A spherical bowling ball with mass m = 3.5 kg and radius R = 0.118 m is thrown d

Question

A spherical bowling ball with mass m = 3.5 kg and radius R = 0.118 m is thrown down the lane with an initial speed of v = 8.5 m/s. The coefficient of kinetic friction between the sliding ball and the ground is mu = 0.26. Once the ball begins to roll without slipping it moves with a constant velocity down the lane. 1) What is the magnitude of the angular acceleration of the bowling ball as it slides down the lane? rad/s^2 2) What is magnitude of the linear acceleration of the bowling ball as it slides down the lane? m/s^2 3) How long does it take the bowling ball to begin rolling without slipping? s 4) How far does the bowling ball slide before it begins to roll without slipping? m 5) What is the magnitude of the final velocity? m/s 6) After the bowling ball begins to roll without slipping, compare the rotational and translational kinetic energy of the bowling ball: KE_rot KE_tran

Explanation / Answer

1.) (5ug)/(2R) = 5*0.26*9.8 / (2*0.118) = 53.98 rad/s^2

2.) ug = 0.26* 9.8 = 2.55 m/s^2

3.) (2Vo)/(7ug) = 2*8.5/(7*0.26*9.8) = 0.95s

4.) (12Vo^2)/(49ug) = 12*8.5^2 / (49*0.26*9.8) = 6.944m

5.) 5*Vo/7 = 5*8.5/7 = 6.07m/s

6.) KErot<KEtran

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