A bowler throws a bowling ball of radius R = 11 cm down a lane. The ball slides

Question

A bowler throws a bowling ball of radius R = 11 cm down a lane. The ball slides on the lane with initial speed vcom,0 = 9.5m/s and initial angular speed ?0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.15. 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.

Explanation / Answer

a) vcm = w/r = w/0.11 = 9.09w

b) f = ma

0.15 x 9.81 = a

a = 1.47 m/s^2

c) rF = I x alpha

0.11 x 0.15 x 9.81 x m =2 x m x 0.11^2 x alpha / 5

alpha = 33.44 rad/s^2

d) 9.5 - 1.47t = 0.11 x (33.44 x t)

t = 1.85 sec

e) S = 9.5 x 1.85 - 1.47 x 1.85^2/2 = 15.01 m

f) v = 9.5 - 1.47 x 1.85 = 6.78 m/s

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