A hollow spherical ball (like a tennis ball, or a basketball) is released from r

Question

A hollow spherical ball (like a tennis ball, or a basketball) is released from rest at the top of a 45 degree inclined plane. The coe¢ cient of static friction is 0.25 and the coe¢ cient of sliding friction is 0.20.

(a) Will it initially slide, or will it initially roll without slipping, and in any event, what will be the initial acceleration o§ the center of mass down the incline?

(b) If the length of the incline is 10 meters, how long will it take for the ball to reach the bottom? (Hint: If the ball slides initially, it will continue to slide, and if the ball rolls initially without slipping it will continue to roll without slipping.)

Explanation / Answer

(A) along the incline,

Fnet = m a

m g sin45 - f = m a .... (i)

Applying torque = I alpha

r f = (2 m r^2 / 3) (a / r)

f = 2 m a / 3

putting in (i)

m g sin45 = m a (1 + 2/3)

a = 4.16 m/s^2

(B) d = v0 t + a t^2 /2

10 = 0 + 4.16 t^2 /2

t = 2.19 sec

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