Question

A block of mass 25kg is raised by a 50kg man in two different ways as shown in the figure. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700N, which mode should the man adopt to lift the block without the floor yielding?

Answer 1

Pulley distributes the net force on two arms equally due to tension gets half on two sides. Therefore, apparent weight in both cases will be different. Apparent weight is the net force on the ground.

Formula used:
Weight $W = mg$ ……(1)
where,
$m$ is the mass of the object
$g$ is the acceleration due to gravity (10$m/{s^2}$)

Complete step by step answer:
Given:
1. Mass of block ${M_{block}} = 25kg$
2. Mass of man ${M_{man}} = 50kg$
3. Yielding limit of floor ${F_{\max }} = 700N$
To find: Which mode (a) or (b) should be adopted by the man.
Figure1 describe the forces acting through free body diagram (FBD) on bodies:
Step 1 of 2:
Find the Force exerted by the man in a vertically downward direction using eq (1):
$\Rightarrow W = 50 \times 10 \\\ \Rightarrow W = 500N \\\$
Find the force exerted by the block on the rope in the vertical direction using eq (1):
$\Rightarrow F = 25 \times 10 \\\ \Rightarrow F = 250N \\\$
Step 2 of 2:
Case (a):
The force applied by the man is in a vertically upward direction. That means the force exerted by the block on the rope will get added to the weight of the man.

$${W_{apparent}} = W + F \\\ \Rightarrow {W_{apparent}} = 500 + 250 \\\ \Rightarrow {W_{apparent}} = 750N \\\$$

Case (b):
The force applied by the man is in a vertically downward direction. That means the force exerted by the block on the rope will get subtracted from the weight of the man.

$$\Rightarrow {W_{apparent}} = W - F \\\ \Rightarrow {W_{apparent}} = 500 - 250 \\\ \Rightarrow {W_{apparent}} = 250N \\\$$

As the apparent weight of the man is greater than the yielding force of the floor. This method should not be used by the man.

The man should use method (b) to lift the block as the force applied on the floor, in this case, is lesser.

Note:
In questions like these, carefully apply the concept of apparent weight. Always remember that the apparent weight of an object means how heavy an object is. Here, we compared the 2 cases to find which one is less.