2. A roller-coaster car has a mass m when fully loaded with passengers. The path of the coaster from its initial

point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to

the left or right. Assume the roller-coaster tracks at points A and B are parts of vertical circles of radii ₁ = R and

r2 = 1.5R, respectively. The centers of the two vertical circles are at the same height above the ground. Find (a)

the maximum speed the roller-coaster car can have at point B and still remain on the tracks; (b) the speed of the

roller-coaster car at point A, if its speed at point B is what you found in the previous question; and (c) the force

exerted by the tracks on the car at point A. Express your answers symbolically, in terms of m, R, and g.

a) max. v at Ⓡ

r₁=R

1₂= 1.5R