Question

Problem 1 (10 points) Block A, with weight 3w, slides down an inclined plane S of slope angle 36.9 at a constant speed while plank B, with weight w, rests on top of A. The plank is attached by a cord to the wall as shown below. (a) Draw a free body diagram for block A. (b) Draw a free body diagram for plank B. (c) If the coefficient of kinetic friction is the same between A and B and between S and A determine its value k 6.9 Problem 2 (10 points) A wedge of inclined angle a and mass M rests on frictionless, horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge as seen in the figure below. What must the magnitude of F be if the block is to remain at a constant height above the tabletop? Express your answer only in terms of M, m, a, and g. where g 9.80 m/s. Ignore the friction between the wedge m and the block m.

Answer 1

(c)Now for plank B, equation N_2 = W_B cos theta equation (1) For block A, N_1 = N_2 - W_A cos Theta equation (2) Also W_A sin theta - M_k N_1 - M_k N_2 = 0 equation (3) (constant speed means not force zero) using (1), (2), (3) W_A sin Theta - M_k (N_1 + N_2) = 0 W_A sin Theta - M_k (W_B cos theta + W_A cos Theta + W_B cos theta) = 0 M_k = W_A/2W_B + W_A tan Theta = 3w/2w + 3w tan 36.9 degrees = 3/5 times tan 36.9 degrees = 0.45