Question

A man with a box on his head is climbing up a ladder. The work done by the man on the box is
A. Positive
B. Negative
C. Zero
D. Undefined

Answer 1

In order to answer this question, see whether the man is applying force on the box that is being carried up the ladder. Along with the force applied, if there is a resultant displacement, a work is definitely done. For checking whether the work done is positive or negative, use the expression of work done as the dot product of force and displacement.

Formula Used:
Expression for work done,
$W=F\bullet S$

Complete step-by-step answer :
We are given the case of a man who carries a box on his head while climbing up a ladder and we are asked to find the work done by the man on the box.
Let us recall the definition of work done. A work is said to be done only when there is a displacement caused due to the force exerted.
In the given case, the man is exerting a force against the weight of the body on his head. Since, the body is brought by the man to a higher altitude, there is also a displacement caused due to the force. So, as there is a force as well as displacement, work is definitely done in this case. Now we have to see whether the work done is positive or negative. For that, let us recall that work done is the dot product of force and displacement. That is, we can express work done as,
$W=F\bullet S$ …………….. (1)
Where, W= work done
F= force exerted
S=resultant displacement
Equation (1) simply means that work done can be given by the product of the magnitudes of force and displacement and also the cosine of the angle between them. That is,
$W=\left| F \right|\left| S \right|\cos \theta$ ……………….. (2)
In the given case, we see that the force exerted is against gravity (weight of the body) which is directed upward, and the resultant displacement of the body is to a higher altitude, which is again directed upward. That is, both F and S are directed in the same direction and hence the angle between them is zero. So,
$\theta =0$
Equation (2) now becomes,
$W=\left| F \right|\left| S \right|\cos (0)$
But, $\cos (0)=1$
$W=\left| F \right|\left| S \right|\ge 0$
Since, neither F nor S is zero here, the work done by the man carrying a box on his head up the ladder is positive. Also, note that this work is stored as the potential energy of the box.
Hence, the answer to this question is option A.

Note : While dealing with problems like this it is better that you draw a free body diagram representing all the forces acting on the body. Doing so, you could easily understand what exactly happens for the body under consideration. In the given case, we know that there is a change in potential energy of the box since it is carried to greater height, and this energy is provided by the man who is carrying the box.