Question

Find the work done by the force when the body moves from \[A\] to \[B\].

Answer 1

Hint: In this question, we must calculate the distance that the body moves. Work done by the force is directly proportional to the force and distance through which the body moves.

Complete step by step answer:
Consider the figure, We are given that the body moves from point \[A\] to point \[B\].
On a body, the work done by a force depends upon the two factors, first is the magnitude of the force and second, it depends on the distance through which the body moves.
Therefore, we can say that work done is directly proportional to product of the force applied on the body and the distance travelled through the body moves. So, the work done is,
\[ \Rightarrow W = F \times s......\left( 1 \right)\]

Where \[W\] represent the work done by the body, \[F\] represent the force applied on the body and \[s\] represent the distance through which the body moves.
Calculate the distance from point \[A\] to point \[P\]
Using Pythagorean Theorem,
\[ \Rightarrow ac = \sqrt {a{b^2} + b{c^2}} \]

Now we substitute the values,
\[ \Rightarrow AP = \sqrt {{{1.2}^2} + {{0.9}^2}} \]

Adding inside the square root,
\[ \Rightarrow AP = \sqrt {1.44 + 0.81} \]

Further solving, we get
\[ \Rightarrow AP = \sqrt {2.25} \]

Simplify the term and we get,
\[ \Rightarrow AP = 1.5\;{\text{m}}\]

Now consider the displacement of point \[P\], when the body moves from point \[A\] to point \[B\],
\[ \Rightarrow 1.5 - 0.9 = 0.6\;{\text{m}}\]

Now we calculate the work done by substituting the value in equation (1),
\[ \Rightarrow W = 300 \times 0.6\]

After simplification, we get
\[\therefore W = 180\;{\text{N}} \cdot {\text{m}}\]

Therefore, the work done by the force when the body moves from point \[A\] to point \[B\] is \[180\;{\text{N}}{\text{.m}}\].

Note: Do not forget to convert all the values into the standard units. Work is said to be done, when the body displaces some distance. The Si unit of work done is \[{\text{N}}{\text{.m}}\] and it is also calculated in \[{\text{Joule}}\].