Question

A porter lifts a luggage of 15 kg from the ground and puts it on her head 2 m above the ground. Calculate the work done by her on the luggage? Take g = 10 $ms^{-2}$

Answer 1

Work done on an object to displace it by height h is the product of force and displacement. The work done in lifting the luggage from the ground to a height h will be stored in the form of potential energy.

Formula used:
The potential energy for a body at a height h is:
P.E. = mgh ;
where g is the acceleration due to gravity.

Complete answer:
Energy of a body is its capacity to do work. The luggage was lifted by application of a certain amount of force and was placed at a height of 2 m from the ground. This will be stored in the form of potential energy which is given as:
P.E. = mgh.
We are given g =10m$s^{-2}$, mass m = 15 kg and h = 2 m. Therefore,
$P.E. = 15 \times 10 \times 2$ J
P.E = 300 J.
This stored potential energy at the height of 2 meters is the amount of work that was done in lifting the luggage.

Additional information:
Another example of potential energy is the potential energy of a spring. A spring when compressed creates a restoring force within it, which is proportional to the displacement (compression). Like the case of gravitational potential energy, when we just let go of our luggage or the spring, it makes an attempt to come back to its mean position, a position where the potential energy is zero like on ground in case of gravitational potential energy.

Note:
In our case, the opposing force was due to gravity, so in order to lift the luggage, work hard to be done against gravity. The force of gravity appears as the weight mg of the body. Therefore the work done against gravity is mgh. Work done is a scalar quantity.