Question

Block 𝐴 has a weight 𝑤𝐴 and block 𝐵 has a weight 𝑤𝐵. Once block 𝐵 is set into downward motion, it descends at a constant speed. a) Calculate the coefficient of kinetic friction between block 𝐴 and the tabletop. b) A cat, also of weight 𝑤𝐴, falls asleep on top of block 𝐴. If block 𝐵 is now set into downward motion, what is its acceleration (magnitude and direction)? 

Answer 1

(a) If the blocks move at constant speed, the net force is zero, and forces acting on Block B are

$$0=W_B-T=0.$$

Forces on block A are:

$$T-\mu W_A=0,\\\space\\ \mu=\frac{T}{W_A}=\frac{W_B}{W_A}.$$

(b) When there is a cat on top of block A, the force of friction increases (because the normal force increases proportionally to the combined weight of block A and weight of the cat), while the weight of block B (and, thus, the tension in the cord) remains constant, thus, the acceleration is zero.