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:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Work and Kinetic Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.1 Pulling a suitcase

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.1 Pulling a suitcase

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.1 Pulling a suitcase

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.1 Pulling a suitcase

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Tactics: Calculating the work done by a constant force

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Tactics: Calculating the work done by a constant force

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Tactics: Calculating the work done by a constant force

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.6 Calculating work using the dot product QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.6 Calculating work using the dot product

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.6 Calculating work using the dot product

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.6 Calculating work using the dot product

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.7 Using work to find the speed of a car

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.7 Using work to find the speed of a car

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.7 Using work to find the speed of a car

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.9 Using work and potential energy together QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.9 Using work and potential energy together

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.9 Using work and potential energy together

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.9 Using work and potential energy together

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.9 Using work and potential energy together

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.9 Using work and potential energy together

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Conservation of Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.11 Energy bar chart I

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.11 Energy bar chart I

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.12 Energy bar chart II

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.12 Energy bar chart II

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Problem-Solving Strategy: Solving Energy Problems

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Problem-Solving Strategy: Solving Energy Problems

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Problem-Solving Strategy: Solving Energy Problems

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Problem-Solving Strategy: Solving Energy Problems

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.15 Choosing a motor QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

EXAMPLE 11.15 Choosing a motor

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 11. Summary Slides

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Applications

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Applications

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 11. 11. Questions

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

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 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.

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.

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.

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.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.