Question

A pulley-rope-mass arrangement is shown in Fig.6.137. Find the acceleration of block m1​ when the masses are set free to move. Assume that the pulley and the ropes are ideal.



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Answer 1

Answer:

The acceleration of block $\large\rm {m_{1}}$ and pulley 2 will be same in magnitude. Now considering pulley 2 and block 2 and 3.

Change in the length of segment (1)

$\large\rm { ∆1_{1} = (+y_{2}) + (-y_{P2}) = y_{2} - p_{2}}$

change in the length of segment (2),

$\large\rm {∆1_{2} = (+y_{3}) + (-y_{P2}) = y_{3} - p_{2}}$

Total sum of change in the segment length of string should be zero.

$\large\rm { ∆1 = 0 = [y_{2} - y_{P2}] + [y_{2} - y_{P2}] }$

$\large\rm { ⇒ ∆1 = 0 = y_{2} + y_{3} - 2y_{P2}}$

$\large\rm { ⇒ 2a_{1} = a_{3} + a_{2}}$