Question

A roller coaster has a vertical loop with radius 15.8 m. with what minimum speed should the roller coaster car be moving at the top of the loop so that the passengers do not lose contact with the seats?

Answer 1

The centripetal force will balance the gravitional:
m*g=m*v^2/R
v=sqrt(g*R)
Plug in the numbers
v=sqrt(9.81*15.8)
v= 12.45 m/s