1. A bowling ball of mass M and radius R ( treated as a uniform solid sphere ) i

Question

1. A bowling ball of mass M and radius R (treated as a uniform solid sphere) is thrown along a level floor with initial kinetic energy K0. It is thrown so that initially (at t = 0) it has a linear speed Vo but does not rotate. As the ball starts sliding, kinetic friction slows down translational motion from Vo to v = vcom, while at the same time providing torque with respect to the center of mass of the ball; this torque speeds up the rotational motion with angular speed changing from 0 to w. That process stops when the balls center of mass velocity becomes equal to wR. After that moment, the ball rolls without sliding (smooth rolling). The coefficient of kinetic friction between the ball and the floor is Uk and coefficient of static friction is Us .

a) At what time t > 0 does the bowling ball begin rolling smoothly along the floor? What is the linear speed Vcom at that time? Express your answers in terms of Vo , g, and Uk , as needed.

(b) What is the change in K in the bowling balls kinetic energy during this entire process (i.e., from the beginning of the sliding motion to the beginning of the rolling without slipping)? Express your answer in terms of Ko.

Explanation / Answer

Solution: -

initial KE = Ko =

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