A 14 lb bowling ball is thrown onto a lane with a backspin angular speed ω0= 10 rad/s and...

A 14 lb bowling ball is thrown onto a lane with a backspin angular speed ω0= 10 rad/s and forward velocity υ0 = 17 mph. After a few seconds, the ball starts rolling without slip and moving forward with a speed υf = 17.2 ft/s. Let r = 4.25 in. be the radius of the ball, and let kG = 2.6 in. be its radius of gyration.

Figure P8.14

Knowing that the coefficient of kinetic friction between the lane and the ball is μk = 0.1, determine the length Lf over which the friction force acts in order to slow down the ball from υ0 to υf. Does Lf also represent the distance traveled by the center of the ball? Explain.