# In this particular problem: Is the mass of the system the mass of the person?

I am doing this problem:

The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N.

What is the magnitude of the acceleration?

This is how I solved it:

$$\sum F = F_1+F_2=N+(-W)=ma$$

I am saying here that the sum of all forces is equal to the $$Normal \ Force + Weight$$ and that all of this should equal $$ma$$.

I then re-arrange my equation:

$$(N-W)/m=a$$

Now here is where I am making a huge assumption, and where I am having problems. I decided to solve for $$m$$ by imagining that $$m$$ is the mass of the person. So in a way I am saying that the whole system in this problem is really the person. Is this a logical way to solve this kind of problem or will I run into problems by thinking this way?

If it is not clear what I did here is in equation format:

$$(N-W)/(W/g)=a$$

In other words: What is the proper way of thinking about the mass when applying $$F=ma$$? At the moment I am thinking of it as the mass of the objects that affect the problem. So if it was two people in the problem I would add up their masses and use that.

• Good homework question. +1 – BMS May 25 '14 at 3:57
• What is the proper way of thinking about the mass when applying F=ma? There is no wrong way to solve a problem if you come up with the correct answer. – LDC3 Mar 16 '15 at 2:09

$m$ is the mass of the person, not of the combined system, since the normal force is exerted on the person, not the combined system (person $+$ elevator) itself.