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Lecture Outline

Chapter 5

College Physics, 7th Edition

Wilson / Buffa / Lou

Chapter 5Work and Energy

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Units of Chapter 5

Work Done by a Constant Force

Work Done by a Variable Force

The Work–Energy Theorem: Kinetic Energy

Potential Energy

Conservation of Energy

Power

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5.1 Work Done by a Constant Force

Definition of work:

The work done by a constant force acting on an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to that displacement.

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5.1 Work Done by a Constant Force

In (a), there is a force but no displacement: no work is done. In (b), the force is parallel to the displacement, and in (c) the force is at an angle to the displacement.

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5.1 Work Done by a Constant Force

If the force is at an angle to the displacement, as in (c), a more general form for the work must be used:

Unit of work: newton • meter (N • m)

1 N • m is called 1 Joule after James Prescott Joule.

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5.1 Work Done by a Constant Force

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cosxFxFW

A dot product is basically a CONSTRAINT on the formula. In this case it means that F and x MUST be parallel. To ensure that they are parallel we add the cosine on the end.

5.1 Work Done by a Constant Force

If the force (or a component) is in the direction of motion, the work done is positive.

If the force (or a component) is opposite to the direction of motion, the work done is negative.

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5.1 Work Done by a Constant ForceIf there is more than one force acting on an object, it is useful to define the net work:

The total, or net, work is defined as the work done by all the forces acting on the object, or the scalar sum of all those quantities of work.

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5.2 Work Done by a Variable Force

The force exerted by a spring varies linearly with the displacement:

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5.2 Work Done by a Variable Force

A plot of force versus displacement allows us to calculate the work done:

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5.3 The Work–Energy Theorem: Kinetic Energy

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5.3 The Work–Energy Theorem: Kinetic Energy

A Proof to derive the W-E Equation

The net force acting on an object causes the object to accelerate, changing its velocity:

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5.3 The Work–Energy Theorem: Kinetic Energy

We can use this relation to calculate the work done:

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5.3 The Work–Energy Theorem: Kinetic Energy

Kinetic energy is therefore defined:

The net work on an object changes its kinetic energy.

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5.3 The Work–Energy Theorem: Kinetic Energy

This relationship is called the work–energy theorem.

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5.4 Potential Energy

Potential energy may be thought of as stored work, such as in a compressed spring or an object at some height above the ground.

Work done also changes the potential energy (U) of an object.

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5.4 Potential Energy

We can, therefore, define the potential energy of a spring; note that, as the displacement is squared, this expression is applicable for both compressed and stretched springs.

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Work Done by a Constant Force

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Example W=FxcosA 70 kg base-runner begins to slide into second base when

moving at a speed of 4.0 m/s. The coefficient of kinetic friction between his clothes and the earth is 0.70. He slides so that his speed is zero just as he reaches the base (a) How much energy is lost due to friction acting on the runner? (b) How far does he slide?

)8.9)(70)(70.0(

mgFF nf

f

of

f

W

mvW

KWa

22 )4)(70(21

210

)

= 480.2 N-560 J

x

x

xFW ff

)180(cos)2.480(560

cos

1.17 m

5.4 Potential Energy

Gravitational potential energy:

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5.4 Potential EnergyOnly changes in potential energy are physically significant; therefore, the point where U = 0 may be chosen for convenience.

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5.5 Conservation of Energy

We observe that, once all forms of energy are accounted for, the total energy of an isolated system does not change. This is the law of conservation of energy:

The total energy of an isolated system is always conserved.

We define a conservative force:

A force is said to be conservative if the work done by it in moving an object is independent of the object’s path.

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5.5 Conservation of EnergySo, what types of forces are conservative? Gravity is one; the work done by gravity depends only on the difference between the initial and final height, and not on the path between them.

Similarly, a nonconservative force:

A force is said to be nonconservative if the work done by it in moving an object does depend on the object’s path.

The quintessential nonconservative force is friction.

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5.5 Conservation of Energy

Another way of describing a conservative force:

A force is conservative if the work done by it in moving an object through a round trip is zero.

We define the total mechanical energy:

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5.5 Conservation of Energy

For a conservative force:

Many kinematics problems are much Many kinematics problems are much easier to solve using energy conservation.easier to solve using energy conservation.(and not what we have been doing for the last few units…)

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5.5 Conservation of Energy

All three of these balls have the same initial kinetic energy; as the change in potential energy is also the same for all three, their speeds just before they hit the bottom are the same as well.

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5.5 Conservation of EnergyIn a conservative system, the total mechanical energy does not change, but the split between kinetic and potential energy does.

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5.5 Conservation of Energy

If a nonconservative force or forces are present, the work done by the net nonconservative force is equal to the change in the total mechanical energy.

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5.6 Power

The average power is the total amount of work done divided by the time taken to do the work.

If the force is constant and parallel to the displacement,

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5.6 Power

Mechanical efficiency:

The efficiency of any real system is always less than 100%.

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5.6 Power

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Review of Chapter 5

Work done by a constant force is the displacement times the component of force in the direction of the displacement.

Kinetic energy is the energy of motion.

Work–energy theorem: the net work done on an object is equal to the change in its kinetic energy.

Potential energy is the energy of position or configuration.

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Review of Chapter 5

The total energy of the universe, or of an isolated system, is conserved.

Total mechanical energy is the sum of kinetic and potential energy. It is conserved in a conservative system.

The net work done by nonconservative forces is equal to the change in the total mechanical energy.

Power is the rate at which work is done.

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