PHYSICS - Faculty/Staff Websites & Bios

FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E PHYSICS

RANDALL D. KNIGHT

Chapter 9 Lecture

© 2017 Pearson Education, Inc.


Chapter 9 Work and Kinetic Energy

IN THIS CHAPTER, you will begin your study of how energy is transferred and transformed.

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Chapter 9 Reading Questions

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A. Law of conservation of energy. B. Energy principle. C. Kinetic energy equation. D. Weight–kinetic energy principle.

The statement ΔKsys = Wext is called the

Reading Question 9.1

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A. Law of conservation of energy. B. Energy principle. C. Kinetic energy equation. D. Weight–kinetic energy principle.

The statement ΔKsys = Wext is called the


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A. Mass times velocity. B. ½ mass times speed-squared. C. The area under the force curve in a force-

versus-time graph. D. Velocity per unit mass.

Kinetic energy is


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A. Mass times velocity. B. ½ Mass times speed-squared. C. The area under the force curve in a force-

versus-time graph. D. Velocity per unit mass.

Kinetic energy is


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The transfer of energy to a system by the application of a force is called

A. Dot product. B. Power. C. Work. D. Watt. E. Energy transformations.


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The transfer of energy to a system by the application of a force is called

A. Dot product. B. Power. C. Work. D. Watt. E. Energy transformations.


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A vector has magnitude C. Then the dot product of the vector with itself, is

A. 0 B. C/2 C. C D. 2C E. C2


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A vector has magnitude C. Then the dot product of the vector with itself, is

A. 0 B. C/2 C. C D. 2C E. C2


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Hooke’s law describes the force of

A. Gravity.

B. A spring.

C. Collisions.

D. Tension.

E. None of the above.


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Hooke’s law describes the force of

A. Gravity.

B. A spring. C. Collisions.

D. Tension.

E. None of the above.


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A. Always zero. B. Always positive. C. Always negative.

The work done by a dissipative force like friction is


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A. Always zero. B. Always positive. C. Always negative.

The work done by a dissipative force like friction is


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Light bulbs are typically rated in terms of their watts. The watt W is a measure of

A. The change in the bulb’s potential energy. B. The energy consumed. C. The force exerted on the bulb holder. D. The power dissipated.


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Light bulbs are typically rated in terms of their watts. The watt W is a measure of

A. The change in the bulb’s potential energy. B. The energy consumed. C. The force exerted on the bulb holder. D. The power dissipated.


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Chapter 9 Content, Examples, and QuickCheck Questions

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Energy Overview

Everyone has some sense of what energy means. • Moving objects have energy.

• Energy is the ability to make things happen.

• Energy is associated with heat and with electricity.

• We’re constantly told to conserve energy.

• Living organisms need energy.

• Engineers harness energy to do useful things.

Some scientists consider the law of conservation of energy to be the most important of all the laws of nature.

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Kinetic Energy K

Kinetic energy is the energy of motion.

All moving objects have kinetic energy.

The more massive an object or the faster it moves, the larger its kinetic energy.

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Potential Energy U

Potential energy is stored energy associated with an object’s position.

The roller coaster’s gravitational potential energy depends on its height above the ground.

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Thermal Energy Eth

Thermal energy is the sum of the microscopic kinetic and potential energies of all the atoms and bonds that make up the object.

An object has more thermal energy when hot than when cold.

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The System and the Environment Within a system, energy can

be transformed from one type to another.

As long as the system is not interacting with the environment, the total energy of the system is unchanged.

A process that transfers energy to or from a system by mechanical means is called work, with the symbol W.

A process that transfers energy to or from a system by thermal means is called heat.

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Energy Transfer Example

System:The shot Transfer: W → K The athlete (the environment) does work pushing the shot to give it kinetic energy.

Putting a shot

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Energy Transfer Example

System:The slingshot Transfer: W → U The boy (the environment) does work by stretching the rubber band to give it potential energy.

Pulling a slingshot

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Energy Transformation Example

System:The diver and the earth Transfer: U → K The diver is speeding up as gravitational potential energy is transformed into kinetic energy.

A falling diver

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Energy Transformation Example

System:The meteor and the air Transfer: K → Eth

The meteor and the air get hot enough to glow as the meteor’s kinetic energy is transformed into thermal energy.

A speeding meteor

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The Energy Principle Transformations of energy within a system move the energy

around but don’t change the total energy of the system.

Change occurs only when there’s a transfer of energy between the system and the environment.

If we treat incoming energy as a positive transfer and outgoing energy as a negative transfer, and with work being the only energy-transfer process that we consider for now, we can write

where the subscript on W refers to external work done by the environment.

This is called the energy principle.

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The Basic Energy Model

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A skier is gliding down a slope at a constant speed. What energy transformation is taking place? A. K → U B. U → K C. Eth → K D. U → Eth E. K → Eth

QuickCheck 9.1

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A skier is gliding down a slope at a constant speed. What energy transformation is taking place? A. K → U B. U → K C. Eth → K D. U → Eth E. K → Eth

QuickCheck 9.1

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Work and Kinetic Energy for a Single Particle Consider one particle acted

on by one constant force that acts parallel to the direction of motion, pushing or pulling on the particle as it undergoes a displacement ∆s.

We define the particle to be the system while the agent of the force is in the environment.

The figure shows both an interaction diagram and a before-and-after representation.

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Work and Kinetic Energy for a Single Particle

We can define a new quantity called the kinetic energy of the particle:

K depends on the particle’s mass and speed but not on its position.

For the case in which a single constant force acts on a single particle, K changes in direct proportion to the distance traveled.

The SI unit of K is given its own name, the joule:

1 joule = 1 J = 1 kg m2/s2

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Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio vA/vB? A. 16 B. 4 C. 2 D. 1/4 E. 1/16

QuickCheck 9.2

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Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio vA/vB? A. 16 B. 4 C. 2 D. 1/4 E. 1/16

QuickCheck 9.2

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Work and Kinetic Energy for a Single Particle

The work done on a one-particle system causes the system’s kinetic energy to change:

For the case of a constant force parallel to the direction of motion (the s-axis), the work is an integral:

The SI unit of W is the same as for K: the joule.

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Signs of Work Work can be either

positive or negative. If the force causes the

particle to speed up, then the work done by that force is positive.

Negative work means that the force is causing the object to slow and lose energy.

The sign of W is determined by the force direction and the displacement direction.

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Work Done by a Constant Force

A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement

The work done by this force is

Here θ is the angle makes relative to Slide 9-44


Example 9.2 Pulling a Suitcase

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Example 9.2 Pulling a Suitcase

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A crane lowers a girder into place at constant speed. Consider the work WG done by gravity and the work WT done by the tension in the cable. Which is true? A. WG > 0 and WT > 0

B. WG > 0 and WT < 0

C. WG < 0 and WT > 0

D. WG < 0 and WT < 0

E. WG = 0 and WT = 0

QuickCheck 9.3

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A crane lowers a girder into place at constant speed. Consider the work WG done by gravity and the work WT done by the tension in the cable. Which is true? A. WG > 0 and WT > 0

B. WG > 0 and WT < 0

C. WG < 0 and WT > 0

D. WG < 0 and WT < 0

E. WG = 0 and WT = 0

QuickCheck 9.3

The downward force of gravity is in the direction of motion → positive work.

The upward tension is in the direction opposite the motion → negative work.

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Tactics: Calculating the Work Done by a Constant Force

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Robert pushes the box to the left at constant speed. In doing so, Robert does ______ work on the box. A. positive B. negative C. zero

QuickCheck 9.4

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Robert pushes the box to the left at constant speed. In doing so, Robert does ______ work on the box. A. positive B. negative C. zero

QuickCheck 9.4

Force is in the direction of displacement → positive work

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QuickCheck 9.5

A constant force pushes a particle through a displacement . In which of these three cases does the force do negative work?

D. Both A and B E. Both A and C

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QuickCheck 9.5

A constant force pushes a particle through a displacement . In which of these three cases does the force do negative work?

D. Both A and B E. Both A and C

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Example 9.3 Launching a Rocket

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Which force below does the most work? All three displacements are the same. A. The 10 N force. B. The 8 N force C. The 6 N force. D. They all do the same work.

QuickCheck 9.6

sin60º = 0.87 cos60º = 0.50

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Which force below does the most work? All three displacements are the same. A. The 10 N force. B. The 8 N force C. The 6 N force. D. They all do the same work.

QuickCheck 9.6

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sin60º = 0.87 cos60º = 0.50


A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart.

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A. greater than B. equal to C. less than D. Can’t say. It depends on how big the force is.

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A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart.

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A. greater than B. equal to C. less than D. Can’t say. It depends on how big the force is.

Same force, same distance → same work done Same work → change of kinetic energy

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The Dot Product of Two Vectors

The figure shows two vectors, and , with angle α between them.

The dot product of and is defined as

The dot product is also called the scalar product because the value is a scalar.

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The Dot Product of Two Vectors

The dot product as α ranges from 0º to 180º.

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Example 9.4 Calculating a Dot Product

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If and , the dot product is the sum of the products of the components:

The Dot Product Using Components

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Example 9.5 Calculating a Dot Product Using Components

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Work Done by a Constant Force

A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement .

The work done by this force is

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Example 9.6 Calculating Work Using the Dot Product

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Zero-Work Situations

The figure shows a particle moving in uniform circular motion.

At every point in the motion, Fs, the component of the force parallel to the instantaneous displacement, is zero.

The particle’s speed, and hence its kinetic energy, doesn’t change, so W = ΔK = 0.

A force everywhere perpendicular to the motion does no work.

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A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____. A. positive

B. negative

C. zero

QuickCheck 9.8

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A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____. A. positive

B. negative

C. zero

QuickCheck 9.8

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Zero-Work Situations

Consider the roller skater shown who straightens her arms and pushes off from a wall.

By Newton’s third law, the wall applies a force on her.

Although the skater’s center of mass is displaced, the palms of her hands—where the force is exerted—are not.

The force acts, but the force doesn’t push any physical thing through a displacement.

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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 curve, or by actually doing the integration.

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Example 9.7 Using Work to Find the Speed of a Car

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Restoring Forces and Hooke’s Law If you stretch a rubber band, a force tries to pull the rubber

band back to its equilibrium, or unstretched, length.

A force that restores a system to an equilibrium position is called a restoring force.

If you stretch (or compress) an elastic object such as a spring, measurements show that

• The force provided by the spring is opposite the displacement.

• If you don’t stretch or compress the spring too much, the force provided by the spring is proportional to the displacement from equilibrium.

The relationship between the force and displacement of a spring was discovered by Robert Hooke, a contemporary of Newton. Slide 9-82


Hooke’s Law

One end of a spring is attached to a fixed wall.

(FSp)s is the force produced by the free end of the spring.

Δs = s – seq is the displacement from equilibrium.

The minus sign is the mathematical indication of a restoring force.

The constant k is called the spring constant of the spring.

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The restoring force of three springs is measured as they are stretched. Which spring has the largest spring constant?

QuickCheck 9.9

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The restoring force of three springs is measured as they are stretched. Which spring has the largest spring constant?

QuickCheck 9.9

Steepest slope. Takes lots of force for a small displacement.

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Example 9.8 Pull Until It Slips

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Stick-Slip Motion Earthquakes are an example of stick-slip motion. Tectonic plates are attempting to slide past each other,

but friction causes the edges of the plates to stick together.

Large masses of rock are somewhat elastic and can be “stretched.”

Eventually the elastic force of the deformed rocks exceeds the friction force between the plates.

An earthquake occurs as the plates slip and lurch forward.

The slip can range from a few centimeters in a relatively small earthquake to several meters in a very large earthquake.

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Work Done by Springs

Shown is a spring acting on an object as it moves from si to sf.

The spring’s work can be computed by integrating:

The solution to this integral is

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Figure (a) shows a mass M moving with velocity with macroscopic kinetic energy Kmacro = ½ Mvobj

2. Figure (b) is a microphysics

view of the same object. The total kinetic energy of

all the atoms is Kmicro. The total potential energy

of all the atoms is Umicro. The thermal energy of the

system is

Thermal Energy

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A tow rope pulls a skier up the slope at constant speed. What energy transfer (or transfers) is taking place?

A. W → U B. W → K C. W → Eth D. Both A and B E. Both A and C

QuickCheck 9.10

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A tow rope pulls a skier up the slope at constant speed. What energy transfer (or transfers) is taking place?

A. W → U B. W → K C. W → Eth D. Both A and B E. Both A and C

QuickCheck 9.10

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Dissipative Forces

As two objects slide against each other, atomic interactions at the boundary transform the kinetic energy Kmacro into thermal energy in both objects:

Kinetic friction is a dissipative force.

K → Eth

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Dissipative Forces

The figure shows a box being pulled at a constant speed across a horizontal surface with friction.

Both the surface and the box are getting warmer as it slides:

Dissipative forces always increase the thermal energy; they never decrease it.

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Example 9.10 Increasing Kinetic and Thermal Energy

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Power Work is a transfer of energy between the environment

and a system. In many situations we would like to know how quickly

the energy is transferred. The rate at which energy is transferred or transformed

is called the power P:

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

The English unit of power is the horsepower, hp: 1 hp = 746 W

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Examples of Power

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Power

When energy is transferred by a force doing work, power is the rate of doing work: P = dW/dt.

If the particle moves at velocity while acted on by force , the power delivered to the particle is

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Four students run up the stairs in the time shown. Which student has the largest power output?

QuickCheck 9.11

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A. B. C. D.


Four students run up the stairs in the time shown. Which student has the largest power output?

QuickCheck 9.11

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A. B. C. D.

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