. Block 1 has a mass of 8 kg and block 2 has a mass of 12 kg. The coefficient of static friction between block 1 and block 2 is μs=0.4. The coefficient of kinet

Question

Block 1 has a mass of 8 kg and block 2 has a mass of 12 kg. The coefficient of static friction between block 1 and block 2 is μs=0.4. The coefficient of kinetic friction between block 2 and the ground is μk=0.2. A person pulls horizontally on block 2 with a rope as shown in the figure. What is the maximum possible acceleration of the system and the maximum force that the person can exert on block 2 so that block 1 does not slip off block 2? Discuss whether your results are reasonable or not.

Answer 1

Block 1 will not slip as long as the horizontal net force on M₁ is less than the static friction force between M₁ and M₂.

M₁a ≤ µ_sM₁g ⇒ a ≤ µ_sg

 

So the maximum acceleration of the system so that block 1 does not slip off block 2 is

a = µ_sg

   = (0.4)(9.8)

   = 3.9 m/s²

 

The maximum force that the person can exert on block 2 so that block 1 does not slip off block 2 is given by

F - µ_k(M₁ + M₂)g = (M₁ + M₂)a

 

F = (M₁ + M₂)(a + µ_kg)

  = (8 + 12) (3.9 + 1.96)

  = 117.2 N