# Homework Help: Roller coaster in a circular loop problem

1. Sep 4, 2009

### razis_wwf13

1. The problem statement, all variables and given/known data
A roller coaster car is on a track that forms a circular loop of radius R in the vertical plane.

(a) If the car is to maintain contact with the track at the top of the loop, what is the minimum speed v that the car must have at the bottom of the loop? Ignore air resistance and rolling friction.
(b) If the car has a speed 6v/5 at the bottom of the loop, then what will be force vector acting on the car by the track when it reaches the top of the loop? [v is the minimum speed calculated in (a).]
(c) If the car has a speed 4v/5 at the bottom of the loop, locate the point on the track where the car ceases to maintain contact with the track.

2. Relevant equations
0.5mv12 + mg(2R) - 0.5mv22 - mg(0) = 0.
Fc = N - mg

3. The attempt at a solution
For a), i just used the first eqn, sub in all the known datas, i got v = 2sqrt(gR) as the min speed needed.

For b), i assumed force vector needed is normal force. So at the top, i used the 2nd eqn, and i got N = Fc - mg = mv2/R - mg.

For c), i dunno how to attempt the qn. Hope you guys can help thx!!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 4, 2009