A bowler throws a bowling ball of radius R = 11 cm down a lane. The ball slides

Question

A bowler throws a bowling ball of radius R = 11 cm down a lane. The ball slides on the lane with initial speed vcom,0 = 7.0 m/s and initial angular speed ?0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.23. The kinetic frictional force fk 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 ? has increased enough, the ball stops sliding and then rolls smoothly.

Explanation / Answer

for ball,

forces on it = mass * acceleration
f=ma (b) a=kg=2.254m/s2 until the ball starts rolling
where f is frictional force=mgk
where k is coefficient of friction.

now after time t its Vcom be V and initial be U
so V=U-gkt

for torque,
f(R)=I? (c) ? is in rad /sec2 until the ball starts rolling
where I=2/5 m(R)^2

after time t let angular speed be ?.
so, ?=kmgRt/2/5m(R)^2
=5kgt/2R

for rolling V=?R=5kgt/2=U - kgt .....(d)

so final V .........(f)

distance travelled=U^2-V^2/2a ......(e)

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