A roller coaster starts from rest at height h and travels through a loop of radius r. What is the minimum h for the coaster to maintain contact at the top of the loop?

Core Concept

At the top of the loop, minimum speed satisfies mg = mv²/r, so v² = gr. By energy conservation from height h: mgh = mg(2r) + ½mv². So h = 2r + v²/2g = 2r + r/2 = 5r/2.