MyQuestionIcon

8

You visited us 8 times! Enjoying our articles? Unlock Full Access!

Intro to Torque

In the arrang...

Question

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.

Open in App

Solution

Let us write the fundamental equation of dynamics for all the three blocks in terms of projections, having taken the positive direction of x and y axes as shown in fiigure below and using the fact that kinematical relation between the accelerations is such that the blocks move with same value of acceleration (say $w$ )
$m_{0} g - T_{1} = m_{0} w$ ......(1)
$T_{1} - T_{2} - k m_{1} g = m_{1} w$ ......(2)
and $T_{2} - k m_{2} g = m_{2} w$ ......(3)
The simultaneous solution of equations (1), (2) and (3) yields:
$w = g \frac{[m_{0} - k (m_{1} + m_{2})]}{m_{0} + m_{1} + m_{2}}$
$T_{2} = \frac{(1 + k) m_{0}}{m_{0} + m_{1} + m_{2}} m_{2} g$
As the block $m_{0}$ moves down with acceleration $w$ , so in vector form:
$\to w = \frac{[m_{0} - k (m_{1} + m_{2})] \to g}{m_{0} + m_{1} + m_{2}}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. In the arrangement shown in figure above 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 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. What is the minimum acceleration with which bar

A

(shown in figure above) should be shifted horizontally to keep bodies 1 and 2 stationary relative to the bar? The masses of the bodies are equal and the coefficient of friction between the bar and the bodies is equal to

k

. The masses of the pulley and the threads are negligible, the friction in the pulley is absent.

Q. In the system shown in figure above, the masses of the bodies are known to be

m_{1}

m_{2}

, the coefficient of friction between the body

m_{1}

and the horizontal plane is equal to

k

, and a pulley of mass

m

is assumed to be a uniform disc. The thread does not slip over the pulley. At the moment

t = 0

m_{2}

starts descending. Assuming the mass of the thread and the friction in the axle of the pulley to be negligible, find the work performed by the friction forces acting on the body

m_{1}

t

seconds after the beginning of motion.

Q. In the arrangement shown in the figure above the masses of the wedge

M

m

are known. The appreciable friction exists only between the wedge and the body m, the friction coefficient being equal to

k

. The masses of the pulley and the thread are negligible. Find the acceleration of the body m relative to the horizontal surface on which the wedge slides. (

F r i c t i o n = k \times N o r m a l R e a c t i o n

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Torque: How Much Does a Force Turn?

PHYSICS

Watch in App

explore_more_icon

Explore more

Intro to Torque

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon