Solving the Billiard Ball Problem: Finding Work Lost to Friction

[aldee11]

Billiard ball rotating and slipping. help

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

Homework Equations

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

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+volt+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.

 

[aldee11]

Anybody?? I really need help

 

[aldee11]

Please heLP!

 

[aldee11]

nobody?

 

[diazona]

Sorry... maybe it's just me but I can't really understand the problem as you've stated it. Is the axis of rotation of the ball supposed to be parallel to the table? (The way you wrote it, it sounds like the ball is spinning around a vertical axis)

 

[aldee11]

Sorry... maybe it's just me but I can't really understand the problem as you've stated it. Is the axis of rotation of the ball supposed to be parallel to the table? (The way you wrote it, it sounds like the ball is spinning around a vertical axis)

Its a billiard ball rotating on the table. If you ever played pool before, you know that once you hit the ball its both rotating and slipping then it rolls without slipping