Billiard ball rotating and slipping

[aldee11]

. Homework Statement
A ball radius "a" and mass "m" initially spinning counterclockwise with angular speed w=-v0/a with a forward speed vo. The coefficient kinetic friction between the ball and the billiard table is Mu, [Given a,m,vo,mu]
Determine the work lost to friction while slipping using two methods (they should be equal)
W=-Ffs where s the distance ball slips not travels
W= delta Kt + delta Kr


2. Homework Equations
F=ma
Torque= I*alpha
W=v/r
V=vo+at
W=Wo+alpha*t



3. The Attempt at a Solution

I found a from equation F= ma where F=-Ff
Then plug in a to eq V=Vo+at

I also found alpha from eq Torque= I alpha
then plug in alpha to eq W=Wo+ alpha t

set V=RW i got T where the slipping becomes rolling without slipping.

The questions are
1. Can i use this t and plug it into eq X=Xo+Vot+0.5at^2 to find The distance the ball SLIPS??
2. If i can't use that equation, then How can i find the distance the ball slips?
3. In finding W= delta Kt + delta Kr, Do I have to use final angular and forward speed that i found from previous calculation or Do i have to find them?

Thank you for your help.

 

[Jhero]

Dear forum post author,

1. Yes, you can use the equation X=Xo+Vot+0.5at^2 to find the distance the ball slips. However, you need to make sure that the acceleration a you use is the tangential acceleration of the ball as it slips, not the linear acceleration. This can be found by taking into account both the frictional force and the tangential component of the ball's weight.

2. Alternatively, you can use the equation W=Fd to find the distance the ball slips, where F is the frictional force and d is the distance over which the force acts. This distance can be found by considering the fact that the ball starts with an initial linear velocity and ends with an angular velocity due to rolling without slipping.

3. To find the work lost to friction using the method W= delta Kt + delta Kr, you need to use the final angular and linear velocities that you have calculated. These velocities represent the change in kinetic energy due to the slipping and the rolling without slipping, respectively.