A billiard ball that is initially at rest is given a sharp blow by a cue stick.
ID: 1977397 • Letter: A
Question
A billiard ball that is initially at rest is given a sharp blow by a cue stick. The force is horizontal and is applied at a distance h = 2R/3 below the centerline, as shown in the figure below. The speed of the ball just after the blow is v0 and the coefficient of kinetic friction between the ball and the billiard table is k. (Use the following as necessary: v0, k, m for the mass and R for the radius of the billiard ball.)
(a) What is the magnitude of the angular speed of the ball just after the blow? (Note: Write h in terms of R, and assume no friction the instant the ball is struck.)
Explanation / Answer
The mass of the ball is m
The point of application of force h = 2R/3
The speed of the ball just after the blow v0
The coefficient of kinetic friction is k
Radius of the ball is R
a)
The angular spped of the ball just after the hit is given by
I0 = mv0h
Where? I0 ????is the rotational impulse
0 = mv0h/I
0 = mv0(2R/3)/(2/5mR2)
0 = 5v0/3R
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