# Elevator Problem: What is the Normal Force Acting on a Person?

• TheFlemster
In summary, a 74.0 kg person is inside an elevator that is moving from the 3rd floor to the 21st floor. As the elevator passes the 4th floor, it is moving at 2.30 m/s and is increasing speed at a rate of 1.43 m/s2. At this moment, the normal force acting on the person is 831.02 N.
TheFlemster

## Homework Statement

A 74.0 kg person is standing inside an elevator. The elevator is moving from the 3rd floor to the 21st floor. As the elevator passes the 4th floor it is moving at 2.30 m/s and is increasing speed at a rate of 1.43 m/s2 . At this moment, what is the normal force that acts on the person?

## Homework Equations

normal Force, N = m(a+g)
F = ma

## The Attempt at a Solution

The attempt at solution is on the attached image. Am I working it correct or should I have used F=ma?

#### Attachments

• physics participation ws #3.png
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Remember that the F in F=ma denotes the vector sum of all external forces. There are two external forces on the person.

I believe your answer is correct. The formula N = m(a+g) looks like something pulled out of thin air. If you want to show that you understand the physics, start with Fnet = ma.

So then I ignore the acceleration of 1.43 m/s^2? I am still confused as to which way I am supposed to work it

TheFlemster said:
So then I ignore the acceleration of 1.43 m/s^2? I am still confused as to which way I am supposed to work it
No, don't ignore it. The acceleration of 1.43 m/s2 is the "a" in F = ma. Start with F = ma and fill in the left-hand side as suggested by @jbriggs444.

F=mg + ma
F=(74)(9.8) + (74)(1.43)
F=831.02 N
Wouldn't this be the total force acting on the person?

No, ma does not represent a force acting on the person. mg + ma does not represent the total force acting on the person.

What are the two actual forces acting on the person?

The normal force and the force due to gravity?

TheFlemster said:
The normal force and the force due to gravity?
Yes, good. So, how would you combine these two forces to represent (symbolically) the net force acting on the person?

Your answer can then be used for the left side of Fnet = ma.

N=mg

#### Attachments

• IMG_3426.JPG
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Your diagram of the forces looks good. But there is no reason why the two forces should equal one another. The net force is the combination of the two forces. How would you combine the normal force N (which is upward) with the gravitational force mg (which is downward) to get an expression for the total force Fnet?

Fnet=N-mg
Fnet=ma
combining the two, ma=N-mg
then, N=ma + mg
N=(74)(1.43) + (74)(9.8)
N=831.02

Yes, good. Include units.

so the correct answer would be a 831.02 N normal force acting on the person?

Yes. Do you have the correct number of significant figures in you answer?

## 1. What is a normal force in the context of an elevator?

The normal force in the context of an elevator is the force that the floor of the elevator exerts on an object or person in the elevator. It is perpendicular to the surface of the floor and prevents the object or person from falling through the floor.

## 2. How is the normal force affected by the movement of the elevator?

The normal force is affected by the movement of the elevator because it is related to the acceleration of the elevator. As the elevator accelerates upwards or downwards, the normal force will change in order to keep the object or person in the elevator stationary.

## 3. What happens to the normal force when the elevator is at a constant speed?

When the elevator is at a constant speed, the normal force will also be constant. This is because there is no acceleration, so the force required to keep the object or person in place does not change.

## 4. How does the normal force differ between an elevator going up and an elevator going down?

The normal force will be greater when the elevator is going up compared to when it is going down. This is because when the elevator is going up, the normal force has to counteract the force of gravity, while when it is going down, the normal force is working with the force of gravity.

## 5. Can the normal force ever be greater than the force of gravity?

Yes, the normal force can be greater than the force of gravity in some situations. For example, if the elevator is accelerating upwards at a fast rate, the normal force will need to be greater in order to keep the object or person in place. However, the normal force can never be greater than the force of gravity when the elevator is at a constant speed or accelerating downwards.

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