetic energy: the form of energy due to their motion.

• Mechanical energy may be in the form of either potential energy or kinetic energy, or both.

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Potential energy

• An object may store energy because of its position relative to some other object. This energy is called potential energy because in the stored state, it has the potential to do work.

• The potential energy of a body due to elevated positions is called gravitational potential energy.

Gravitational potential energy = weight height = mgh

m = 3 kg

h = 4 m

Potential energy of the ball = mgh = (3 kg 10 m/s2) 4 m = 120 J

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Gravitational potential energy = weight height

• Weight of the ball = 10 N

• Height of all three shapes = 3 m.

• What is the potential energy of the ball in each of the three cases?

The potential energy of the ball at the top of the ledge depends on the height but does not depend on the path taken to get there!

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• One of the kinds of energy into which potential energy can change is energy of motion, or kinetic energy.

• The potential energy of the elevated ram is converted to kinetic energy when released.

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Kinetic energy

• If an object is moving, then by virtue of that motion it is capable of doing work. We call energy of motion kinetic energy.

• The kinetic energy of an object depends on mass and speed:

Kinetic energy = (1/2) mass speed 2

• So, if the speed of an object is doubled, its kinetic energy is quadrupled.

The downhill “fall” of the roller coaster results in its roaring speed in the dip, and this kinetic energy sends it up the steep track to the next summit.

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Energy transition between potential energy and kinetic energy

• Energy transition in a pendulum. Potential energy is relative to the lowest point of the pendulum, when it is vertical.

• At the lowest point, its potential energy is 0, but its kinetic energy is the largest.

• At its initial position, its potential energy is the largest, but its kinetic energy is 0.

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Work-energy theorem• Work equals change in kinetic energy. This is the

work-energy theorem.Work = Change in kinetic energy

– Consider the long-range cannon example discussed in the previous chapter.

• The work in this equation is the net work.– For example, if you push something when there is

friction present, then part of the work goes into generating heat, and the rest of the work goes to changing the object’s kinetic energy.

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Conservation of energy

• The law of conservation of energy, one of the greatest generalizations in physics:

Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

• A circus diver at the top of a pole has a potential energy of 10,000 J. As he dives, his potential energy converts to kinetic energy. Note that the total energy is constant.

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Homework

• Chapter 7, P. 127, Exercises: 11, 28, 51, 52.

• The above problems are from the 10th edition of the textbook by Hewitt.