Question

A force is applied upon a body of 40 kg then its velocity increases from 1m/s to 2m/s. Determine work done by the force?

Answer 1

Hint:
In order to solve these types of questions we have to analyse the need of question and apply the correct required formula here we will use work energy conversion theorem i.e., Work done by the force is equal to change in kinetic energy.
                                                             $W = \Delta K.E$

Complete step-by-step solution:
According to question a force is applied on any body of 40 kg due to applied force the velocity of that body increases from 1 m/s to 2 m/s and we have to calculate the work done by the force :
As we know by work energy conservation theorem that work done by any foce to the body is equal to change in kinetic energy of that body i.e, final initial kinetic energy subtracted by final kinetic energy.
By formula-
\[W = K.{E_f} - K.{E_i}\]
$W = \Delta K.E$
$W = \dfrac{{1m({v^2} - {u^2})}}{2}$ ……………….(1).
Here-
W is work done by the force on the body, m is mass of the body, u is initial speed and v is final speed of body.
As in question it is given that m=40kg, u=1m/s and v=2m/s.
Now pitting all these values in (1) we get
$W = \dfrac{{1 \times 40({2^2} - {1^2})}}{2}$
On further solving we will get
W=60$J$
So our answer will be 60$J$.

Note:- While solving these types of problems the first thing which should be kept in mind is that without the knowledge of work energy conversion we can’t solve these types of questions .So we should have the knowledge of work energy theorem. And if the work done is positive then it means work is done on the body, while if the work done is negative then it states that work is done by the body.