Chapter 11. Work In this chapter we explore • How many kinds of energy there are; • Under what conditions energy is conserved; • How a system gains or loses energy. Chapter Goal: To develop a more complete understanding of energy and its conservation. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 11. Work Topics: • The Basic Energy Model • Work and Kinetic Energy • Calculating and Using Work • The Work Done by a Variable Force • Force, Work, and Potential Energy • Finding Force from Potential Energy • Thermal Energy • Conservation of Energy • Power Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The Basic Energy Model

W > 0: The environment does work on the system and the system’s energy increases. W < 0: The system does work on the environment and the system’s energy decreases. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Work and Kinetic Energy Consider a force acting on a particle as the particle moves along the s-axis from si to sf. The force component Fs parallel to the s-axis causes the particle to speed up or slow down, thus transferring energy to or from the particle. We say that the force does work on the particle.

The unit of work is J. As the particle is moved by this single force, its kinetic energy changes as follows:

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Work and Kinetic Energy

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Work Done by a Constant Force Consider a particle which experiences a constant force which makes an angle θ with respect to the particle’s displacement. The work done is

Both F and θ are constant, so they can be taken outside the integral. Thus

You should recognize this as the dot product of the force vector and the displacement vector: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.1 Pulling a suitcase QUESTION:

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EXAMPLE 11.1 Pulling a suitcase

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EXAMPLE 11.1 Pulling a suitcase

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EXAMPLE 11.1 Pulling a suitcase

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EXAMPLE 11.1 Pulling a suitcase

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Tactics: Calculating the work done by a constant force

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Tactics: Calculating the work done by a constant force

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Tactics: Calculating the work done by a constant force

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EXAMPLE 11.6 Calculating work using the dot product QUESTION:

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EXAMPLE 11.6 Calculating work using the dot product

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EXAMPLE 11.6 Calculating work using the dot product

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EXAMPLE 11.6 Calculating work using the dot product

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The Work Done by a Variable Force To calculate the work done on an object by a force that either changes in magnitude or direction as the object moves, we use the following:

We must evaluate the integral either geometrically, by finding the area under the cure, or by actually doing the integration.

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EXAMPLE 11.7 Using work to find the speed of a car QUESTION:

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EXAMPLE 11.7 Using work to find the speed of a car

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EXAMPLE 11.7 Using work to find the speed of a car

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EXAMPLE 11.7 Using work to find the speed of a car

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The Work-Kinetic Energy Theorem when Nonconservative Forces Are Involved A force for which the work is not independent of the path is called a nonconservative force. It is not possible to define a potential energy for a nonconservative force. If Wc is the work done by all conservative forces, and Wnc is the work done by all nonconservative forces, then

But the work done by the conservative forces is the negative of the change in potential energy, so the workkinetic energy theorem becomes

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EXAMPLE 11.9 Using work and potential energy together QUESTION:

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EXAMPLE 11.9 Using work and potential energy together

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EXAMPLE 11.9 Using work and potential energy together

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EXAMPLE 11.9 Using work and potential energy together

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EXAMPLE 11.9 Using work and potential energy together

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EXAMPLE 11.9 Using work and potential energy together

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Conservation of Energy

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Energy Bar Charts We may express the conservation of energy concept as an energy equation.

We may also represent this equation graphically with an energy par chart.

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EXAMPLE 11.11 Energy bar chart I

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EXAMPLE 11.11 Energy bar chart I

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EXAMPLE 11.12 Energy bar chart II

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EXAMPLE 11.12 Energy bar chart II

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Problem-Solving Strategy: Solving Energy Problems

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Problem-Solving Strategy: Solving Energy Problems

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Problem-Solving Strategy: Solving Energy Problems

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Problem-Solving Strategy: Solving Energy Problems

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Power The rate at which energy is transferred or transformed is called the power, P, and it is defined as

The unit of power is the watt, which is defined as 1 watt = 1 W = 1 J/s.

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EXAMPLE 11.15 Choosing a motor QUESTION:

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EXAMPLE 11.15 Choosing a motor

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Chapter 11. Summary Slides

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General Principles

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General Principles

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General Principles

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Important Concepts

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Important Concepts

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Important Concepts

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Important Concepts

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Applications

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Applications

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Chapter 11. 11. Questions

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A child slides down a playground slide at constant speed. The energy transformation is A. B. C. D. E. There is no transformation because energy is conserved.

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A child slides down a playground slide at constant speed. The energy transformation is A. B. C. D. E. There is no transformation because energy is conserved.

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A particle moving along the x-axis experiences the force shown in the graph. If the particle has 2.0 J of kinetic energy as it passes x = 0 m, what is its kinetic energy when it reaches x = 4 m?

A. 0.0 J B. 2.0 J C. 6.0 J D. 4.0 J E. −2.0 J Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

A particle moving along the x-axis experiences the force shown in the graph. If the particle has 2.0 J of kinetic energy as it passes x = 0 m, what is its kinetic energy when it reaches x = 4 m?

A. 0.0 J B. 2.0 J C. 6.0 J D. 4.0 J E. −2.0 J Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

A crane lowers a steel girder into place at a construction site. The girder moves with constant speed. Consider the work Wg done by gravity and the work WT done by the tension in the cable. Which of the following is correct? A. B. C. D. E.

Wg and WT are both zero. Wg is negative and WT is negative. Wg is negative and WT is positive. Wg is positive and WT is positive. Wg is positive and WT is negative.

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A crane lowers a steel girder into place at a construction site. The girder moves with constant speed. Consider the work Wg done by gravity and the work WT done by the tension in the cable. Which of the following is correct? A. B. C. D. E.

Wg and WT are both zero. Wg is negative and WT is negative. Wg is negative and WT is positive. Wg is positive and WT is positive. Wg is positive and WT is negative.

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Which force does the most work?

A. the 10 N force B. the 8 N force C. the 6 N force D. They all do the same amount of work. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Which force does the most work?

A. the 10 N force B. the 8 N force C. the 6 N force D. They all do the same amount of work. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

A particle moves along the x-axis with the potential energy shown. The force on the particle when it is at x = 4 m is

A. –1 N. B. –2 N. C. 1 N. D. 2 N. E. 4 N.

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A particle moves along the x-axis with the potential energy shown. The force on the particle when it is at x = 4 m is

A. –1 N. B. –2 N. C. 1 N. D. 2 N. E. 4 N.

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A child at the playground slides down a pole at constant speed. This is a situation in which A. U → Eth. Emech is conserved. B. U → Eth. Emech is not conserved but Esys is. C. U → Wext. Neither Emech nor Esys is conserved. D. U → K. Emech is not conserved but Esys is. E. K → Eth. Emech is not conserved but Esys is.

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A child at the playground slides down a pole at constant speed. This is a situation in which A. U → Eth. Emech is conserved. B. U → Eth. Emech is not conserved but Esys is. C. U → Wext. Neither Emech nor Esys is conserved. D. U → K. Emech is not conserved but Esys is. E. K → Eth. Emech is not conserved but Esys is.

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Four students run up the stairs in the time shown. Rank in order, from largest to smallest, their power outputs Pa to Pd.

A. B. C. D. E.

Pd > Pb > Pa > Pc Pd > Pa = Pb > Pc Pb > Pa = Pc > Pd Pc > Pb = Pa > Pd Pb > Pa > Pc > Pd

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Four students run up the stairs in the time shown. Rank in order, from largest to smallest, their power outputs Pa to Pd.

A. B. C. D. E.

Pd > Pb > Pa > Pc Pd > Pa = Pb > Pc Pb > Pa = Pc > Pd Pc > Pb = Pa > Pd Pb > Pa > Pc > Pd

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