Work and Energy (part I):

Question: How do you raise an object?

Answer: Apply an upward force to it. The force must be at least as large as the weight of the object.

Weight

appliedforce

appliedforce

Weightforce

in order to lift box

1 meter

moreforceapplied

1 meter

moreweight

lessweight

lessforceapplied

Which one makes a louder “bang”if dropped?

Obviously the big one……

Question: But what is the difference between lifting the box bya height of, say 2 meters as opposed to 1 meters?

Answer: The force is the same in each case BUT:

(1) force is applied to the box over different amount of distance

(2) box makes louder “bang” when dropped on the floor

We say that the applied force does the WORK on the box:

Question: But what if we compare the process of lifting a “big” box tothat of lifting a “small” box?

Answer: Now the forces are different, it takes more force to lift a bigbox than to lift a small box

Summary of our observations:

1) More WORK is done ON a system (the box) when a LARGER force is applied to it.

2) More WORK is done ON the system when the force applied causes the system to move through a larger distance

3) In order to do any work, applied force must be in the same direction as motion

WorkDoneby

Force

= The ForceDistance

Movedby

Force

X

Joules Newtons Meters

WorkDoneby

Force

= The ForceDistance

Movedby

Force

X

Joules Newtons Meters

1 Joule = (1 Newton) X (1 meter) 1 J = 1 N X m

W = F X dF and dAlong the same line!!

TYPICAL VALUES FOR WORK!

quick-examples:

1) An 800 N person steps up onto a 1 meter tall stool, how much work ? What force does this work?

1 meter

force applied by legson body lifts the weightof the person

Work = W = 800N X 1 meter force lift

of lifting

= 800 N X 1 m = 800 Joules

800 Joules = 191.2 calories

NOTE : 1 joule = 0.239 cal 4186 J = 1 kcal

Work and Energy

2) You pull a box along the floor. How much work is done in moving the box 10 m?

20 Newtons

10 meters

friction

which force does the work?

The 20 N applied force! W = (20N) X (10 m) = 200 Nm = 200 JoulesWork – Force Graphs: If we plot the Force that was applied to thebox as a function of distance we can find the total work done!

Forc

e

Position

x = 0x = 10

x = 10

20 N The area under theplot represents the total Work done!!!!!

Area = length x height = (10 m) x (20 N) = 200 Joules

These graphs are great for more complex forces:Fo

rce

Positionx = 4 m

10 N

What’s the work done from x =0to x = 4m?

Area of a triangle is ½ base x height

= ½ (4 m) x (10 N) = 20 Joules!

Position

Forc

e

3 N

x = 1m x = 3m

10 N

x = 6m

8 N

Calculate the work done fromx =0 to x = 6 m.

Spring forceproportional tothe stretch distance

h

do work on mass

work = mass x 10 m/s2

Mass

1 2

h = height of mass

Now mass can do workresulting in a flying monkey

3 How? Drop it! Mass speeds up as itfalls

maximum speed upon impact

4

Look at frame 2:The mass CAN do work (but hasn’t) by virtue of its position or“configuration”

Look at frame 4:The mass CAN do work (but hasn’t) by virtue of its speed and impact

When a force does work on an object it gives the object Energy of one form or another. Energy is the ability to do work. But, what does this mean, really?

EnergyThe ABILITY to do WORK

e.g.A “raised” mass has the potential to pop a monkeyup into the air!

How to actually do the work is not the issue.

The issue is simply that “it” CAN.

Two types of energy:

1. Kinetic Energy: energy by virtue of motion

2. Potential Energy: energy by virtue of position (configuration

Forms of Energy

Kinetic (KE): energy by virtueof motion

1. Translational

KE = ½ x mass x (speed)2

2. Rotational

3. Thermalremember: motion temperature of

“atoms”

Potential (PE): energy by virtueof position (configuration)

1. Gravitational

PE = (mass x 10 m/s2) x height = Weight x height

2. Elastic (spring)

3. Chemical

4. Nuclear

5. Electromagnetic

Work Energy relationship

• Work = Force x Distance

– Work changes energy (work = change in energy)

– Energy increases when work is done on or to an object

– Energy decreases when work is done by an object

Spring• Work is done to compress a spring a distance x. • The change in the potential energy is identical to the work

done. W = P.E.

P.E. = 1/2 k x2

k is the spring constant

(a characteristic of the spring)

• The spring can now do work on something else.

Potential Energy• The motor pulls the cart up against gravity

WORK = Force x distance

mg x height

• Muscles do work against the tension in the bow string

• Muscles do work against gravity to lift the

axe above the ground

Potential Energy• The roller coaster cart, the bow and the axe were all

given potential energy. The change in the potential energy

is identical to the work done. W = P.E.

• These objects now have the potential to do work and

convert that stored potential energy.

Kinetic Energy• The energy associated with an objects motion.

K.E. = 1/2 m v2

m = mass

v = velocity

Without velocity, there is no KE

Chop, Chop

Law of Conservation of Energy (The 1st Law of Thermodynamics)

Energy is never created nor is it destroyed.

Energy can be transformed from type to type, BUTWhen you add up all of the energy AFTER a process you will havethe exact same amount as BEFORE the process

Example Let’s look at the simple pendulum:

•The pendulum swings to and fro,

where it stops, conservation of energy knows.

TOTAL ENERGY = Potential Energy + Kinetic Energy

The Simple Pendulum The total energy of this system is zero.

This simple pendulum could be the

sway in a grandfather clock,

a child on a swing,

a hypnotists watch, etc

Suppose someone does work against

gravity to give it some potential energy?

The Simple Pendulum Suppose someone does work against

gravity to give it some potential energy?

The work done = Force x Distance

Force = m g

Distance = h

The work done = potential energy gained (PE)

W = m g h

The total energy of the system is now (m g h), reflecting the work done to the system.

h

To and Fro

To and Fro

To and Fro

To and Fro

To and Fro

To and Fro

To and Fro

To and Fro

h

The pendulum swingsuntil it has reached thesame height on the otherside, before pausing toswing (oscillate) back.

Energy ExchangeWhen paused, the pendulum has its maximumpotential energy (mg h) and zero kineticenergy. Total energy = mgh + 0

When at the bottom of its swing its heightis zero, therefore it has its minimumpotential energy (0) and its maximumkinetic energy. It travels the fastest at thebottom of its swing. Total energy = 0 + 1/2 m v2

EVERYWHERE the TOTAL energy remains unchanged.

Energy ExchangeThe energy sloshes from PE to KE and back again.

A pendulum weighing 5 kg is lifted againstgravity to a height of 2 m from itsequilibrium position. What is its speed atthe bottom of its swing?

Energy ExchangeThe energy sloshes from PE to KE and back again.

A pendulum weighing 5 kg is lifted againstgravity to a height of 2 m from itsequilibrium position. What is its speed atthe bottom of its swing?

TOTAL Energy = PE + KE = mg h + 0 = 5 kg 10 m/s2 2 m = 100 Joules

Energy ExchangeAt the bottom of its swing the total energy is still 100 Joules.

100 Joules = TOTAL Energy = 0 + KE = 1/2 m v2

= 1/2 5 kg v2

Energy ExchangeAt the bottom of its swing the total energy is still 100 Joules.

100 Joules = TOTAL Energy = 0 + KE = 1/2 m v2

100 = 1/2 5 kg v2

2(100)/5 = v2

40 = v

6.3 m/s = velocity

Drum Roll DiverThe platform diver does work against gravity by climbing the pole to theplatform at height h. This gives himpotential energy PE = mg h.

At the bottom, he is traveling themaximum speed and has traded hispotential energy into the energy ofmotion, kinetic energy.

TOTAL Energy is conserved at everypoint along the way!

Drum Roll DiverIf the idiot climbed to a heightof 20 meters, how much is his mass?

PE = 10,000 = mg h

Drum Roll DiverIf the idiot climbed to a heightof 20 meters, how much is his mass?

PE = 10,000 = mg h

m = 10,000/gh = 10,000/10(20)

= 50 kg

The Curved Track:

Q1: How did the ball get to the “starting position” in the first place?

Q2: What forms of energy does the ball possess at each point of itsjourney? Where did it get the energy?

The Curved Track:“Ideal Case”: no friction, no rolling

no sound no air resistance

“Real Case”:friction sound air resistance, etc.

The Curved Track:

Some of the energy appears to be “lost” in the transfer. Where doesit go?

In the track example.

Reversible Part:

some of……

gravitational PE rotational KE gravitational PE translational KE

Irreversible Part:

Remainder of Thermal (friction)gravitational PE

Sound

lost to the surroundings

By building a curved track, we can get some of the energy back…..but never all of it. The ball gives up its gravitational energy not onlyto rotational and translational kinetic forms but also to thermalforms and to sound (another example of translational Kinetic)

Point: We can “get back” the ordinary rotational and translational KEWe cannot “get back” the thermal, sounds, etc…

Actual Efficiency (AE) of a process: “what percentage of the INPUT produces useful OUTPUT”

%100

INPUTEnergyTotal

OUTPUTEnergyUsefulAE

Or, since POWER is the rate of energy flow (or work performance)

%100

INPUTPowerTotal

OUTPUTPowerUsefulAE

Example

Lift a 2 kg brick to height of 2 meters. Drop it and do 15 Joulesof work in driving a nail. What is this processes actual efficiency?

%100

INPUTEnergyTotal

OUTPUTEnergyUsefulAE

%5.37%1004015

%1002102

15

2

JoulesJoules

ms

mkg

JoulesAE

The energy (or Power) which is NOT converted to a useful form is called exhaust for the process…..

Common Examples:Thermal Energy Output (friction, air resistance, etc.)Sound (friction, collisions)Light (friction, “dissipative atomic processes

Example continued:

The brick does 15 Joules of useful work, thus the process has anexhaust of

40 Joules – 15 Joules = 25 Joules

input usefuloutput

scattered, non-usefuloutput [thermal, sound, etc.]