Energy Something that enables an object to work is called energy. What are some different forms of energy? –Potential –Electrical –Mechanical –Kinetic

Energy

• Something that enables an object to work is called energy.

• What are some different forms of energy?– Potential– Electrical– Mechanical– Kinetic

Potential Energy

• Potential Energy: energy that is stored and held in readiness to do work.

• Any substance that can do work has potential energy.– Fossil Fuels– Electric Batteries– Food

Potential Energy

• Work is required to elevate objects

• This potential energy is called– Gravitational Potential Energy (GPE)

• The amount of gravitational potential energy is equal to the work done against gravity by lifting it.

• Energy is the physical agent that allows work to be done.• Energy has many forms:

– In motion (KE)– In position (GPE)– In the physical/chemical properties of materials (EPE)

• Energy, like work, is measured in Joules (J).

A B

Energy

Which path will take the most work to get the ball to the top of the tower?

Gravitational Potential Energy• Work = Force x Distance• Upward Force = weight

– Work = Weight x Distance– Work = mg x Distance– GPE = mg x Distance (height)

• GPE = mgh

GPE ExampleThe ball has a mass of 2kg, the tower is 3m tall. What is the GPE when the ball is on top of the tower?

GPE = mgh

22 (9.8 )(3 )ms

GPE kg m58.8GPE J


GPE = mgh

22 (9.8 )(3 )ms

GPE kg m58.8GPE J


GPE = mgh

22 (9.8 )(3 )ms

GPE kg m58.8GPE J

Which path will take the most work to get the ball to the top of the tower?

GPE ExampleA cannon fires a 10kg cannon ball 150m into the air.

What is the GPE at its highest point?

GPE mgh210 (9.8 )(150 )ms

GPE kg m

14,700GPE J

h=150m

GPE ExampleA cannon fires a 10kg cannon ball 150m into the air.

What is the GPE at when the cannonball lands back on the ground?

GPE mgh210 (9.8 )(0 )ms

GPE kg m

0GPE J

Kinetic EnergyKinetic Energy: is the energy of motion

Note that KE quadruples when the velocity doubles

21

2KE mv

30km/hr

60km/hr

120km/hr

Skid 10m

Skid 40m

Skid 160m

How far would a car skid?

21(30)

2KE m

21(60)

2KE m

21(120)

2KE m

Sample Problem #1 (KE)• A train (m = 340000kg) travels along a stretch of

track with a velocity of 16m/s.

212 340000 16 m sKE kg

43,520,000KE J

212KE mv

Tunnel

What is the KE of the train?

• A train (m = 340000kg) travels along a stretch of track with a velocity of 16m/s. 43,520,000KE J

2 1v v at

How much work is required to stop the train in 84.6s?

2 1v va

t

2.189m

sa

2 22 1 2v v ad

2 22 1

2

v vd

a

677.2d m

F ma 6430.6F NW Fd 6430.6 (677.2 )W N m

43,520,000W J

• A train (m = 340000kg) travels along a stretch of track with a velocity of 16m/s. How much work is required to stop the train in 84.6s? 43,520,000KE J

43,520,000W J

Work-Energy Theorem

W KE0 43,520,000W J J

Elastic Potential EnergyEPE: is the energy stored in a spring or flexible object

21

2EPE kx

• k is the spring constant (Units N/m) (material dependent)– Which spring would be harder to compress?

• x is the distance compressed or stretched

(Units m)

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

potential energy is stored within the spring.

222

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

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

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

potential energy is stored within the spring.

222

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

Sample Problem 3 (EPE)Consider a small toy dart gun. The dart is pushed 0.05m into the spring (k = 330N/m) within the gun.

•What is the EPE of the spring?21

2EPE kx

212 330 0.05N

mEPE m

0.4125EPE J

Load

The Need For Algebra• Some energy problems will require algebraic

manipulation in order to be solved. • Each energy equation can be broken down.

212KE mv GPE mgy 21

2EPE kx

2

2KEm

v

2KEv

m

GPEm

gy

GPEy

mg 2EPE

xk

2

2EPEk

x

GPEg

ym

Conservation of Energy ExampleRecall the ball on top of the tower.

What is the velocity of the ball if it falls from the tower?

2 2 2f iV V ad

2 2fV gh

22(9.8 / )(3 )fV m s m

7.66 /fV m s

Conservation of Energy Example

What was the KE of the ball just before landing? 21

2KE mv

21(2 )(7.66 / )

2KE kg m s

58.8KE J

Energy was Conserved PE at the top of the tower

KE at the bottom of the tower

58.8KE J

58.8PE J

The Law of Conservation of Energy

• The Law of Conservation of Energy: in a closed and isolated system, the total energy remains constant.

– Energy can not be destroyed.

– Energy transforms, but the total amount never changes.

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211

21 IkxmgymvwIkxmgymv other

What energy transformation take place in this example?

Conservation of Energy

What energy transformation take place in this example?

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211



2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Conservation of EnergyWhat energy transformation take place in this example?


PE

PE + KE

KE

PE + KE

PE

Simple Harmonic Motion

X1

X2

mgh1

mgh0

V=0

V=0

Hooke’s Law

sF kx

The Law of Conservation of Energy

In terms of the energy:

• In terms of the components:

Before AfterE E

1 1 1 o 2 2 2KE EPE GPE W KE EPE GPE

Simple Harmonic Motion

Simple Harmonic Motion: Motion caused by a linear restoring force that has a period independent of amplitude.

Period: The time required to repeat one complete cycle

Amplitude: Maximum displacement from equilibrium.

External Work (Wo)• You may have wondered what the Wo term was for.

• Wo is any work done by the system or on the system during an energy transition.

• In cases where energy is added to the system, Wo is positive(+). Examples include motors and muscles.

• In cases where energy is lost by the system, Wo is negative(-). Examples include friction and air resistance.

Kinetic Energy & Work-Energy PrincipleWork-Energy Principle - the net work done on a

body is equal to the change in its kinetic energy.

Kinetic Energy

Work Energy Theorem

Units of W & KE

221 mvKE

KEKEKEWTotal 12

JmNms

mkgW

2

Pronounced as a Joule

Conservation of EnergyWhat 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


• 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

2 21 21 2 2

21 2

21

2 2

1 1

2 2

1 1

2

1 1

2 22 otherkx kmv mv xmgy w mgyI I

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

Understanding the MVE - Launch

2 2 2 21 1 1 2 2 2

1 1 1 1

2 2 2 2

othermv mgy kx w mv mgy kx

The projectile will be launched up from the ground.

Key Factor

What did the explosion do to the ball?

Work-Kinetic Energy Principle?

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

2 2 2 21 1 1 2 2 2

1 1 1 1

2 2 2 2


Understanding the MVE – Free Fall

Key FactorWhat 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.

2 2 2 21 1 1 2 2 2

1 1 1 1

2 2 2 2


MVE – Free Fall WS 11a #3

• Find GPE of the ball at the surface of the table

• Find GPE of the ball at the top of the platform

A beach ball is .82m above a picnic table which is .45m tall. The table is on a 2.9m platform.

Compressing2 2 2 2

1 1 1 2 2 2

1 1 1 1

2 2 2 2


Understanding the MVE – Hoops, Anyone?

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Conservation of Energy Example• A ball, initially traveling at a velocity of 14m/s is

rolled up a frictionless hill until it stops..• How high up the hill did it go?

21 2

1

2mv mgh

2 2 2 21 1 1 2 2 2

1 1 1 1

2 2 2 2othermv kx mgy w mv kx mgy

2

2 2vh g

2 10h m

Understanding the MVE - Archery

2

1

2

1

2

1

2

1

2

1

2

1

22

222

22

21

211


Key Factor

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

Why?

8-25

Understanding the MVE – More Archery

2 2 2 21 1 1 2 2 2

1 1 1 1

2 2 2 2


• Let’s get a bulls eye hit this time!

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

Understanding the MVE – In the Factory

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


MVE – Archery WS Intro #3

2 2 2 21 1 1 2 2 2

1 1 1 1

2 2 2 2


• An arrow (m=.15kg) is drawn back in a bow (k=1120N/m) a distance of .35m.

• What is the EPE?

• What is the GPE

212EPE kx

212 (1120 )(.35 )N

mEPE m68.6EPE J

GPE mgh2(.15 )(9.8 )(1.3 )ms

GPE kg m1.9GPE J


• Roller Coaster • Down Hill Skier

Homework

• 11a #4

• 11b #2

• 11c #1-3

• 11d #1

• 11e #1,2

End CH 11

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?

Conservation of Energy Examples

Documents

Energy Something that enables an object to work is called energy. What are some different forms of energy? –Potential –Electrical –Mechanical –Kinetic