Question

Problem #1 (3+1+1+1-6 points) A thin-walled hollow cylinder is released from rest and rolls down the hill that slops downward at 500 from the horizontal without slipping. The mass of the cylinder is 3 kg and its radius is 0.5 m. hemomento mertiited linder is 1 -M Re Find: (a) the minimum value of the coefficient of static friction between the cylinder and the hill for no slipping to occur (1 point); (b) using the answer to part (a) calculate the acceleration of the cylinder (in m/s2) when it's rolling down the hill (I point); (c) when the cylinder's center of mass moves with a speed of 1.5 m/s how fast the cylinder is rotating (in rad/sec) (1 point).

Answer 1

The Coefficient of friction (mu) = tan theta [k^2/k^2 + k^2] For bellow cylinder z = pi2^2 = pi k_2 = > k^2 = R^2 = > mu = tan (50 degree) [1/2] = .2979. (b) a = 1/2 sin theta = 1/2 times 9.8 times sin 50 degree = 3.75 m/s^2 Frictional deceleration = mu times g cos theta = 1.876 m/s^2 a_Net = 3.78 - 1.876 (c) w = v/r = 1.5/0.5 = 3 rad/s