Rolling balls on tracks with different paths · CAP 2005 #3
Physics · mechanics
Problem
At some time t, two identical balls, A and B, are set rolling without slipping at the same speed from one end of two tracks which are identical with the same horizontal length, except that track B has a dip in the path of ball B, as shown in the figure. The straight portions of the tracks are horizontal. Gravity is uniform throughout. Which ball reaches the other end first?
[Figure: Two horizontal tracks A and B of equal length. Track A is straight. Track B has a dip (downward curve) in the middle of its path.]
(a) Ball A;
(b) neither, since both arrive at the same time;
(c) ball B;
(d) ball A, but only if the dip is deep enough.