Conservation of Energy

Forces• Conservative Force - Gives back work done

against it. (Gravity & springs)

• Non-conservative Force - Does not give back work done against it. (Friction)

• Criteria for a conservative force

0 rdF

Work on aClosed Path

• What total work is done by gravity going from A to B to C and back to A again?

0m-1m 1m

1m

A

B

C

Potential Energy• If a force is conservative, it can be related

to potential energy.

• For gravity near the earth’s surface

rdFUB

AAB

jdyjmgUy

yABˆ ˆ

1

0

ymgU AB

Falling Brick• A 5.0 kg brick is tossed from a 14 m tall

building. If the initial velocity were 20 m/s upward, what is the change in potential energy when the brick hits the ground?

h

Millenium Force

• Are the predictions of the Millenium Force speed accurate?

mghmv 221

PK EE

hgv 2

300ft Drop

>92mph

Mechanical Energy

• From the work energy theorem

netWK

nonconscons WWK

nonconsWUK

nonconsWUK

1100 UKUK 0 UK

• If only conservative forces working, then

Springs• The potential energy in a spring is

idxikxUx

xABˆ ˆ

1

0

202

1212

1 kxkxU AB • Ex. As a compound bow is drawn, it exerts

a force of F=(300x+150x3)N. What is the change in potential as it is drawn from x=0m to x=0.75m?

Arrow Speed• What is the velocity of a 0.15 kg arrow

fired by a composite bow with a force of

F=(300x+150x3)N and drawn to 0.75m?

Force and Potential

• If the potential is known, the force can be determined.

• Ex. The potential energy for a spring is given by the function U=5(2x)2 J. What is the spring constant for this spring?

dx

dUFx

Energy Sources

Oil38%

Natural Gas25%

Nuclear8%

Coal22%

Renewable Sources

Solar

Wind

Hydroelectric

Energy & Well Being

• Basis of HDI– Longevity– Education– Standard of

Living

Chemical Fuels

• Gas– Hydrogen (143 kJ/g)– Natural, Syngas (56 kJ/g)

• Liquid– Gasoline, Kerosene,

heating oil (44 - 48 kJ/g)

• Solid– Coal (32 kJ/g)– Wood (10 – 19 kJ/g)– Stearic acid (40 kJ/g)

Einstein and Energy

• Relativity - Speed of Relativity - Speed of Light is the same for Light is the same for everybody.everybody.

• ConsequencesConsequences– Light bent by massLight bent by mass– Energy related to massEnergy related to mass

2mcE •Ex. A nuclear power plant generates 300 GW of power. In one day how much mass is converted to energy?

Nuclear Power

Nuclear FusionNova

Tokomak

1 gallon sea water = 300 gallon gasoline