How to find height of original hill (roller coaster loop problem)

[Mikhowl]

Homework Statement

Radius of loop: 20 m
Mass of cart: 225 kg
Gravity: 10 m/s/s (once I figure out how to do this I'll use 9.8 in the final project)

Found so far:

B) Velocity (top of loop) = 14.14 m/s
C) GPE at the top of the loop = 90000 N
C) KE top of loop = 22500 N

D) KE (bot) = 180000 N

Homework Equations

A) Fg = mg = 225 kg * 10 m/s/s = 2250 N
B) Fg = mv^2/r
C) GPE (top of loop) = KE (top of loop) - heat (lost going through loop)

The Attempt at a Solution

B) Using these equations I found that the velocity at the top of the loop is 14.14 m/s.

C) 90000 N (GPE = mgh) = 22500 (KE =1/2mv^2) - heat.
That means heat would have to be (-)67500 N. Because of conservation of energy, those three energies added together should be the energy at the bottom (before) the loop. Where all energy would be allocated to KE because height at that point is 0. So

D) KE (bot) = 180000 N


I'm confused as to where to go next. The KE (bot) should be equal to the GPE at the top - whatever heat was lost going down the hill. But how would I find the heat lost there? Would it be the same as before (67500 N)?

 

[HallsofIvy]

I think you mean "energy" where you are using the word "heat". Heat is a very specific form of energy that does not really apply here. Also you say 'GPE= 9000 N'. N is standard for "Newton" which is a unit of force, not energy. The MKS unit of energy is the "Joule".

 

[mfb]

C) GPE (top of loop) = KE (top of loop) - heat (lost going through loop)

Why should that be true? In particular, GPE depends on the arbitrary definition of "zero height", the other two expressions do not.
Energy conservation gives GPE(starting point) = GPE(top of loop) + KE (top of loop) + losses