A roller-coaster vehicle has a mass of 506 kg when fully loaded with passengers

Question

A roller-coaster vehicle has a mass of 506 kg when fully loaded with passengers (see figure).
(a) If the vehicle has a speed of 19.0 m/s at point A, what is the force of the track on the vehicle at this point?
__________________N

(b) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track?
__________________m/s

Explanation / Answer

F = ma radially at A gives N - mg = mv^2/r N = mg + mv^2/r = 506(9.81) + 506(19^2/rA) = answer F = ma radially at B gives mg - N = mv^2/r but N will be zero if roller-coaster leaves track. mg = mv^2/r => v^2 = gr = 9.81 x rB = answer^2 (take square root) You forgot to tell me what the radius of both loops are. Plug in the radius for rA and rB and you got your answers.

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