Problem 14: Two blocks sliding
Two blocks are arranged one on top of each other on a table, as shown in Fig: 2.33. The coefficient of kinetic friction between the blocks is μk. Provided the two blocks are in relative motion, the magnitude of the frictional force that each block exerts on the other is μkN, where N is the normal force that each block exerts on the other. There is no friction between the lower block (mass m2) and the table. A known force is applied to the upper block (mass m) which causes both blocks to accelerate. The goal of this problem is to find the blocks' acceleration, namely a1 for the upper block and a2 (a2 < a1) for the lower block, as shown in the figure, in terms of known quantities: F, m1, m2, g, and μk.
Sketch force diagrams, one for each block, indicating all relevant forces. Write down Newton's second law for each mass.
What are the blocks' accelerations in the vertical direction? Give both vertical accelerations. Using your answers to (b) and (c), determine a1 and a2?