Two people, each of 70 kg mass, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the force $\overrightarrow{\mathbf{F}}_{{F}}$ the floor exerts on the first person to the force $\overrightarrow{\mathbf{F}}_{{R}}$ the rope exerts on the second person. Which statement is correct?
A)They are equal and opposite in direction.
B)They are equal and have the same direction.
C) $\overrightarrow{\mathbf{F}}_{{R}}$ is greater than $\overrightarrow{\mathbf{F}}_{{F}}$ , but they have the same direction.
D) $\overrightarrow{\mathrm{F}}_{R}$ is greater than $\overrightarrow{\mathbf{F}}_{{F}}$ , but they have opposite directions.
E) $\overrightarrow{\mathrm{F}}_{R}$ is less than $\overrightarrow{\mathbf{F}}_{{F}}$ , but they have the same direction.

Question

Quizplus · Accepted Answer

Both people are in the same elevator and therefore experience the same acceleration. Since they have the same mass, the force exerted on them by the elevator will be the same. Therefore, the force the floor exerts on the first person and the force the rope exerts on the second person will be equal in magnitude and direction. So, option B is correct.

Two People, Each of 70 Kg Mass, Are Riding in an Elevator