Question

a) Define the term 'work'. Write the formula for the work done on a body when a force acts on the body in the direction of its displacement. Give the meaning of each symbol which occurs in the formula.
b) A person of mass 50kg climbs a tower of height 72 meters. Calculate the work done.

Answer 1

Hint : In the field of physics, the term work can be expressed in accordance to force and displacement. It is basically a process of transferring energy to an object by applying a force upon it. We can say work is done only when there is some sort of displacement. Also, there are scalar quantities which have only the magnitude and the vector quantities which have magnitude as well as the direction.

Complete Step By Step Answer:
(a) We can define work as the product of the force acting on the body and the displacement caused by the force. When a force acts on a body, it should necessarily undergo a displacement. Only then we can say that work is being done on the body. Mathematically we can express work as
$W=F\times d$
Where W is the work done on the object. F is the force acting on the object and d is the displacement undergone by the object. SI unit of work is Joule (J).
(b) We are given that the mass of the person is 50Kg and the height of the tower is 72m.
We know that acceleration due to gravity is 9.8m/s.
Hence work done is
W=F\times d \\\ =mgh \\\ =50\times 9.8\times 72=35820J \\\
So, the work done is 35820 J.

Note :
If the force acts at an angle $\theta$ to the displacement, we can calculate the work done using the formula $W=Fd\cos \theta$ . Hence when the angle is given, the students can use this formula as well. Work is a scalar quantity but it does not mean that it cannot be negative. Work can be positive, negative as well as zero. Also, while solving the numerical problems we need to keep in mind that all the quantities must be taken in standard SI units.