Question

In the Figure, the blocks A, B and C have masses 3 kg, 4 kg, and 8 kg respectively. The coefficient of sliding friction between any two surfaces is 0.25. A is held at rest by a massless rigid rod fixed to the wall, while B and C are connected by a light flexible cord passing around a fixed frictionless pulley. Find the force F necessary to drag C along the horizontal surface to the left at a constant speed. Assume that the arrangement shown in the Figure. i.e. B on C and A on B, is maintained throughout. (Take g =10ms²)

Answer 1

Maximum friction between A and B = µm_Ag

or f₁ = 0.25(3)(10) = 7.5 N

Maximum friction between B and C = µ(m_A + m_B)g

or f₂ = 0.25 (3 + 4)(10) = 17 5 N

Maximum friction between C and ground

f₃ = µ (m_A + m_B + m_C)g

= 0.25(3 + 4 + 8)(10)

= 37.5 N

Block C and hence block B are moving in opposite directions with constant velocities and block A is at rest. Hence, net force no all three blocks should be zero. Free body diagrams have been shown below (Only horizontal forces are shown)

For equilibrium of B

T = f₁ + f₂ = 25 N

For equilibrium of C

F = T + f₂ + f₃ = 80 N

Answer 2

The necessary force to drag C is 37.5 N.