A roller coaster car is at the top of a vertical circular loop of radius 20 m. What is the minimum speed the car must have at the top of the loop to maintain contact with the track?

Core Concept

At the top of the loop, the car must have enough speed so that the centripetal acceleration is at least equal to g. If the centripetal acceleration were less than g, the track would need to push downward on the car, which is impossible. The minimum centripetal acceleration is g, so v²/r = g, which gives v = √(rg) = √(20 × 9.8) = 14.0 m/s. Option A is approximately √(g) but missing the radius factor. Option C is √(g) times 10, which is incorrect. Option D is √(2g) times 10, which is also incorrect.