Quiz 4

Question 3 There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest? The maximum force of friction: FFrict = μs FN The surface between B and A: FN = mB g

Static Friction There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. The maximum force of friction: FFrict = μs FN The surface between B and A: FN = mB g = 50 N FFrict = μs FN = .75 ∙ 50 N = 37.5 N What forces act on B ?

Forces on B Gravity - mg down Box A - mg up Friction - Box A pulls Box B to right: 37.5 N Fnet = 37.5 N Fnet = ma = 37.5 N a = 37.5 N / m = 37.5/5 = 7.5 m/s2 Everything accelerates at 7.5 m/s2

Forces on A Gravity = mg = 8 ∙10 = 80N Box B pushes down = 50 N Friction from B = 37.5 N to left Table pushes up = String = T to right Fnet = T − 37.5 Fnet = ma = T − 37.5 = 8 kg ∙ 7.5 m/s2 = 60 N = T − 37.5 N T = 60 + 37.5 = 97.5 N 130 N Up

Forces on C Gravity = mC g = String = T = 97.5 Net Force = mC g − T mC a = mC g − 97.5 mC a − mC g = − 97.5 mC (a − g) = − 97.5 mC (7.5 − 10) = − 97.5 mC = − 97.5/(7.5 − 10) = 39 kg 130 N Up