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 \[2\,{\text{m/}}{{\text{s}}^2}\], then the weight recorded in the machine will be
A. 48 kg
B. 32 kg
C. 64 kg
D. 80 kg

Answer 1

Hint:The weight of the person is determined by the normal force provided by the ground. Draw the free body diagram of the accelerated frame of lift and using Newton’s second law, express the net force on the person. Calculate the normal force which is the weight of the person. The weight of the person recorded by the weighing machine is the mass.

Formula used:
Newton’s second law, \[{F_{net}} = ma\]
where, m is the mass and a is the acceleration.

Complete step by step answer:
We have given that the man is standing on the weighing machine placed in the lift which is accelerated upwards with acceleration \[a = 2\,{\text{m/}}{{\text{s}}^2}\]. We know that the weight of the person is determined by the normal force provided by the ground. Let us draw the free body diagram of the accelerated frame of lift as follows,

From the above free body diagram, we can write,
\[N - mg = ma\]
\[ \Rightarrow N = m\left( {a + g} \right)\]
Here, m is the mass of the person, a is the acceleration of the lift and g is the acceleration due to gravity.
Substituting \[m = 40\,{\text{kg}}\], \[a = 2\,{\text{m/}}{{\text{s}}^2}\] and \[g = 10\,{\text{m/}}{{\text{s}}^2}\] in the above equation, we get,
\[N = \left( {40} \right)\left( {2 + 10} \right)\]
\[ \Rightarrow N = 480\,{\text{N}}\]
Thus, the weight of the person is 480 N. But the weight recorded in the machine will be,
\[m = \dfrac{N}{g} = \dfrac{{480}}{{10}}\]
\[ \therefore m = 48\,{\text{kg}}\]

Thus, the weight recorded in the weighing machine will be 48 kg.

Note: The weight we call it that is recorded by the weighing machine is actually the mass of the person. The weight is the normal force provided by the ground on the body in the upward direction. The normal force depends on the value of acceleration due to gravity and therefore, the weight of the person on another planet is different.