Understanding the Force Exerted by a Person in a Moving Elevator

Elevators are a ubiquitous part of our daily lives, and students often encounter problems involving forces in a moving elevator. This article explores a specific scenario where a person of mass 50 kg is standing in an elevator moving downward with an acceleration of 3 m/s2. We'll break down the concept of net force, mutual force, and how to calculate the force exerted by the person on the elevator floor.

Concept of Force in a Moving Elevator

When an elevator moves, the person inside experiences forces due to both gravity and the acceleration of the elevator. In this scenario, the person experiences a downward acceleration of 3 m/s2. The key forces involved are the gravitational force acting downward and the normal force exerted by the elevator floor acting upward.

The Role of Gravitational Force

The gravitational force, often labeled as Fg, is the force exerted by the Earth on the person. It is given by the formula:

Fg m times; g

where

m is the mass of the person (50 kg) g is the acceleration due to gravity (10 m/s2)

Calculating the gravitational force:

Fg 50 kg times; 10 m/s2 500 N (downward)

This is the force that would act downward if the elevator were stationary.

Elevator's Downward Acceleration

When the elevator moves downward with an acceleration of 3 m/s2, it imposes an additional force. This net force takes into account both the gravitational force and the acceleration of the elevator.

When the elevator accelerates downward, the person feels a sensation of weightlessness, but the forces acting on them still involve the normal force exerted by the floor and the gravitational force.

Calculating the Normal Force

Let's denote the normal force as Fn. The net force on the person is the difference between the gravitational force and the normal force. The net force can be calculated using Newton's second law of motion:

Fn m(g - a)

where

m is the mass of the person (50 kg) g is the acceleration due to gravity (10 m/s2) a is the acceleration of the elevator (3 m/s2)

Substituting the values:

Fn 50 kg times; (10 m/s2 - 3 m/s2) 50 kg times; 7 m/s2 350 N

The force exerted by the person on the floor of the elevator, or the normal force, is therefore 350 N.

Force Exertion and Mutually Acting Forces

Forces in physics are always mutual. The normal force exerted by the floor on the person acts upward, and the force exerted by the person on the floor acts downward. This concept is a direct application of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

Conclusion

Understanding the forces involved in a moving elevator can help in comprehending complex scenarios in physics. The force exerted by a person on the elevator floor when the elevator is accelerating downward is a critical concept in physics and engineering. By applying these principles, we can solve a wide range of problems involving force calculations and accelerations.

Additional Resources

For further exploration of this topic, consider studying the following resources:

Physics textbooks that cover Newton's laws of motion Online tutorials and simulations demonstrating forces in moving elevators Interactive physics software for hands-on learning