A bowler throws a bowling ball of radius R along a lane. The ball (the figure) s

Question

A bowler throws a bowling ball of radius R along a lane. The ball (the figure) slides on the lane with initial speed vcom0 and initial angular speed ?0 = 0. The coefficient of kinetic friction between the ball and the lane is ?k. The kinetic frictional force fk acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speed vcom has decreased enough and angular speed ? has increased enough, the ball stops sliding and then rolls smoothly. During the sliding, what are the ball's (a) linear acceleration and (b) angular acceleration? (c) How long does the ball slide? (d) How far does the ball slide? (e) What is the linear speed of the ball when smooth rolling begins? State your answer in terms of the given variables, using g when applicable. Note that the clockwise direction is taken as negative.

Explanation / Answer

a) a = -µ*g

b) = µ*g/(k*R) where k is found in I =k*m*R²; for a solid sphere, k = 0.4

c) t = k*vcom/[µ*g*(1+k)]

d) Xs = vcom*t - ½µg*t²

e) Vs = vcom - µg*t

Note that can be either + or - depending on which direction (right or left) the ball is thrown. The expression gives the absolute value of .

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