Question

A man is standing on a weighing machine placed in a lift, when stationary, his weight is recorded as 40 kg. If the lift is accelerated upwards with an acceleration of $2\,m/{s^2}$ , then the weight recorded in the machine will be
A) 48 kg
B) 32 kg
C) 64 kg
D) 80 kg

Answer 1

The weight of a person will be the product of mass and the acceleration of the object. We will first find the mass of the person and then calculate his weight when the lift is accelerated upwards.

Formula used: In this solution, we will use the following formula:
Weight of the person: $W = mg$ where $m$ is the mass and $g$ is the gravitational acceleration.

Complete step by step answer
We’ve been given that a man is standing on a weighing machine placed in a lift, when stationary, has a weight of 40 kg. Now since the weight of a person is calculated as
$40 = mg$ .
As the value of $g = 9.8\,m/{s^2}$ , we can write
$40 = m \times 9.8$
Which gives us
$m = 4.08\,kg$
When the lift is moving upwards, it will experience a net acceleration due to gravity as well as the acceleration of the lift upwards. Hence the net acceleration of the person will be a sum of the gravitational acceleration and the acceleration of the elevator:
$W = m(g + a)$
So, it will be equal to
$W = 4.08\left( {9.8 + 2} \right)$
$\Rightarrow W = 48.14\,kg \approx 48\,kg$
Hence the weight of the man will be 48 kg which corresponds to option (A).

Note
We must be careful to not get confused between the mass and weight of the person. While weight is often expressed in terms of kilograms, what we are actually measuring is the weight of the person which is a product of the person’s mass and gravitational acceleration. Since the lift is accelerating upwards, the pseudo force that we will experience will be downwards direction. This is why the weight of the person will increase when measured by the weighing scale.