4. (25 points) A billiard ball initially at rest is given asharp blow by a cue s

Question

4. (25 points) A billiard ball initially at rest is given asharp blow by a cue stick. The

force is horizontal and is applied a distance (2/3)R belowthe centerline of the ball. The

initial speed of the ball after the blow isvo, and the coefficient ofkinetic friction isk.

(a) What is the initial angular speedo? (Careful with signs!)[7 pts]

(b) What is the speed of the ball once it begins rollingwithout slipping? [6 pts]

(c) How far does the ball slide before it starts rollingwithout slipping? [6 pts]

(d) What is the work done by friction on the ball? [6pts]

Tosee this problem with its picture...see this link:

http://tbp.berkeley.edu/examfiles/physics/physics7a-fall_2005-final-boggs-exam.pdf

Explanation / Answer

(a) Use rotation impulse, Pt = mv0r; r = 2R/3 Pt = Iw0; w0 =(2mv0R/3)/[(2/5)mR2] = 5v0/3R (b) Since F is below the center line, the spin is backward, i.e., the ball will slow down. w0 =-5v0/R. w = w0 + (5/2)mkgt/R; v = v0 - mkgt; set wR =v v0 - mkgt = -(5/3)v0 + (5/2)mkgt; t =(16/21)v0/mkg v = (5/21)v0 = 0.238v0 (c) Ki = 1/2mv02 +1/2Iw02 Ki = 1/2mv02 +1/2(50/45)mv02 =(19/18)mv02 = 1.056mv02 (d) Find Kf; then Wfr = Ki - Kf Kf = (7/10)mv2 = (0.7 *0.2382)mv02 =0.0397mv02 Wfr = 1.016mv02

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