Question

A man of mass $50kg$ carries a bag of weight $40N$ on his shoulder. The force with which the floor pushes up his feet will be:
     $A)\text{ }882N$
     $B)\text{ 530}N$
     $C)\text{ 90}N$
     $D)\text{ 600}N$

Answer 1

Hint: This problem can be solved by considering the man and the bag to be a single system and finding out their total weight. This total weight has to be balanced by the normal force from the floor and will be the magnitude of the force with which the floor pushes up his feet.
Formula used:
$W=Mg$
$\sum{\overrightarrow{F}}=0$

Complete step by step solution:
We will consider the man and the bag to be a single system.
Let the weight of the system be ${{W}_{s}}$.
Let the weight of the man be ${{W}_{m}}$.
The mass of the man is ${{M}_{m}}=50kg$.
The weight of the bag is given to be ${{W}_{b}}=40N$.
Now, the weight $W$ of an object of mass $M$ is given by
$W=Mg$ --(1)
where $g=9.8m/{{s}^{2}}$ is the acceleration due to gravity.
Using (1), we get the weight of the man as
${{W}_{m}}={{M}_{m}}g=50\times 9.8=490N$ --(2)
Now, since the system consists of the man and the bag, the weight of the system will be the sum of the weight of the bag and the man.
$\therefore {{W}_{s}}={{W}_{m}}+{{W}_{b}}$
Using (2) in the above equation, we get
${{W}_{s}}=490+40=530N$ --(3)
Now, let the normal force from the floor on the man’s feet be $N$.
When a body is at equilibrium, the sum of the forces $\overrightarrow{F}$ on it are zero.
$\therefore \sum{\overrightarrow{F}}=0$ --(4)
Now, since, the system is in equilibrium in the vertical axis, we can say that the downward weight of the system is balanced by the normal force upwards from the floor to the feet of the man.
Therefore using (4) and considering downward forces to be negative, we get
$N-{{W}_{s}}=0$
$\therefore N={{W}_{s}}$
Using (3) in the above equation, we get
$N=530N$
Hence, the magnitude of the force from the floor upon the feet of the man is $530N$.
Therefore, the correct option is $B)\text{ 530}N$.

Note: Students must pay attention to the question that the weight of the bag is given whereas the mass of the man is given. Since the magnitudes of the values are close, often students do not read the question properly and proceed by thinking that the masses of the bag and the man are given. This will lead to a completely wrong answer and wastage of time and effort on the part of the student.