Question

If the work done by a body on the application of a constant force is directly proportional to the distance traveled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as $5$ units. Also read from the graph the work done when the distance traveled by the body is $2$ units

Answer 1

Step 1: Given Data

Given, constant force $F=5$ units

Displacement $S=x=2$ units

Step 2: Formula Used

As per the given condition, if $W$ is the work done, $F$ is the force applied, and $S$ is the displacement,

$W=F.S=FS\cos \theta$

Since the force will be in the same direction as the displacement, the angle between them will be zero, $\theta =0\Rightarrow \cos \theta =0$. Hence, the above equation can be written as

$W=FS\dots \left(1\right)$

Given, constant force $F=5$ units

Let the work done be $y$ units and the distance traveled by the body be $x$ units

Upon substituting these values in equation $\left(1\right)$ we get

$y=5x$

Step 3: Plot the Graph

Let us make a table for different points of the graph

$x$	$y$
$0$	$0$
$1$	$5$

Hence, these points can be plotted as

Step 4: Calculate Work Done

Let us extend the graph to $S=x=2$ units.

Hence, the work done when the distance traveled by the body is $2$ units is $10$ units.