Question

A cord runs over two pulleys A and B with fixed axles, and carries a movable pulleys ‘c’ if P = 40N, P₁ = 20N, P₂ = 30N and the cord lies in the vertical plane. Determine the acceleration of pulley ‘C. Neglect the friction and weight of the pulley.

Answer 1

a = a₁ + a₂

For pulley A, Apply F = ma

T – 20 = (20/10) a₁ , take g = 10m/sec²

T – 20 = 2a₁ ...(2) 

For pulley C, 40 – 2T = (40/10)a₄₀ – 2T = 4a ...(3) 

For pulley B, T – 30 = (30/10) a₂ T – 30 = 3a₂ ...(4)

From equation (2) and (4)

2a₁ – 3a₂ = 10 ...(5)

Equation (3) can be rewritten as

40 – 2T = 4(a₁ + a₂) ...(6)

Now (6) + 2 (4)

40 – 2T + 2T – 2 X 30 = 4(a₁ + a₂) + 6a₂

–20 = 4a₁ + 10a₂ ...(7)

Solving equation (5) and (7), we get 

a₁ = 5/4 m/sec²

a₂ = -5/2m/sec² 

Acceleration of ‘C’ = a = a₁ + a₂

= 5/4 – 5/2 = –1.25m/sec²