Chapter 11. Work - Physics & Astronomyphysics.gsu.edu/dhamala/Physics2211/Chapter11.pdf · Chapter 11. Work In this chapter we explore • How many kinds of energy there are; •

Chapter 11. WorkChapter 11. Work

In this chapter we explore

• How many kinds of

energy there are;

• Under what

conditions energy is

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

conditions energy is

conserved;

• How a system gains

or loses energy.

Chapter Goal: To develop

a more complete understanding

of energy and its conservation.

Topics:

• The Basic Energy Model

• Work and Kinetic Energy

• Calculating and Using Work

Chapter 11. WorkChapter 11. Work


• The Work Done by a Variable Force

• Force, Work, and Potential Energy

• Finding Force from Potential Energy

• Thermal Energy

• Conservation of Energy

• Power

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.

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:

Work and Kinetic Energy


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


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:

EXAMPLE 11.1 Pulling a suitcase

QUESTION:










Tactics: Calculating the work done by a

constant force



constant force



constant force


EXAMPLE 11.6 Calculating work using the

dot product

QUESTION:



dot product



dot product



dot product


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.

EXAMPLE 11.7 Using work to find the speed

of a car

QUESTION:



of a car



of a car



of a car


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


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 work-

kinetic energy theorem becomes

EXAMPLE 11.9 Using work and potential

energy together

QUESTION:



energy together



energy together



energy together



energy together



energy together


Conservation of Energy


Energy Bar Charts

We may express the conservation of energy concept as an

energy equation.

We may also represent this equation graphically with an


We may also represent this equation graphically with an

energy par chart.

EXAMPLE 11.11 Energy bar chart I


EXAMPLE 11.11 Energy bar chart I


EXAMPLE 11.12 Energy bar chart II


EXAMPLE 11.12 Energy bar chart II


Problem-Solving Strategy: Solving Energy Problems








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.

EXAMPLE 11.15 Choosing a motor

QUESTION:


EXAMPLE 11.15 Choosing a motor


Chapter 11. Summary SlidesChapter 11. Summary Slides


Chapter 11. Summary SlidesChapter 11. Summary Slides

General Principles


General Principles


General Principles


Important Concepts


Important Concepts


Important Concepts


Important Concepts


Applications


Applications


Chapter 11Chapter 11. Questions. Questions


Chapter 11Chapter 11. Questions. Questions

A.

B.

A child slides down a playground slide

at constant speed. The energy

transformation is


B.

C.

D.

E. There is no transformation because energy

is conserved.

A.

B.

A child slides down a playground slide

at constant speed. The energy

transformation is


B.

C.

D.

E. There is no transformation because energy

is conserved.

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


A. 0.0 J

B. 2.0 J

C. 6.0 J

D. 4.0 J

E.−2.0 J

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


A. 0.0 J

B. 2.0 J

C. 6.0 J

D. 4.0 J

E.−2.0 J

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. Wg and WT are both zero.

B. Wg is negative and WT is negative.

C. Wg is negative and WT is positive.

D. Wg is positive and WT is positive.

E. Wg is positive and WT is negative.

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. Wg and WT are both zero.

B. Wg is negative and WT is negative.

C. Wg is negative and WT is positive.

D. Wg is positive and WT is positive.

E. Wg is positive and WT is negative.

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.

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.

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.


B. –2 N.

C. 1 N.

D. 2 N.

E. 4 N.

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.


B. –2 N.

C. 1 N.

D. 2 N.

E. 4 N.

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.


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.

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.


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.

Four students run up the stairs in the time shown.

Rank in order, from largest to smallest, their power

outputs Pa to Pd.


A. Pd > Pb > Pa > Pc

B. Pd > Pa = Pb > Pc

C. Pb > Pa = Pc > Pd

D. Pc > Pb = Pa > Pd

E. Pb > Pa > Pc > Pd

Four students run up the stairs in the time shown.

Rank in order, from largest to smallest, their power

outputs Pa to Pd.


A. Pd > Pb > Pa > Pc

B. Pd > Pa = Pb > Pc

C. Pb > Pa = Pc > Pd

D. Pc > Pb = Pa > Pd

E. Pb > Pa > Pc > Pd

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Chapter 11. Work - Physics & Astronomyphysics.gsu.edu/dhamala/Physics2211/Chapter11.pdf · Chapter 11. Work In this chapter we explore • How many kinds of energy there are; •