Question

A bucket full of water is drawn up by a person. In this case the work done by the gravitational force is:
A. Negative because force and displacement are in opposite directions.
B. Positive because force and displacement are in the same directions.
C. Negative because force and displacement are in the same directions.
D. Positive because force and displacement are in opposite directions.

Answer 1

Work is defined as the energy spent in time t to complete the process. Mechanically it is defined as follows:
$Work = \overrightarrow F .\overrightarrow {ds} = \left| {\overrightarrow F } \right|\left| {\overrightarrow {ds} } \right|\cos \theta \widehat n$.

Complete step by step answer:
In mechanics, we define work in its simplest form. It is the energy spent in time to complete the whole process. Or it can also be defined as the energy transferred from one body to another via application of force (ike in collisions). Mathematically it is defined as the product of force and the displacement of the body.
Work done is defined by $Work = \overrightarrow F .\overrightarrow {ds} = \left| {\overrightarrow F } \right|\left| {\overrightarrow {ds} } \right|\cos \theta \widehat n$
So, now we need to find the direction of the force and the displacement. It will then give the angle between them so that we can calculate cosine of that angle.
The direction of gravitational field is downwards and the direction displacement is upwards therefore, the angle between the displacement and gravitational force is and $\cos {180^ \circ } = - 1$.
The work is negative.
Therefore, the answer is negative because the force and displacement are in opposite directions.

So, the correct answer is “Option A”.

Note:
Let us consider the direction of the gravitational field as positive than the direction of displacement by the person becomes negative. The direction of force applied by the person is upwards along the displacement. Hence the work done by the person is positive because force and displacement are in the same direction.