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Standard XII

Physics

Force Couple

In the arrang...

Question

In the arrangement shown in figure above the bodies have masses $m_{0}$ , $m_{1}$ and $m_{2}$ , the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of the body $m_{1}$ . Look into possible cases.

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Solution

Let us write Newton's second law for masses $m_{1}$ and $m_{2}$ and moving pulley in vertical direction along positive x-axis (figure shown below):
$m_{1} g - T = m_{1} w_{1 x}$ (1)
$m_{2} g - T = m_{2} w_{2 x}$ (2)
$T_{1} - 2 T = 0 (a s m = 0)$
or $T_{1} = 2 T$ (3)
Again using Newton's second law in projection form for mass $m_{0}$ along positive $x_{1}$ direction (figure shown below), we get
$T_{1} = m_{0} w_{0}$ (4)
The kinematical relationship between the accelerations of masses gives in terms of projection on the x-axis
w_{1x}+w_{2x}=2w_0 (5)
Simultaneous solution of the obtained five equations yield:
$w_{1} = \frac{[4 m_{1} m_{2} + m_{0} (m_{1} - m_{2})] g}{4 m_{1} m_{2} + m_{0} (m_{1} + m_{2})}$
In vector form
$_{1} = \frac{[4 m_{1} m_{2} + m_{0} (m_{1} - m_{2})] \to g}{4 m_{1} m_{2} + m_{0} (m_{1} + m_{2})}$

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In the arrangement shown in figure above the bodies have masses m0, m1 and m2, the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of the body m1. Look into possible cases.

In the arrangement shown in figure above the bodies have masses $m_{0}$ , $m_{1}$ and $m_{2}$ , the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of the body $m_{1}$ . Look into possible cases.