Question

A bowler throws a bowling ball of radius R = 11 cm along a lane. The ball slides on the lane with initial speed vcom,0 = 6.0 m/s and initial angular speed ω0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.35. The kinetic frictional force f with arrowk 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 ω has increased enough, the ball stops sliding and then rolls smoothly.(a) What then isvinterms ofω? (b) During the sliding, what are the ball’s translational and angularacceleration? (c) How far does the ball slide?

Answer 1

The velocity of the center of mass (vcom) is equal to the product of the angular speed (ω) and the radius (R) of the ball. During the sliding, the ball experiences linear acceleration and angular acceleration. The distance that the ball slides can be calculated using the equation s = (vcom,0^2 - vcom^2) / (2a).

Step-by-step explanation:

(a) When the ball stops sliding and rolls smoothly, the velocity of the center of mass (vcom) is equal to the product of the angular speed (ω) and the radius (R) of the ball. So, vcom = ωR. Therefore, ω = vcom/R.

(b) During the sliding, the ball experiences linear acceleration and angular acceleration. The linear acceleration is given by a = f/m, where f is the kinetic frictional force and m is the mass of the ball. The angular acceleration is given by α = fR/I, where I is the moment of inertia of the ball.

(c) The distance that the ball slides can be calculated using the equation s = (vcom,0^2 - vcom^2) / (2a), where s is the distance, vcom,0 is the initial velocity of the center of mass, and vcom is the final velocity of the center of mass when the ball stops sliding.

Answer 2

Please see attachment

Step-by-step explanation:

Please see attachment