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

AI Thread Summary
The discussion centers on calculating the normal force acting on a 74.0 kg person in an accelerating elevator. The relevant equation is N = m(a + g), where 'a' is the elevator's acceleration and 'g' is the acceleration due to gravity. Participants clarify that the total force acting on the person is not simply the sum of gravitational and inertial forces but rather the net force, which combines these two. The correct calculation yields a normal force of 831.02 N, emphasizing the importance of including units and significant figures in the final answer. The conversation highlights the need to properly account for both forces to determine the normal force accurately.
TheFlemster
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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?
 

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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. :oldsmile:
 
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.
 
  • #10
N=mg
 

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  • #11
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?
 
  • #12
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
 
  • #13
Yes, good. Include units.
 
  • #14
so the correct answer would be a 831.02 N normal force acting on the person?
 
  • #15
Yes. Do you have the correct number of significant figures in you answer?
 
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