Question

A block A whose weight is $200N$ is pulled up a slope of length $5m$ by means of a constant force (=$150N$) as illustrated in the figure. The difference in work done by the force and increase in potential energy of the block is:
(A). $0J$
(B). $150J$
(C). $750J$
(D). $600J$

Answer 1

The block is under the effect of two forces. The constant force moves it up the slope and its weight increases its potential energy. The work done is the product of force and displacement and potential energy is the product of weight and height of the body. Substituting corresponding values, we can calculate both work and potential of the body and then find the difference.
Formulas used:
$W=Fx$
$P=F'h$

Complete answer:

In the given figure, $F$ is the constant force while $F'$ is the weight of the block.
The work done is given by-
$W=Fx$
Here, $W$ is the work done
$F$ is the force acting on the body
$x$ is the displacement travelled by the body
Given, $F=150N$, $x=5m$ substituting given values in the above equation, we get,
$\begin{aligned} & W=150\times 5 \\\ & \Rightarrow W=750J \\\ \end{aligned}$
The work done on the block by the constant force is $750N$.
The potential energy of a body is given by-
$P=F'h$
Here, $P$ is the potential energy of the body
$F'$ is the weight of the body
$h$ is the height
Given, $F'=200N$, $h=3m$ substituting given values in the above equation, we get,
$\begin{aligned} & P=200\times 3 \\\ & \Rightarrow P=600J \\\ \end{aligned}$
The difference between work done and the potential energy of the block is
$\begin{aligned} & W-P=750-600 \\\ & \Rightarrow W-P=150J \\\ \end{aligned}$
Therefore, the difference of work done and potential energy is $150J$.

Hence, the correct option is (B).

Note:
The potential and work done have the same units. The potential of a body due to gravity is always negative. Work done is a scalar quantity. Both forces acting on the body are constant, hence the acceleration of the body will also be constant. Energy is the ability of a body to do work.