Date post: | 19-Dec-2015 |
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Quiz
This is a one-dimensional problem. Suppose a particle is attracted to the origin with a force
3x
kFx
Find the potential function.
Work-energy theorem:
12212121 KEKEWWW nccontotal
122112 KEKEWUU nc
112221 UKEUKEW nc
constIf 112221 ,0 UKEUKEW nc
Mechanical energy is conserved!
Examples
Strategy: write down the total mechanical energy, E,
E = KE + U at the initial and final positions of a particle:
Roller CoasterYou are in a roller coaster car of mass M that
starts at the top, height H, with an initial speed V0=0. Assume no friction.
a) What is the speed at the bottom?b) How high will it go again?
c) Would it go as high if there were friction?
H
Roller Coaster with FrictionA roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2).
Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?
Conservative Forces
If there are only conservative forces in the problem, then there is conservation of mechanical energy
• Conservative: Can go back and forth along any path and the potential energy and kinetic energy keep turning into one another– Good examples: Gravity and Springs
• Non-Conservative: As you move along a path, the potential energy or kinetic energy is turned into heat, light, sound etc… Mechanical energy is lost.– Good example: Friction (like on Roller Coasters)
Law of Conservation of Energy• Mechanical Energy NOT always
conserved• If you’ve ever watched a roller
coaster, you see that the friction turns the energy into heating the rails, sparks, noise, wind etc.
• Energy = Kinetic Energy + Potential Energy + Heat + Others…–Total Energy is what is
conserved! K1+U1 = K2+U2+EHeat…