Question

The force exerted by the floor of an elevator on the foot of a person is ______ the weight of the person if the elevator is going up and speeding up.

Answer 1

Force: Force is an external agent that can change the condition of rest or motion of a specific body.

Explanation:

1. Positive acceleration is defined as an increase in velocity over time.
2. When the elevator is speeding up, the force exerted is greater than the weight of the individual, causing the acceleration to be positive and in the upward direction.
3. The normal force at the point of contact between foot and elevator is acting upward and the weight of the man is acting downward such that $\mathrm{N}>\mathrm{mg}$ because the elevator is moving up.
4. If we write the equation of net force:

$$\begin{gathered} {\mathrm{F}}_{\mathrm{net}}=\mathrm{ma} \\ \Rightarrow \mathrm{N}-\mathrm{mg}=\mathrm{ma} \\ \Rightarrow \mathrm{N}=\mathrm{mg}+\mathrm{ma} \\ \Rightarrow \mathrm{N}=\mathrm{m}(\mathrm{g}+\mathrm{a}) \end{gathered}$$

So we can infer that the force exerted by the floor is greater.

Thus, if the elevator is speeding up, the force exerted by the floor on a person's foot is more than the person's weight.