The rope in the figure has length t. It is attached at one end to a pin at A and

Question

The rope in the figure has length t. It is attached at one end to a pin at A and at the other to mass m after passing under the free, small pulley at D and over the fixed, small pulley at B. The mass M is suspended from the free pulley. Find the height H for equilibrium of the system.

http://i.imgur.com/4EuUu8k.png

The rope in the figure has length t. It is attached at one end to a pin at A and at the other to mass m after passing under the free, small pulley at D and over the fixed, small pulley at B. The mass M is suspended from the free pulley. Find the height H for equilibrium of the system.

Explanation / Answer

Let tension in the rope be T and the angle the rope makes with A be x

so force equations

2Tcosx = Mg

T = mg

so 2mgcosx = Mg

so cos x = M/2m

cos x = L/AD (AD = length of rope in the part AD)

so AD = L*2m/M = 2Lm/M

similarly BD = AD = 2Lm/M

so lenth H = t - AD - BD = (t - (4Lm/M))

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