A classical mechanics problem by Pankaj Joshi

Classical Mechanics Level 4

The arrangement shown in figure has $2$ masses $M = 4\,\text{kg}$ and $m= 1\,\text{kg}$ . The magnitude of acceleration of mass $M$ and $m$ is $p$ and $q$ respectively. The value of $p+q$ is $(g=10 \text{m/s}^2)$ :

The answer is 20.

2 solutions

R.L. Bhat
Jul 6, 2014

Let T1 be the tension in the string attached to M an T2 be the tension in the string attached to m. Now apply Newton's law to the system. Mg - T1 = Mp. T2 - mg = mq. Since the pulleys are mass less,
2T1 - T2 = 0 So T1 = T2 = 0 and p = q = g.

T1=T2.. Why sir?

Kïñshük Sïñgh - 6 years, 11 months ago

Note that the string passing over A has tension T on both sides of A. So the string connected to A(to A's center) will have tension 2T as A is being pulled from both sides. Now note that it is the same string, so tension should be same. 2T=T which can be possible only when T=0, this results in blocks' free fall.

Pankaj Joshi - 6 years, 11 months ago

Why should tension be the same,why is the pulley necessarily in equilibrium?

Lawrence Mayne - 5 years, 4 months ago

@Lawrence Mayne – When mass of the pulleys is not mentioned, we take them to be massless by convention. Massless bodies have no net external force .So tension should be same.

Pankaj Joshi - 5 years, 4 months ago

As mentioned above by me, only one tension T1 is relevant. If T2 is the tension on string connecting m to the pulley, we are not interested in it. As Pankaj Joshi has proved, T1 = 0.

Niranjan Khanderia - 6 years, 6 months ago

Yudha Prasetyatama
Aug 22, 2017

Observe that the string that connects those pulleys are the same string. Since the string is massless then it must have the same tension. We see that on the point A, the equation for the pulleys is $T-2T=0$ then we have $T=0$ Since the tension of the string is zero then we have the acceleration of those mass are equal to $g$ , that is $10m/s^2$ . Then the sum of those accelerations are $p+q=10m/s^2+10m/s^2$ $=20m/s^2$

A classical mechanics problem by Pankaj Joshi

The answer is 20.

2 solutions

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