(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 1500-kg roller coaster car starts from rest at a height H=23.0m above the bottom of a 15.0-m-diameter loop. If friction is negligible, determine the downward force of the rails on the car when the upside-down car is at the top of the loop.

2. Relevant equations

Conservation of energy: U+K=E_{sys}

U=mgh

K=0.5mv^{2}

F=ma

a_{centripetal}=v^{2}/r

3. The attempt at a solution

U_{initial}=E_{sys}because starts from rest. U_{initial}=mgh_{initial}

at the top of the loop: E_{sys}=U+K=mgh_{top}+0.5mv^{2}

meaning mgh_{initial}=mgh_{top}+0.5mv^{2}

simplifying: v^{2}=2(gh_{initial}-gh_{top}).

so:

F=ma_{centripetal}=mv^{2}/r=

1500kg*2(9.81m/s^{2}*23m-9.81m/s^{2}*15)/7.5m

So that gives an answer of 31,392N. I know the answer is 16.7 kN (back of book), and I know you get there by subtracting mg. So why am I subtracting mg? I would think that would be the TOTAL force and not solely the force of the tracks on the car.

Any and all help is much appreciated!

Edit: You know, I think I get it. I solved for centripetal force, which is the total inward force toward the center of the circle. Because mg is in that direction, I subtract it and get the force from the tracks. Is this right?

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# Homework Help: Conservation of energy on loop. Nearly done!

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