A roller coaster at an amusement park is at rest on top of a 30 m hill (point A). The car starts to roll down the hill and reaches point B which is 10 m above the ground, and then rolls up the track to point C, which is 20 m above the ground.
(A) A student assumes no energy is lost, and solves for how fast the car is moving at point C using energy arguments. What answer does he get?
(B) If the final speed at C is actually measured to be 2 m/s, what percentage of energy was "lost" and where did it go?
Kf + Uf = Ki + Uf
K = 1/2mv2
Ug = mgh
The Attempt at a Solution
I believe there is a typo in the book for Part A, I think they got the height wrong, their answer is 20 m/s. For Part B, I think I did something wrong because the height error has been corrected.
My Work for Part A:
I set potential energy at A equal to kinetic energy at C. My reference point is considering the height of C as ground level.
mgh = 1/2mv2
gh = 1/2v2
10*10 = 1/2v2
100 = 1/2v2
200 = v2
14 = v
Their Work for Part A
My Work for Part B
Find ratio of Final Energy to Initial Energy and subtract from 100%
So 98% is lost to heat. This is radically different from their answer:
For this part I again used a reference height of the height at C, but am I not allowed to do that?