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 floor yielding.

Answer 1

Hint: Given that the man is lifting the box in two cases, then he has to do some work in order to lift the box upwards. Work is said to be done when energy is required to move an object by applying some external force. Energy is transferred from one form to another when work is done.

Complete step by step solution:
Given:
Mass of the block is, m = $25kg$
Mass of man, M = $50kg$
Since the box is lifted upwards, acceleration due to gravity is g = $10m/s$
Step II:
Weight is defined as the force applied by gravity to pull the object in a downward direction. Therefore,
Weight of the man, W = Mass × Acceleration due to gravity
W = $50 \times 10$
W= $500N$
Step III:
Force applied on the block is given by
F = mass of block × acceleration due to gravity
F = $25 \times 10$
F = $250N$
Step IV:
Given there are two cases. In the first case when the man is trying to lift the box directly, then the work will be done by him in an upward direction. This is because he has to apply the force in an upward direction. Also, he has to bear the force applied by his arms. As a result, the weight that is to be lifted by him will increase. Also, it is given that the floor yields a normal force of $700N$.
Force applied by the floor on the man is given by
${(F)_{floor}} = $ Weight of the man + Force applied on the block
${(F)_{floor}} = 250 + 500$
${(F)_{floor}} = 750N$
Step V:
Another case is when the man is trying to lift up the box by using a pulley. A pulley is a wheel attached to a long rope. If the man wants to lift up the box, then he has to pull down the rope. As a result, the weight of the man is balanced by the weight of the box just like a see-saw. This will help in lifting the box up and the weight that he has to lift will be reduced.
${(F)_{floor}} = $ Weight of the man - Force applied on the block
${(F)_{floor}} = 500 - 250$
${(F)_{floor}} = 250N$

Therefore, the force applied in the second case is less. The man should use the pulley to lift the box up.

Note:
It is to be noted that in order to lift very heavy weight objects, more wheels can be added to the pulley. That is in place of one wheel, two wheels can be used. With a two-wheel pulley, the amount of weight can be lifted with much less effort. The more the number of wheels in the rope, the more weight can be lifted.