Fewpal
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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.

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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/sec

Acceleration of ‘C’ = a = a1 + a2

= 5/4 – 5/2 = –1.25m/sec2

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