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
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?
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