© 2001-2005 shannon w. helzer. all rights reserved. unit 8 work and energy

© 2001-2005 Shannon W. Helzer. All Rights Reserved.

Unit 8Work and Energy


Work – the result of applying a CONSTANT FORCE on a body and moving it through a displacement d.

Work

8-1

FddFW Parallel

F

d


Kinetic Energy & Work-Energy Principle Work-Energy Principle - the net work done on a body is equal to

the change in its kinetic energy.

8-2

Kinetic Energy

Work Energy Theorem

Units of W & KE

221 mvKE

KEKEKEWTotal 12

JmNms

mkgW

2

Pronounced as a Joule


Work Done by a Constant Force Consider the bulldozer below. It has an initial velocity v1 at time t1

and velocity v2 at time t2.

How can we determine the net work done on the dozer by the constant force?

8-3

KEKEKEWTotal 12

11,vt

22 ,vt

22 ,vt

11,vt

21 vv

21 vv What kind of work do we have in the second case?


Negative Work When a shuttle is launched, the force acts in the direction of the displacement and produces a positive work. When the chute stops the shuttle, the force acts in the opposite direction of the displacement and produces a

negative work.

8-4

F

x

FxW 0W

0W

x

F


A Closer Look at Work

Observe the animation below. Pay close attention to the angle of the Tension

relative to the direction of motion

8-5

cosfdw



What is the angle between the direction of motion and the Tension in the picture below?

Look at WS 35 #4.

8-6cosfdw


WS 35 4b.


8-7cosfdw


WS 35 4c. How does the work done in this figure compare with

that done on 4b?


8-8cosfdw


WS 35 4d. How does the work done in this figure compare with

that done on 4c?


8-9cosfdw


WS 35 4e. What is the angle between the direction of motion

and the Tension in the picture below?


8-10cosfdw


Gravitational Potential Energy The energy a body has due to its position from the

“ground.” The “ground” can be any surface that represents

the origin: a table top, the planet’s surface, the floor of an airplane,….

The Lowest Point is ALWAYS equal to zero. The equation for GPE is as follows:

mgyGPE

8-11

y

GPEyymgGPE 12

2y

1y


Elastic Potential Energy When a spring is compressed or stretched from its neutral position,

elastic potential energy is stored within the spring.

k is a proportionality constant know as the spring constant or the force constant.

We use this constant in Hooke’s Law in order to determine the force required to stretch or compress a spring.

8-12

221 kxEPE

xkxxkFspring 12

The work done to compress or stretch a spring is given by


Compressing When a spring is compressed from its neutral position, elastic

potential energy is stored within the spring.

According to Hooke’s law, the force needed to compress the spring is

222

1 kxEPE The energy required to compress a spring is given by

22 0 kxxkFspring

Note: x is the displacement. x is the value of the number on the number line

8-13


Stretching When a spring is stretched from its neutral position, elastic

potential energy is stored within the spring.

According to Hooke’s law, the force needed to stretch the spring is

222

1 kxEPE The energy required to stretch a spring is given by

22 0 kxxkFspring

8-14


Law of Conservation of Energy The total energy is neither created nor destroyed in any process. Energy can be transferred from one form to another, and transferred

from one body to another, but the total energy amount remains constant.

Alternatively, energy can neither be created nor destroyed only changed in form or transferred to another body.

8-15


Conservation of Energy If there is no work being done on a system, then the total

mechanical energy of the system (the sum of its KE & PE) remains constant.

The following equations apply to the conservation of energy.

0W

constant a KEPETME

221 mvKE mgyGPE

“Energy before equals energy after.”

8-16


Conservation of Energy What are the kinetic and potential

energies at the following points? Explain why.

0W

KEPETME

221 mvKE mgyGPE

A

B

C

y

2

y

oAlmost Zer y

8-17


Conservation of Energy Example A car’s engine (mcar = 1500 kg) puts

10,000 J of energy into getting the car to the top of a hill.

Calculate the GPE & KE of the car at the three points below.

0W

KEPETME

221 mvKE mgyGPE

h3h/4

h/4

A

B

C

8-18


2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211

21 IkxmgymvwIkxmgymv other

The MVE A statement of the conservation of energy that includes most of the

forms of mechanical energy.

KE

GPE

EPE

RKE

Energy Before Energy After

8-19


The MVE

otherWmgykxImv 12

1212

1212

121

22

2212

2212

221 mgykxImv

Energy before equals

energy after.

8-20


Recognizing the Elements of the MVE In order to be successful in applying the MVE (conservation of

energy), we must first be able to recognize the individual elements (energy types) found in the equation.

In the next several slides, you will see different transitions from one energy type to another.

Attempt to understand why each selected term in the MVE is important relative to the physical scenario observed.

Let’s review again the MVE and its individual elements.

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


8-21


2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Understanding the MVE – Free Fall

For our first energy transition, we will exam the energies associated with dropping a ball from a deck.

Key Factor

What is the ball’s final height?

What is the ball’s GPE?

The height is always equal to zero, and the GPE is always equal to zero at the Lowest Point.

8-22


Understanding the MVE - Launch

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


The next transition is similar to the previous except for the fact that the projectile will be launched up from the ground.

Key Factor

What did the explosion do to the ball?

Do you remember the Work-Kinetic Energy Principle?

The net work done on a body is equal to the change in its kinetic energy.

8-23


Basketball demonstrates many wonderful energy transitions. Here we will analyze the scenario starting just as the ball leaves the player’s hand. However, just as with the mortar problem, the player exerted work on the ball causing it to fly.

Understanding the MVE – Hoops, Anyone?

Key Factor

RKE changes very little during the flight of a projectile.

However, you must still be able to recognize it when it exists because it does have a significant impact on many problems.

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


8-24


Understanding the MVE - Archery

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Archery Problems are excellent examples of energy transitions. What energy type is associated with the pulling back of the bow? The releasing of the bow exerts work on the arrow in the same way that the basketball player’s muscles

exerted work on the basketball and in the same way as the exploding powder exerted work on the mortar.

Key Factor

What was the GPE of the arrow just as it struck the target?

Why?

8-25


Understanding the MVE – More Archery

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Let’s get a bulls eye hit this time!

Key Factor

What was the GPE of the arrow at the beginning and the end of the arrow’s flight?

We could treat it as zero since both points have the same GPE and are also the lowest points in the problem.

8-26


Understanding the MVE – In the Factory In this problem we will look at the work done by a conveyor belt. This work is done over several seconds; however, for the sake of analysis, we will assume that the

work was done instantaneously on the crate. We will also more closely examine the impact that friction has in MVE problems.

Key Factor

What role did friction play in this problem?

Friction resulted in the apparent loss of energy to the system.

However, the energy is still accounted for as work other (WO).

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


8-27


2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Understanding the MVE – On the Gym Floor

In this problem we will look at the work done by a weight lifter lifting weights. Again, this work is done over several seconds; however, for the sake of

analysis, we will assume that the work was done instantaneously on the weight.

Key Factor

How much work is the weight lifter doing while holding the weights in the air.

None!

No motion, no work!

Recall: W = f x d

8-28


2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Understanding the MVE – On the Road

Imagine a motorcycle is driving quickly into view from the left. What type of energy does it have?

Key Factor

When the rider squeezed his brakes, what element of the MVE did he introduce?

Work Other (WO) – friction opposed the bike’s motion bringing it to a stop.

Could you ignore the RKE in this problem?

NO!

It was overcome by the work too.

8-29


Energy Transition – WS 38 # 1 Although not required, a FBD may assist you in correctly

answering energy questions especially when looking at work.

8-30

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211



Energy Transition – WS 38 #2 Again, read and understand the entire problem before

you attempt to solve any of the problem.

8-31

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211



How far does it fall? If the block slides a distance d down the plane, then

how far does it fall at the same time?

8-32


Wrap it Up! WS 39 #1 Try to understand what is happening in the

entire problem before you try to solve any of the problem.

Here is a good example.

8-33


Wrap it up! WS 39 #1 You have to love geometry!

8-34

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211



Wrap it up! WS 39 #2 Again, read and understand the entire problem before

you attempt to solve any of the problem.

8-35

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211



This presentation was brought to you by

Where we are committed to Excellence In Mathematics And Science

Educational Services.

© 2001-2005 shannon w. helzer. all rights reserved. unit 8 work and energy

Documents