Question

Two bodies of weight 10N and 1.5N are connected to the two ends of a light inextensible String, passing over a smooth pulley. The weight 10N is placed on a rough horizontal surface while the weight of 1.5N is hanging vertically in air. Initially the friction between the weight 10N and the table is just sufficient to prevent motion. If an additional weight of 0.5N is added to the weight 1.5N, determine 

(i) The acceleration of the two weight. 

(ii) Tension in the string after adding additional weight of 0.5N to the weight 1.5N

Answer 1

Initially when W₁ = 1.5N, then the body is in equilibrium. i.e. both in rest or a = 0,

Then consider block W₁

R_V = 0; T = W₁ = 1.5N ...(1)

Consider block W₂

R_V = 0; R = W₂ = ...(2)

F_r – T = 0; F_r = T = 1.5N ...(3)

But, F_r = µR = µW_2; µW₂ = 1.5; µ X 10 = 1.5, µ = 0.15 ...(4)

Now when Weight W₁ = 2.0N, body moves down Now the tension on both side be T₁

Consider block W₁W₁ – T₁ = ma₂ – T₁ = (2/g)a ...(5)

Consider block W₂

T₁ – F_r = ma

T₁ – µW₂ = (10/g)a 

T₁ – 1.5 = (10/g)a

Solve the equation (5) and (6) for T₁ and a, we get

T₁ = 1.916N, a = 0.408m/sec²