A bowling ball of mass 3.7 kg and radius 11 cm is initially sliding without roll

Question

A bowling ball of mass 3.7 kg and radius 11 cm is initially sliding without rolling with a speed of 1.4 m/s along the horizontal surface of a bowling alley. The coefficients of friction between the bowling ball and the surface are ?(kinetic) = 0.18 and ?(static) = 0.32. (a) How long does it take the bowling ball to start rolling without sliding? (b) How fast is the bowling ball going after it starts rolling without slipping? Hint: analyze the torques in a frame whose origin is at the center of the bowling ball.

Explanation / Answer

Assumre friction acting in backward direction at the base of ball

Now friction will decrease the linear velocity and increase the angular velocity an let frictional force be f

Suppose after time t the ball starts pure rolling so aling linear v=1.4 -f x t /m

along angular using net torque about centre = I x alpha (I is moment of inertia)

alpha= 5f/ 2mr (assuming ball to be solid sphere)

now in angular direction final andular velocity (W) = 5f/2mr x t

as we know for pure rolling v= r x w

putting in equations 1.4 - ft/m = 5f/2m x t this gives 7ft/2m = 1.4 which gives ft/m = 0.4

put in equations to get v = 1 m/s and final angular velocity = 5.56 rad/sec

Now f = mu kinetic X g

substitute value of f m and g in equation to get

TIME=37/45 = 0.823 sec

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