Homework Help: Car on loop

1. Sep 24, 2015

Anne Armstrong

1. The problem statement, all variables and given/known data
In a loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has a mass m = 260 kg and moves with speed v = 15 m/s. The loop-the-loop has a radius of R = 10 m. What is the minimum speed of the car so that it stays in contact with the track at the top of the loop?

2. Relevant equations
ac=v2/r
F=ma

3. The attempt at a solution
At the top of the loop, the forces acting on the car are Fgravity, FNormal, and Fcentrifugal (I think). So I think the minimum speed would be one that made all the forces cancel to zero (aka, Fc is just strong enough to counteract Fgravity and FNormal). If that's true, then Fc=FN+Fg. Since Fc=m*ac=v2/r , so far I have: m*ac=v2/r = m*g+m*g.
..but I don't think that makes sense... Is FN in this case equal and opposite to Fc?

2. Sep 24, 2015

haruspex

If the car is only just staying in contact, what will the normal force equal? Remember, this the force the track and car exert on each other.

3. Sep 24, 2015

Anne Armstrong

The normal force will equal the force of gravity, m*g?

4. Sep 25, 2015

haruspex

Why would it have to be that?
A normal force is the reaction that results when attempting to push an object through something that resists. When you place an object on solid ground, the weight of the object acts to push the object through the floor. The normal force is the reaction necessary from the floor to prevent it. When you place on object on an incline, only part of the weight is trying to push the object into the incline, so the normal force is less. In this case, what is trying to push the object through the top of the loop?