Question: A 45N girl sits on an 8N bench. How much work is done on the bench?...

Question

A 45N girl sits on an 8N bench. How much work is done on the bench?

Answer 1

Solution

A system of girl and bench is given in which both are at rest, gravitational forces are the external forces acting on them but since forces of gravity do zero work, the energy of the system is conserved. Using Newton’s second law, we can make FBD diagrams and calculate forces from the equation. We can calculate work by substituting the corresponding values in its formula.
Formulas used:
$W=Fx$

Complete step-by-step solution:
According to Newton’s second law of motion, force is required to change the state of rest or motion of a body. Using Newton’s second law, we can draw FBD diagrams for objects of a system.
A system of girls and bench is given in which their weights are $45N$ and $8N$ respectively. There FBD diagrams will be as shown-

The forces acting on the girl are-
$\begin{aligned} & mg-N=0 \\\ & \Rightarrow 45-N=0 \\\ & \therefore N=45N \\\ \end{aligned}$
The normal reaction acting between the girl and bench is $45N$ . Therefore, the force acting on the bench due to the girl is $45N$ .
Work done is the product of force and displacement. Its SI unit is joules ( $J$ ). It is given by-
$W=Fx$
Here, $W$ is the work done
$F$ is the force applied
$x$ is the displacement of the object on which force is being applied.
As the bench is at rest, its displacement is 0. From the above equation, work done by the girl on the bench is-
$\begin{aligned} & W=45\times 0 \\\ & \therefore W=0 \\\ \end{aligned}$
Therefore, no work is done on the bench by the girl.

Note: FBD diagrams are free body diagrams of objects of a system. The normal reaction is the force applied by two surfaces on each other to prevent them from passing through each other. By Newton’s third law, the normal reaction is equal in magnitude and opposite in direction. We can also calculate the work done on the bench by the work-energy theorem which states that work done is equal to a change in kinetic energy of a body. Since kinetic energy and change in kinetic energy is zero, work done is also zero.