How Do You Calculate the Normal Force on a Person in an Accelerating Elevator?

In summary, a person of mass m standing in an elevator of mass M experiences a resultant upwards force due to the reaction at the floor and gravity. This force can be expressed as m(g+a) and is equal to m times the acceleration of the elevator.
  • #1
jg727
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Homework Statement


A person of mass m is standing in an elevator of mass M. The elevator is moving downward, but has an upward acceleration of a. To an observer fixed on the Earth, the force exerted on the person by the floor of the elevator is

a. (m+M)g b. m(g+a) c. m(g-a) d. M(a-g) e. M(a+g)

Homework Equations


I think I have the Free Body Diagrams correct, but I am confused by finding the normal force on the person by the floor of the elevator.

Any help would be great. Thank you.
 
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  • #2
There are only 2 forces acting on the person of mass m.
1)The downwards force of gravity (the weight of the person)
2) The upwards force due to the reaction at the floor.
If the person is accelerating upwards there must be a resultant force upwards.
Can you use 1) and 2) to write down an expression for the resultant upwards force.
Then resultant force = m x acceleration
 

FAQ: How Do You Calculate the Normal Force on a Person in an Accelerating Elevator?

What is the force involved in operating an elevator?

The main force involved in operating an elevator is the force of gravity, which pulls the elevator downward. However, there are also other forces at play, such as the force of the elevator's motor and the force of the cables that support the elevator car.

How does an elevator's weight affect its movement?

An elevator's weight has a direct impact on its movement. The heavier the elevator, the more force is needed to move it. This means that a heavier elevator will require a more powerful motor and stronger cables to support its weight.

What role do pulleys play in elevator mechanics?

Pulleys are an essential part of an elevator's mechanics. They are used to redirect the force from the elevator motor to the cables that lift and lower the elevator car. Without pulleys, it would be much more difficult to operate an elevator.

How is the force of an elevator's motor calculated?

The force of an elevator's motor can be calculated using the formula F=ma, where F is the force, m is the mass of the elevator, and a is the acceleration. The acceleration of the elevator can be determined by dividing the distance it travels by the time it takes to travel that distance.

What are some safety measures in place to prevent elevator accidents?

There are several safety measures in place to prevent elevator accidents, such as emergency brakes, limit switches that stop the elevator at specific floors, and sensors that detect any obstructions in the elevator shaft. Regular maintenance and inspections are also crucial in ensuring the safety of elevator passengers.

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