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

[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?

 

[jbriggs444]

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

 

[TSny]

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 F_net = ma.

 

[TheFlemster]

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]

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.

 

[TheFlemster]

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]

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?

 

[TheFlemster]

The normal force and the force due to gravity?

 

[TSny]

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 F_net = ma.

 

[TheFlemster]

N=mg

 

[TSny]

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 F_net?

 

[TheFlemster]

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

 

[TSny]

Yes, good. Include units.

 

[TheFlemster]

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

 

[TSny]

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