A bowler throws a bowling ball of radius R = 11 cm along a lane. The ball (the f

Question

A bowler throws a bowling ball of radius R = 11 cm along a lane. The ball (the figure) slides on the lane with initial speed V com, 0 = 8.5 m/s and initial angular speed omega 0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.33. The kinetic frictional force f k acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speed y com has decreased enough and angular speed phi has increased enough, the ball stops sliding and then rolls smoothly. During the sliding, what are the ball's (a) linear acceleration and (b) angular acceleration? (c) How long does the ball slide? (d) How far does the ball slide? (e) What is the linear speed of the ball when smooth rolling begins? Note that the clockwise direction is taken as negative.

Explanation / Answer

Linear Velocity V and Angular velocity W are related by V = RW

if V has decreased, W has to increase

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part A:

inear accleration a = -uK g

a com = -0.33 * 9.8

acom = 3.23 m/s^2

B : angular acceration A = Torqur T/MOI

A = uk mg R/I

here I = 2mR^2/5

A = 5 * 0.33* 9.8/(2* 0.11)

A = 73.5 rad/s^2

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C:

use V = Vo -uk gt

-0.11 W = 8.5 - 0.33* 9.8 t

but W = At

W= 73.5 * t

so

-0.11* 73.5 t = 8.5 -0.33* 9.8t

t = 1.75 secs

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D. disatnce d = ut -0.5 u gt^2

x = 0.5 * 0.33* 9.8 * 1.75^2

x = 2.83 m

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use V = u - u g t

V = 0 - 0.33* 9.81 * 1.75

V = 5.66 m/s

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