1. (20 pts.) A bowling ball of mass M and radius R (treated as a uniform solid s
ID: 1378847 • Letter: 1
Question
1. (20 pts.) 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 ?0 but does not rotate. As the ball starts sliding, kinetic friction slows down translational motion from ?0 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 ?. That process stops when the balls center of mass velocity becomes equal to ?R. After that moment, the ball rolls without sliding (smooth rolling). The coefficient of kinetic friction between the ball and the floor is ?k and coefficient of static friction is ?s .
(a) (5 pts.) At what time t > 0 does the bowling ball begin rolling smoothly along the floor? What is the linear speed ?com at that time? Express your answers in terms of ?0 , g, and ?k , as needed.
(b) (5 pts.) What is the change ?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 K0.
(c) (5 pts.) After rolling along the horizontal floor for a while, the bowling ball rolls without slipping up a ramp made of the same material as the floor, with the coefficient of static friction ?s, ?s =? 0, as shown below. What maximum height H, above its original location, does the bowling balls center of mass attain? Express your answers in terms of ?0 , g, and ?s , as needed.
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(d) (5 pts.) Suppose instead that the bowling ball rolls up a frictionless ramp, as shown below. What maximum height h, above its original location, does the bowling balls center of mass attain in this case? Express your answer as a multiple of H, the height it attained on the ramp in part (c).
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Explanation / Answer
Please, note that, you did not provide the question clearly. I have done part-(a) and part-(b) only because, other parts are not clear enough to understand the symbols. Even though, I did the first two parts, I could not understand the symbols clearly because there are only
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