Question

A person off mass 60kg is inside a lift of mass 940kg and presents the button of the control panel. The lift started moving upward with acceleration 1.0m/s2 . If g=10m/s2, the tension in the supporting cable is?

Answer 1

Hint: We can easily solve this question by applying Newton’s law on moving lift.
Newton’s second law gives us $F = ma$ states that if there is acceleration in the body then we can find force by multiplying mass and acceleration of the system.

Complete step by step answer:
We take man and lift as a system and make a free body diagram and mark all the forces acted on it.
As in the question it is given that the lift is moving in upward direction with acceleration $a$.

Mass of the system =mass of man +mass of lift
Mass of system =1000kg
Force acted on system is
Weight of system (man and lift) in downward direction ${W_{total}} = 1000g = 1000 \times 10 = 10000N$
Tension in supporting wire $T$ in upward direction
Life is moving in upward direction with acceleration $a$ so the net force in upward direction is ${m_{total}} \times a$
$ \Rightarrow 1000 \times a = T - 1000 \times g$
$\because a = 1m/{s^2}$
$ \Rightarrow 1000 = T - 10000$
Solving it value of tension
$T = 1000 + 10000$
$T = 11000N$ In upward direction
So, the tension in the supporting cable is $T = 11000N$ in upward direction.

Note: We use here Newton’s second law it states that if a body moving with acceleration there must be a force in that direction so we use
Net force in upward direction= all force on the system in upward direction –all forces on the system in downward direction.