A roller coaster car (mass = M) is on a track that forms a circular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its speed at that point? A) rg B) 2rg C) (rg)^1/2 D) (2rg)^1/2 E) (0.5rg)^1/2

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Quizplus · Accepted Answer

At the top of the loop, the gravitational force must provide the necessary centripetal force to keep the car on the track. The minimum speed is when gravitational force equals centripetal force: Mg = Mv^2/r, solving for v gives v = (rg)^1/2.

A Roller Coaster Car (Mass = M) Is on a Track