Chapter 5Chapter 5

EnergyEnergy

EnergyEnergy Universe is made up of matter and

energy. Energy is the mover of matter. Energy has several forms:

– Kinetic

– Potential

– Electrical

– Heat– etc.

Worka force for how long in distance.

Work = Force Distance W = F d

The unit for work is the Newton-meter which is also called a Joule.

Work = Force|| x Distance

In this case, the distance is the magnitude of the displacement.

Only the component of force parallel or anitparallel to the displacement does work

x

F

xFW x

xF

yF

M= 10kg

Mg = 100N

In this case, the weight does positive work

d = 2 m

Work = Mgd = (100N)(2m)

Work = 200 Nm =200J

M= 10kg

M= 10kg

Mg = 100N

In this case, the weight does negative work

d = 2 m

Work = -Mgd = -(100N)(2m)

Work = -200 Nm = -200J

Fa

M= 10kg

Mg = 100N

Fa

1. WORK

Now instead of a force for how long in time we consider a force for how long in distance.

Work = Force x distance or W = F.dUnits - Joules (J) or ft.lbBTU = 778 ft.lb (energy of one wooden kitchen

match)Pushing on a wall and wall doesn’t move

(no work done on the wall)

Questions:

How much work is done when a weight lifter lifts a barbell weighing 1000 Newtons 1.5 meters above the ground?

How much work is done when a weight lifter pushes on a stationary wall with a force of 1000 Newtons for 15 seconds?

Power

Power is equal to the amount of work done per unit time.

interval time

donework Power

The unit for power is the Joule/second which is also called a Watt.

POWER

Power = Work/time or P = W/t

Units - J/s = W 550 ft.lb /s = 1 hp

1 hp = 750 J/s = 750 W

1 BTU/hr = .293 W

100 W bulb = 0.1333 hp250 hp engine = 187,500 W

Light Bulbs and Appliances

How much energy does a 100 Watt light bulb use in one hour?

How about a 40 Watt light bulb? Which bulbs shines brighter?

interval time

usedenergy electricalRatingPower

Mechanical EnergyWhen work is done on an object, the

object generally has acquired the ability to do work.

This "ability to do work" is called energy and it has the same units as work….Joules.

Two Types of Mechanical Energy– Potential Energy and Kinetic Energy

Potential EnergyThe energy that is stored is called

potential energy.

An object’s ability to do work by virtue of its position.

Examples: – Rubber bands– Springs– Bows– Batteries– Gravity?

Gravitational Potential Energy

PE = Weight height

PE = m g h

Question:– How much potential energy does a

10kg mass have relative to the ground if it is 5 meter above the ground?

mgh

mg

h

How much work does gravity do on the falling mass?

Work = mgh

PE = mgh

mgh

mg

h

How much energy does the mass have at the bottom just before it hits the ground?

Work = mgh

PE = mgh

v

Kinetic EnergyKinetic Energy is the energy of

motion.

Kinetic Energy = ½ mass speed2

2mv2

1KE

Question: How much kinetic energy does a 1kg mass have if it is moving at 10 meters/second?

mg

h

How much energy does the mass have at the bottom just before it hits the ground?

Work = mghv

mg

This is the kinetic energy

KE = ½ mv2

PE = mgh

gtV

22

VVV

t

hV o

22

VVV

t

hV o

gtV

V

gh

V

hg

V

hgV

2

2/

ghV 22

ghmmVKE 22

1

2

1 2

PEmghKE Energy is conserved

Kinetic Energy Depends on Speed:In fact, your kinetic energy is proportional

to the square of your velocity - if you go twice as fast, your kinetic energy

quadruples. If you go three times as fast,you have nine times the kinetic energy.

Kinetic Energy Depends on Mass:Your kinetic energy is proportional to your

mass. If mass doubles, kinetic energy doubles. If

mass triples, kinetic energy triples, too.

Difference between momentum and Kinetic

energy

Scalar Versus Vector:An important difference is that

momentum is a vector quantity - it has a direction in space, and momenta combine like forces do.

Kinetic energy is a scalar quantity -it has no direction in space, and kinetic energies combine like "regular numbers

Dependence on Velocity:The momentum of an object is

proportional to the object's velocity - if you double its velocity, you double its momentum.

The kinetic energy of an object is proportional to the square of the object's velocity - if you double its velocity, you quadruple its velocity.

A Thought Experiment:Suppose that you were captured by an

evil physicist who gave you the following choice:

You must either:Stand in front of a 1000 kg. truck

moving at 1 m/s, or Stand in front of a 1 kg. frozen

meatball moving at 1000 m/s.

Truck:Truck's momentum = mv = (1000 kg)(1 m/s)

= 1000 kg m/sTruck's kinetic energy = 0.5 mv2 = (0.5)

(1000 kg)(1 m/s)2 = 500 JoulesMeatball:Meatball's momentum = mv =

(1 kg)(1000 m/s) = 1000 kg m/sMeatball's kinetic energy = 0.5 mv2 = (0.5)

(1 kg)(1000 m/s)2 = 500 000 Joules

PE = 1000J

KE = 0J

PE = 800J

KE = 600J

KE = 1000J

KE = 200J

PE = 400J

PE = 0J

PE = 500J

KE = 0J

PE = 100J

KE = 400J PE = 0J

KE = 500J

PE = 100JKE = 400J

Machines

Fulcrum MgWork = FD = Nd

D

d

M

N

F

Work/Energy RelationshipIf you want to move something, you

have to do work.

The work done is equal to the change in kinetic energy.

Work = KE

Example Question

When the brakes of a car going 90 km/h are locked, how much farther will it skid than if the brakes lock at 30 km/h?

• Answer: 9 times

4. CONSERVATION OF ENERGY

Galileo's inclines

Demo - Loop the loopDemo - Loop the loop

Energy lost due to friction is actually

not a loss; it is just a conversion.

Conservation of EnergyEnergy cannot be created or

destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

Demos– Galileo's incline– Bowling ball pendulum– Loop the loop

Example ProblemA 100 kg mass is dropped from rest from a

height of 1 meter.How much potential energy does it have

when it is released?How much kinetic energy does it have just

before it hits the ground?What is its speed just before impact?How much work could it do if it were to

strike a nail before hitting the ground?

100 kg

100 kg

100 kg

1 meter

0mvKE 221

J980)m1)(s/m8.9)(kg100(mghPE 2

Joules 980mvKE 221

Joules 0mghPE

Joules 980DistaceForceDone Work nail

Machines

A device used to multiply forces

or simply to change the direction of forces

Components of MachinesLever…a bar that is free to

pivot, or turn, about a fixed pointFulcrum….Fixed point of the

LeverEffort Arm….Part of lever on

which the effort force is applied Resistance arm…. Part of the

lever that exerts the resistance force

Type I or First Class Lever

The fulcrum between the force and the load, or between input and output.

Type II or Second Class LeverReverse the position of the load

and the fulcrum. The load is in between the

fulcrum and the effort force.

Type III or Third Class LeverFulcrum is at one end the load is

at the other end….Input force is applied between them

Pulley

A Kind of a lever that can be used to change the direction of a force.

Mechanical advantage

The ratio of resistance force to effort force

MA = Fr/Fe

Fe….effort force

Fr…..resistance force

Ideal Mechanical advantage

Workout = Workin

Frdr = Fede

IMA = de/dr

Efficiency

Workout = Workin

efficiency = wo/ Wi X 100%

Compound MachinesConsists of two or more simple

machines linked…..so that the resistance force of one

machine………becomes the effort force of the

second.

Machines - An Application of Energy Conservation

If there is no mechanical energy losses then for a simple machine...

work input = work output

(F d)input = (F d)output

Examples - levers and tire jacks

Efficiency

Useful energy becomes wasted energy with inefficiency.

Heat is the graveyard of useful energy.

usedenergy

donework fficiencyE

Comparison of Kinetic Energy and Momentum

Kinetic energy is a scalar quantity.

Momentum is a vector quantity.

Discuss rubber bullets as compared to lead bullets.

Example Questions

A 10 lb weight is lifted 5 ft. A 20 lb weight is lifted 2.5 ft. Which lifting required the most work?

(a) 10 lb weight(b) 20 lb weight(c) same work for each lifting(d) not enough information is given to work

the problem

(c) same work for each lifting(c) same work for each lifting

An object of mass 6 kg is traveling at a velocity of 30 m/s. How much total work was required to obtain this velocity starting from a position of rest?

(a) 180 Joules

(b) 2700 Joules

(c) 36 Joules

(d) 5 Joules

(e) 180 N

(b) 2700 Joules(b) 2700 Joules

A 20 Newton weight is lifted 4 meters. The change in potential energy of the weight in Newton.meters is

(a) 20

(b) 24

(c) 16

(d) 80

(e) 5

(d) 80(d) 80