Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward but is gradually slowing down at a rate of 9 m/s²? _f is the force of the floor on the person and _g is the force of gravity on the person.

Question

Quizplus · Accepted Answer

According to Newton's second law, the net force acting on an object is equal to its mass times its acceleration. In this case, the force of gravity is always acting downwards with a magnitude of mg, while the force of the floor on the person will be less than mg when the elevator is slowing down. This is because the person will be experiencing a pseudo-force (or apparent force) in the opposite direction of the elevator's motion due to their inertia. Therefore, in order for the person to experience a net force of zero (i.e. to not accelerate), the force of the floor on the person must be equal in magnitude and opposite in direction to the sum of the force of gravity and the pseudo-force.

Option A has the correct downward force of gravity, but the upward force of the floor is too high. 
Option B has the correct magnitudes and direction of both forces, which are equal in magnitude and opposite in direction, representing the zero net force on the person. This is the best choice.
Option C has the correct downward force of gravity, but the upward force of the floor is too high.
Option D has the correct downward force of gravity, but the upward force of the floor is too low.
Option E has the correct downward force of gravity, but the upward force of the floor is too low.

Which One of the Following Free-Body Diagrams Best Represents the Free-Body