Question

A man of mass $75kg$ stands in a lift. What force does the floor exerts on him when the lift moving upwards with the acceleration of $2m{s^{ - 2}}$? $\left( {g = 10m{s^{ - 2}}} \right)$.

Answer 1

Hint:In this question, we had to find the upward force acting on the man who is moving in the lift. The man is experiencing the forces which are normal, acceleration due to gravity and the upward acceleration. Now solving the force equation, we can get our answer.

Complete Step by Step Answer:
Let us consider a man of mass \[75kg\]in a lift. Then the forces being acting on him be:
Normal force $\left( N \right)$ : let the normal force acting upward on man be N. Acceleration due to gravity(mg): this force is acting downward.And the acceleration of the lift(a): this force is given in the question to be upward.When the lift is moving upward the net force will be upward.Now, from the diagram drawn writing the equation of force on the man:

Downward force must be equal to the upward force. Hence forming the equation.
$N - mg = ma$
Substituting the given values:
$m = 75kg$ $g = 10m{s^{ - 2}}$ $a = 2m{s^{ - 2}}$
$
N = m\left( {g + a} \right) \\
\Rightarrow N = 75\left( {10 + 2} \right) \\
\Rightarrow N = 75\left( {12} \right) \\
\therefore N = 900N \\
$
Hence, the lift will apply an upward force of $900Newtons$.

Note:Normal force is the force that any surface exerts on an object. If that object is at rest then the net force acting on the object is zero. The fact is downward force i.e., weight of the object is equal to the upward force i.e., the normal force.