How Does Friction Affect the Transition from Sliding to Rolling in Bowling?

[Xamfy19]

a bowling ball is given an initial speed vo on an alley such that it initially slides without rolling. The coefficient of friction between ball and alley is u.

find the speed of the ball's center of mass vCM at the time pure rolling motion occurs.

i used (1/2)mvo^2=(1/2)mVCM^2 + (1/2)Iw^2
I=(2/5)mr^2

i got vo^2=(7/5)v^2 which is wrong.

how do i solve this problem?

 

[Doc Al]

Originally posted by Xamfy19
i used (1/2)mvo^2=(1/2)mVCM^2 + (1/2)Iw^2
I=(2/5)mr^2

It looks like you are assuming that energy is conserved. Why?

 

[Xamfy19]

Well, I think the friction must have consumed certain energy too. However, I have no idea how to incorporate it into the equation.

 

[Doc Al]

There are several ways to attack this problem. Here's one way:

Picture what's happening. The ball starts with pure translational motion. The friction slows the translational motion, and starts the ball rotating. So write equations for the translational motion and for the rotational motion, due to the friction. The ball will slow down (but increase rotational speed) until the speed is just right to stop slipping.