A roller coaster car of mass 500 kg starts from rest at the top of a hill 30 m high. It then goes through a loop with a radius of 10 m. What is the normal force on the car at the top of the loop?

Core Concept

First, find the speed at the top of the loop using conservation of energy: mgh = ½mv² + mg(2r), where h = 30 m and r = 10 m. Solving for v: v² = 2g(h - 2r) = 2 × 9.8 × (30 - 20) = 196. At the top of the loop, the normal force plus gravity provides the centripetal force: N + mg = mv²/r. Solving for N: N = mv²/r - mg = 500 × 196/10 - 500 × 9.8 = 9800 - 4900 = 4900 N. Option B is incorrect because it's the weight of the car without considering the circular motion. Option C is incorrect because it adds the weight to the centripetal force instead of subtracting it. Option D is incorrect because it's twice the weight of the car.