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 radiusR=11cm down a lane. The ball slides on the lane, with initial speedvcm,0=10.0m/s and initial angular speed?0= 0. The coefficient of kinetic friction between the ball and the lane is0.38. The kinetic frictional forcefkacting on the ball (Fig. 12-35) causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speedvcmhas decreased enough and angular speed?has increased enough, the ball stops sliding and then rolls smoothly.

Explanation / Answer

Let V = initial speed and v the final speed A = angular acceleration (for lack of Greek letters) u = coefficient of friction and w the angular speed Ff = m g u the frictional force Ff = - m a = m g u a = -g u the acceleration of the ball due to frictional force Ff R = I A = 2 A m R^2 / 5 rotational acceleration of ball m g u R = 2 A m R^2 / 5 A = 5 g u /(2 R) this gives us the angular acceleration of the ball V - v = -a t = g u t change in speed of ball in time t V = v + g u t When the ball stops rolling v = w R = A t R V = A t R + g u t Now substitute for A V = (5 g u /2 t + g u t) = 7 g u t/ 2 t = 2 V / (7 g u) Now that you have t you can easily calculate the other requested values using Newton's Laws

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