Preview Objectives Definition of Work Chapter 5 Section 1 Work

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• Objectives

• Definition of Work

Chapter 5 Section 1 Work

Section 1 WorkChapter 5

Objectives

• Recognize the difference between the scientific and ordinary definitions of work.

• Define work by relating it to force and displacement.

• Identify where work is being performed in a variety of situations.

• Calculate the net work done when many forces are applied to an object.

Chapter 5

Definition of Work

• Work is done on an object when a force causes a displacement of the object.

• Work is done only when components of a force are parallel to a displacement.

Section 1 Work

Chapter 5

Definition of Work

Section 1 Work

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Chapter 5 Section 1 Work

Sign Conventions for Work

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• Objectives

• Kinetic Energy

• Sample Problem

Chapter 5 Section 2 Energy

Section 2 EnergyChapter 5

Objectives

• Identify several forms of energy.

• Calculate kinetic energy for an object.

• Apply the work–kinetic energy theorem to solve problems.

• Distinguish between kinetic and potential energy.

• Classify different types of potential energy.

• Calculate the potential energy associated with an object’s position.

Section 2 EnergyChapter 5

Kinetic Energy

• Kinetic Energy

The energy of an object that is due to the object’s motion is called kinetic energy.

• Kinetic energy depends on speed and mass.

2

2

1

21

kinetic energy = mass speed2

KE mv

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Visual Concept

Chapter 5 Section 2 Energy

Kinetic Energy

Section 2 EnergyChapter 5

Kinetic Energy, continued

• Work-Kinetic Energy Theorem– The net work done by all the forces acting on an

object is equal to the change in the object’s kinetic energy.

• The net work done on a body equals its change in kinetic energy.

Wnet = ∆KE

net work = change in kinetic energy

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Visual Concept

Chapter 5 Section 2 Energy

Work-Kinetic Energy Theorem

Section 2 EnergyChapter 5

Sample Problem

Work-Kinetic Energy Theorem

On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

Section 2 EnergyChapter 5

Sample Problem, continued

Work-Kinetic Energy Theorem

1. Define

Given:

m = 10.0 kg

vi = 2.2 m/s

vf = 0 m/s

µk = 0.10

Unknown:

d = ?

Section 2 EnergyChapter 5

Sample Problem, continued

Work-Kinetic Energy Theorem

2. Plan

Choose an equation or situation: This problem can be solved using the definition of work and the work-kinetic energy theorem.

Wnet = FnetdcosThe net work done on the sled is provided by the force of kinetic friction.

Wnet = Fkdcos = µkmgdcos

Section 2 EnergyChapter 5

Sample Problem, continued

Work-Kinetic Energy Theorem2. Plan, continued

The force of kinetic friction is in the direction opposite d, = 180°. Because the sled comes to rest, the final kinetic energy is zero.

Wnet = ∆KE = KEf - KEi = –(1/2)mvi2

Use the work-kinetic energy theorem, and solve for d.

2

2

1– cos

2

–

2 cos

i k

i

k

mv mgd

vd

g

Section 2 EnergyChapter 5

Sample Problem, continued

Work-Kinetic Energy Theorem

3. Calculate

Substitute values into the equation:

2

2

(–2.2 m/s)

2(0.10)(9.81 m/s )(cos180 )

2.5 m

d

d

Section 2 EnergyChapter 5

Sample Problem, continued

Work-Kinetic Energy Theorem

4. Evaluate

According to Newton’s second law, the acceleration of the sled is about -1 m/s2 and the time it takes the sled to stop is about 2 s. Thus, the distance the sled traveled in the given amount of time should be less than the distance it would have traveled in the absence of friction.

2.5 m < (2.2 m/s)(2 s) = 4.4 m

Section 2 EnergyChapter 5

Potential Energy

• Potential Energy is the energy associated with an object because of the position, shape, or condition of the object.

• Gravitational potential energy is the potential energy stored in the gravitational fields of interacting bodies.

• Gravitational potential energy depends on height from a zero level.

PEg = mghgravitational PE = mass free-fall acceleration height

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Chapter 5 Section 2 Energy

Potential Energy

Section 2 EnergyChapter 5

Potential Energy, continued• Elastic potential energy is the energy available for

use when a deformed elastic object returns to its original configuration.

2

2

1elastic PE = spring constant (distance compressed or stretched)

2

1

2elasticPE kx

• The symbol k is called the spring constant, a parameter that measures the spring’s resistance to being compressed or stretched.

Chapter 5

Elastic Potential Energy

Section 2 Energy

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Visual Concept

Chapter 5 Section 2 Energy

Spring Constant

Section 2 EnergyChapter 5

Sample Problem

Potential Energy

A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?

Section 2 EnergyChapter 5

Sample Problem, continued

Potential Energy

1. Define

Given:m = 70.0 kg

k = 71.8 N/m

g = 9.81 m/s2

h = 50.0 m – 44.0 m = 6.0 m

x = 44.0 m – 15.0 m = 29.0 m

PE = 0 J at river level

Unknown: PEtot = ?

Section 2 EnergyChapter 5

Sample Problem, continued

Potential Energy

2. Plan

Choose an equation or situation: The zero level for gravitational potential energy is chosen to be at the surface of the water. The total potential energy is the sum of the gravitational and elastic potential energy.

21

2

tot g elastic

g

elastic

PE PE PE

PE mgh

PE kx

Section 2 EnergyChapter 5

Sample Problem, continued

Potential Energy

3. Calculate

Substitute the values into the equations and solve:

2 3

2 4

3 4

4

(70.0 kg)(9.81 m/s )(6.0 m) = 4.1 10 J

1(71.8 N/m)(29.0 m) 3.02 10 J

2

4.1 10 J + 3.02 10 J

3.43 10 J

g

elastic

tot

tot

PE

PE

PE

PE

Section 2 EnergyChapter 5

Sample Problem, continued

Potential Energy

4. Evaluate

One way to evaluate the answer is to make an order-of-magnitude estimate. The gravitational potential energy is on the order of 102 kg 10 m/s2 10 m = 104 J. The elastic potential energy is on the order of 1 102 N/m 102 m2 = 104 J. Thus, the total potential energy should be on the order of 2 104 J. This number is close to the actual answer.

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• Objectives

• Conserved Quantities

• Mechanical Energy

• Sample Problem

Chapter 5Section 3 Conservation of Energy

Section 3 Conservation of EnergyChapter 5

Objectives

• Identify situations in which conservation of mechanical energy is valid.

• Recognize the forms that conserved energy can take.

• Solve problems using conservation of mechanical energy.

Section 3 Conservation of EnergyChapter 5

Conserved Quantities

• When we say that something is conserved, we mean that it remains constant.

Section 3 Conservation of EnergyChapter 5

Mechanical Energy

• Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects.

ME = KE + ∑PE

• Mechanical energy is often conserved.

MEi = MEf

initial mechanical energy = final mechanical energy (in the absence of friction)

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Chapter 5Section 3 Conservation of Energy

Conservation of Mechanical Energy

Section 3 Conservation of EnergyChapter 5

Sample Problem

Conservation of Mechanical Energy

Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg.

Section 3 Conservation of EnergyChapter 5

Sample Problem, continued

Conservation of Mechanical Energy

1. Define

Given:

h = hi = 3.00 m

m = 25.0 kg

vi = 0.0 m/s

hf = 0 m

Unknown:

vf = ?

Section 3 Conservation of EnergyChapter 5

Sample Problem, continued

Conservation of Mechanical Energy

2. Plan

Choose an equation or situation: The slide is frictionless, so mechanical energy is conserved. Kinetic energy and gravitational potential energy are the only forms of energy present.

21

2

KE mv

PE mgh

Section 3 Conservation of EnergyChapter 5

Sample Problem, continued

Conservation of Mechanical Energy

2. Plan, continued

The zero level chosen for gravitational potential energy is the bottom of the slide. Because the child ends at the zero level, the final gravitational potential energy is zero.

PEg,f = 0

Section 3 Conservation of EnergyChapter 5

Sample Problem, continued

Conservation of Mechanical Energy2. Plan, continued

The initial gravitational potential energy at the top of the slide is

PEg,i = mghi = mgh

Because the child starts at rest, the initial kinetic energy at the top is zero.

KEi = 0

Therefore, the final kinetic energy is as follows: 21

2f fKE mv

Section 3 Conservation of EnergyChapter 5

Conservation of Mechanical Energy3. Calculate

Substitute values into the equations:

PEg,i = (25.0 kg)(9.81 m/s2)(3.00 m) = 736 J

KEf = (1/2)(25.0 kg)vf2

Now use the calculated quantities to evaluate the final velocity.

MEi = MEf

PEi + KEi = PEf + KEf

736 J + 0 J = 0 J + (0.500)(25.0 kg)vf2

vf = 7.67 m/s

Sample Problem, continued

Section 3 Conservation of EnergyChapter 5

Sample Problem, continued

Conservation of Mechanical Energy4. Evaluate

The expression for the square of the final speed can be written as follows:

Notice that the masses cancel, so the final speed does not depend on the mass of the child. This result makes sense because the acceleration of an object due to gravity does not depend on the mass of the object.

v

f2

2mgh

m 2gh

Section 3 Conservation of EnergyChapter 5

Mechanical Energy, continued

• Mechanical Energy is not conserved in the presence of friction.

• As a sanding block slides on a piece of wood, energy (in the form of heat) is dissipated into the block and surface.

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• Objectives

• Rate of Energy Transfer

Chapter 5 Section 4 Power

Section 4 PowerChapter 5

Objectives

• Relate the concepts of energy, time, and power.

• Calculate power in two different ways.

• Explain the effect of machines on work and power.

Section 4 PowerChapter 5

Rate of Energy Transfer

• Power is a quantity that measures the rate at which work is done or energy is transformed.

P = W/∆t

power = work ÷ time interval

• An alternate equation for power in terms of force and speed is

P = Fv

power = force speed

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Chapter 5 Section 4 Power

Power