Anwers will be appreciated. Chapter 11, Problem 15 Flying Circus of Physics A bo

Question

Anwers will be appreciated.

Chapter 11, Problem 15 Flying Circus of Physics 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 vcom,0 = 6.9 m/s and initial angular speed 0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.16. The kinetic frictional force 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 vcom 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. Number Units Number Units Number Units Number Units Number Units

Explanation / Answer

Friction force (f)= m*a

mu*m*g = m*a

a) a=1.57 m/s^2

when rolling starts, v =w*r

v = u+at = 6.9 -1.57t

w = angular accln(alpha) *t = T*t/I

T = f*r

w = mu*m*g*r*t/ 0.4*m*r^2 =mu*g*t / 0.4*r

Using, v= w*r

6.9 -1.57t = mu*g*t*r / 0.4*r

6.9 -1.57t =0.16*9.81*t/0.4

6.9 =(1.57+3.924)t

t = 1.256s

b) alpha = T/I = mu*m*g*r/ 0.4*m*r^2 = 35.67 rad/s^2

c) Ball slides for 1.256s

d) Distance , s =u*t +0.5*a* t^2 =7.428m

e) Linear speed = 6.9 - 1.57*1.256 = 4.92m/s

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