(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Conservation of energy on loop. Nearly done!

**Physics Forums | Science Articles, Homework Help, Discussion**