- #1
w3390
- 346
- 0
Homework Statement
A bowling ball is initially bowled so that it doesn't roll with a translational velocity Vo. Show that when the velocity of the ball drops to (5/7)Vo, the ball will begin to roll without sliding.
I= (2/5)MR^2
mass= M
radius= R
Homework Equations
V=wR
The Attempt at a Solution
I have had several unsuccessful attempts and my latest attempt has gotten me close to the right answer. The correct answer is (5/7)Vo, but I got sqrt(5/7)Vo. Here's what I did:
KE_T= KE_R
(1/2)MVo^2 = (1/2)MV^2 + (1/2)Iw^2
(1/2)Vo^2 - (1/5)R^2*w^2 = (1/2)V^2
Vo^2 - (2/5)R^2*w^2 = V^2
Vo^2 - (2/5)V^2 = V^2
Vo^2 = (7/5)V^2
V = SQRT(5/7)Vo
I am currently trying to figure out where I went wrong. Maybe I forget to account for friction. Any help would be much appreciated.