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.

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.

Work

• The result of force moving an object. Work is therefore done on the object.

• Note: If the object does not move, than no work has been done.– You can try and push the wall for 2 hours, use all that

energy, and still not have done any work!

• Work is a transfer of energy.

Definition of Work

W = Fd

d

F

Definition of Work

W = Fd

Force x Distance =

Newton x meters =

Newton-meters = Joule

Definition of Work

Sign Conventions for Work

Example of Work

W = Fd

Example of Work

W = Fd

Homework• Read and Outline Chapter 3 part 1

– pages 61-73

• Read and Outline Chapter 3 part 2

– Pages 74 - 82

• Vocabulary

– Define Key Terms within outline

– Underline clearly for future study

• Part 1 due Friday

• Part 2 due Monday

Review

W = Fd

Force in same Direction as motion

Force opposes Direction of motion

Force perpendicular to Direction of motion

No Motion

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.

Energy

Law of the Conservation of Energy

Energy can neither be created nor destroyed, it can only be transformed from one form to another.

Within a closed isolated system energy can change form, but the total amount must stay constant.

Energy is the Ability to do work. We cannot do anything without energy. When something happens, energy is transferred

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

Kinetic Energy

• Moving objects have Kinetic Energy. Movement can be in any direction, horizontal, vertical, etc.

• Forms of Kinetic Energy– Vibrational – Due to vibrating– Rotational – Due to rotation– Translational – Motion from one place to another

Note: When using KE, we are referring to Trans. KE

Kinetic Energy

• The kinetic energy of an object is directly proportional to the square of its velocity.

• That means it takes four times an objects kinetic energy to double its velocity. Nine times for three times the velocity.

• Scalar Quantity– You can also use speed to solve for KE.

Kinetic Energy = ½ mass x velocity2

KE = ½ m v2

KE is Measured in Joules

1 Joule = 1 kg x (m/s)2

Kinetic Energy

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

Work-Kinetic Energy Theorem

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 kinetic friction is 25 N

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 kinetic friction is 25 N

Wnet = Change in KE KE = ½ mv2

Review

Wnet = Change in KE

KE = ½ mv2W = Fd

Potential Energy

• Three Forms– Gravitational Energy– Elastic Potential Energy– Chemical Potential Energy

• Both have energy due to their position.

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 = mgh

gravitational PE = mass free-fall acceleration height

Potential Energy

• The greater an object’s Mass, the greater its Gravitational Potential Energy.

• The greater an object’s Height, the greater the Gravitational Potential Energy.

• Doubling an object’s Height will result in a doubling of the PE. Tripling the Height will increase PE by a factor of 3.

Potential Energy

Sample Problem

Potential Energy

A 70.0 kg stuntman is about to jump off a bridge spanning a river from a height of 50.0 m. What is his gravitational potential energy?

Practice Exercise #1

What is the Potential Energy of each Ball?

A = 30 J B = 30 J

C = 20 J

D = 10 J

E = 0 J

Practice Exercise #2

1. What is the PE of a 50 Kilogram object that is 10 meters above the ground?

2. Calculate the PE of 75 Kilogram rock sitting on the edge of a 235 meter high cliff.

3. What is the mass of an object that has a PE of 400 Joules at a height of 70 meters?

4. How high is a 50 gram mass that has a PE of 14,000 J?

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.

Potential Energy, continued

• Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration.

• It is based on two things:– The spring constant

• (i.e. how strong the spring is)– The displacement of the spring

• (i.e. how far you push it or stretch it from a relaxed position)

Elastic Potential Energy

Spring Constant

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.

Conserved Quantities

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

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)

Conservation of Mechanical Energy

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.

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 = ?

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

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

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

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

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

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.

Objectives

• Review ideas connecting work and energy

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

• Calculate power in two different ways.

• Explain the connection between power, work and energy

HW Problem

Power• Power is the rate of doing work.

• A more powerful system is one which is producing/transferring a larger amount of energy.

• or one that transfers the same amount, just in a shorter period of time.

• Units for Power are Watts.

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

Power

Power

Power =Work (= F x D)

Time (in seconds)

Watts = sJoules

Practice

• How much power is required to do 100 J of work on an object in a time of 0.5 s?

• How much power is required if the same work is done in 1s?

Rate of Energy Transfer

• How much work is required to pull a sled if you use 60J of work in 5 seconds?

• How much work does an elephant do while moving a circus wagon 20meters with a pulling force of 200N?

• If it takes 5 seconds for you to do 1000J of work, what is your power output?

Rate of Energy Transfer

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

P = Fv

power = force speed

Practice

• How much power is required to lift a 500 N block of ice with a velocity of 4 m/s?

Practice

• If the power is 2000 Watts, over 5 seconds, how much Work is done?

Practice

• By the way, if the velocity is 4 m/s and it takes 5 seconds, what is the height? What is the Potential Energy of the 500 N block?