Question

A person of mass $50kg$ carrying a load of $20kg$ walks up to a staircase. If the width and height of each step are $0.25m$ and $0.2m$ respectively, the work done by the man in walking up $20$ steps is, (\[g = 10m{s^{( - 2)}}\] ).
A. $1400J$
B. $800J$
C. $2000J$
D. $2800J$

Answer 1

Hint:Energy cannot be created or destroyed, but it can be transferred from one form into another. As the man moves, his kinetic energy is transferred into potential energy, so use the formula for potential energy. We only need to find the energy in the man’s initial and final position and not at all the positions.

Complete step by step answer:
Here, let the mass of the person be m1 and the mass of the load be m2. Thus the total mass of the system M will be
\[
M = {m_1} + {m_2} \\
\Rightarrow M = 50 + 20 = 70kg \\
\]
Now, we need to calculate the work done. Here we will use the law of conservation of energy. The law of conservation of energy states that energy cannot be created nor can it be destroyed. It can only be transferred from one form into another. In our case, the kinetic energy of the man is converted into the potential energy of the system. The potential energy of the spring is denoted by U. Here the man does kinetic energy by moving, and it is converted into potential energy by going from one height to another. The potential energy U of a system is given as follows:
\[U = mgh\]
Here, h is the height and g is the acceleration due to gravity.
Here, the man walks up to 20 steps. The height of each step is shown as h and the total height which he walks up is given as H. Thus the total height is given as:
 Thus the work done by the man would be equal to the potential energy of the system which is given as follows:
\[
\Rightarrow U=MgH \\
\Rightarrow U=70\centerdot 10\centerdot 4 \\
\therefore U=2800J \\
\].
Thus the work done is 2800J.Hence, option (D) is correct.

Note: Here, the potential energy of the system only depends upon the height and not the width of the step. So we must ensure that not all the parameters which are given are needed to solve the question. Here, only the initial and final position is enough to find the work, because work done is a state function and not a path function.