physics problems woo?

C

cleveland

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7. B is changing the tire of her car on a steep hill 20.0 m high. she trips and drops the 10.0-kg spare tire, which rolls down the hill with an initial speed of 2.00 m/s. What is the speed of the tire at the top of the next hill, which is 5.00 m high ? (ignore the effects of the rotation KE and friction.)

9. A 500.-kg pig is standing at the of a muddy hill on a rainy day. The hill is 100.0 m long with a vertical drop of 30.0 m. The pig slips and begins to slide down the hill. What is the pig's speed at the bottom of the hill? use the law of conservation of energy.
 
7) Just use the Law of Conservation of Energy, which states that all the potential energy in the tire will be conserved as it rolls down the hill:

PE + KE = KE' + PE' [' denotes after the tire rolls to the 5 m hill]
mgh + 0.5mv^2 = 0.5mv'^2 + mgh' [all m cancel]
gh + 0.5v^2 = 0.5v'^2 + mgh'
(9.8m/s/s)(20m) + 0.5(2m/s)^2 = 0.5(v^2) + (9.8m/s/s)(5m)
v = 17.3 m/s

9) This problem involves the same concept: the pig's potential energy at the top of the hill will be turned into kinetic energy at the bottom:

PE = KE'
mgh = 0.5mv^2 [m cancel out]
gh = 0.5v^2
(9.8m/s/s)(30m) = 0.5v^2
v = 24.2m/s

Notice that the velocity is independent of the length of the hill (100m) because potential energy only relies on the initial height from an arbitrary 0 point (to say it relies on the change in height is a more accurate statement).
 
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