Question

A roller coaster slides down a frictionless ramp. What is the minimum height of the ramp such that the roller coaster will maintain contact at the to of the loop the loop with radius r

Answer 1

for the coaster to stay at in contact the centripetal force must be equal to the gravity

so we get the equation

so velocity of the coaster at the height r must be

now applying conservation of energy we get the equation

by solving it we get

I hope you found my answer helpful you did a thumbs would be appreciated otherwise comment your issues and doubts and I will address them