conservation energy.....?

Question

A roller coaster car of mass 1500 kg starts a distance H = 23 m above the bottom of a loop 15 m in diameter. Friction is negligible.

a) Find the speed of the coaster when it is upside down at the top of the loop.

b) Find the downward force of the rails on the car when it is upside down at the top of the loop.

Answer 1

I assume it's at rest at the start 23 m above the bottom.

a) You need to find the potential energy at the start. Since both questions are about the top of the loop, use h = 23-15 meters.
U = m*g*h

At the top of the loop, all that energy will be in the kinetic form.
U = KE = (1/2)*m*v^2

b) The centripetal force toward the center of the loop needed to bend the car's path in a circle is given by
Fc = m*v^2 / r
Compare that value with the car's weight
W = m*g
The weight will provide some of the required centripetal force. The downward force by the rails will provide the rest of Fc.