"A 0.18-kg billiard ball whose radius is 2.8 cm is given a sharp blow by a cue stick. The applied force is horizontal and the line of action of the force passes through the center of the ball. The speed of the ball just after the blow is 3.9 m/s and the coefficient of kinetic friction between the ball and the billiard table is 0.64."
How long does the ball slide before it begins to roll without slipping?
How far does it slide?
What is its speed once it begins rolling without slipping?
translational kinetic=(1/2)mv^2 Rotational kinetic = (1/2)Iω^2
(when rotating without slipping) v=rω a=rα
Force of friction = force normal * coefficient of friction
Iα=r x F
L= r x p = rmvsin θ (i'm not sure if that is useful yet)
The Attempt at a Solution
I know that it's losing kinetic energy to friction
Force of friction*distance to point where it begins rotating
so I know that after that amount of energy loss... v=rω a=rα will hold true
but I don't know what to do with this...
The net force should just be the force of friction right? so a= Ff/m
I'm confused as to what to do with any of this... it seems like I'm missing something...
I have (1/2)mVi^2=Ff*Δx+.7mVf^2 (added rotational and kinetic assuming that it is rotating)
and that's about all I can do I rearranged somethings and got about .7 seconds for the time. . . but I'm pretty sure that is wrong...