A 100 kg block B rests on a rough horizontal surface with μ = 1/3. A rope passes over a pulley and is climbed by a 25 kg boy A as shown. Find the maximum upward acceleration of the boy for which block B does not move.

Question

G1 Physics · Accepted Answer

Let rope tension be T. For the boy, T-25g = 25a. On block B, horizontal pull is T cos37° and normal is 100g-T sin37°. At limiting friction: T cos37° = (1/3)[100g-T sin37°]. Using 4/5 and 3/5 gives T=1000/3 N, and then a=g/3.