# Elevator Problem Normal Force

## 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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jbriggs444
Homework Helper
Remember that the F in F=ma denotes the vector sum of all external forces. There are two external forces on the person.

TSny
Homework Helper
Gold Member
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

TSny
Homework Helper
Gold Member
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?

TSny
Homework Helper
Gold Member
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?

TSny
Homework Helper
Gold Member
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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TSny
Homework Helper
Gold Member
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

TSny
Homework Helper
Gold Member
Yes, good. Include units.

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

TSny
Homework Helper
Gold Member
Yes. Do you have the correct number of significant figures in you answer?