Question

A 50kg person stands on a 25 kg platform. He pulls on the rope which is attached to the platform via a system of frictionless pulleys as shown in the figure. The platform moves in upward direction at a steady rate if the force with which the person pulls the rope is:

A. 500 N
B. 250 N
C. 25 N
D. None of these

Answer 1

First we will draw a free body diagram and mention in it all the forces acting in the system then we will find the relations between by balancing the forces. The net force on all the components must be zero as there is no acceleration and all the parts are either at rest or moving at a steady rate.

Complete answer:
First, we will draw all the forces acting on all the different bodies (man and the platform) in the system. The man applies a force F on the pulley. As we consider all pulleys and rope to be ideal i.e. massless and frictionless, the rope will also apply a force back on the man which will be of the same magnitude as F, but in the opposite direction This tension will be the same throughout the string. Although, there are forces being applied on the top portion we will ignore them as we will consider that to be a rigid ceiling which provides necessary reaction force and does not move. So, a force diagram would look like this

The forces acting on both the man and the platform in downward direction is their weight. The tension in the string will be acting in the upwards direction on them. For a steady motion, the forces must be balanced. Hence, total upward force must be equal to total downward force.
Total downward force = $mg+Mg=(m+M)g=(25+50)\times 10=750$N.
Total upward force = $3T=3F$
$3F=750\Rightarrow F=250$N.

So, the correct answer is “Option B”.

Note:
Students must note that by using pulleys significantly less force is required to move the heavy man and platform upwards. However, it must be noted that the work done to move them by a specific distance will still be the same, whether we use a pulley or not.