You visited us 7 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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.

Open in App

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
$_{1} = \frac{[4 m_{1} m_{2} + m_{0} (m_{1} - m_{2})] \to g}{4 m_{1} m_{2} + m_{0} (m_{1} + m_{2})}$

Suggest Corrections

Similar questions

Q. In the arrangement shown in Fig. 1.16 the bodies have masses

m_{0}, m_{1}, 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.

Q. In the arrangement of figure shown above, the masses

m_{0}

m_{1}

and

m_{2}

of bodies are equal, the masses of the pulley and the threads are negligible, and there is no friction in the pulley. Find the acceleration

\to w

with which the body

m_{0}

comes down, and the tension of the thread binding together the bodies

m_{1}

and

m_{2}

, if the coefficient of friction between these bodies and the horizontal surface is equal to

k

. Consider possible cases.

A pulley fixed to the ceiling carried a thread with bodies of masses $m_{1}$ and $m_{2}$ attached to its ends. The masses of the pulley and the thread are negligible and friction is absent. Find the acceleration of the center of mass of this system.

Q. Find the acceleration

w

of body

2

in the arrangement shown in figure above, if its mass is

η

times as great as the mass of bar

1

and the angle that the inclined plane forms with the horizontal is equal to

α

. The masses of the pulleys and the threads, as well as the friction, are assumed to be negligible. Look into possible cases.

Join BYJU'S Learning Program

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.