Our job is to

(1) ignore the forces acting in the horizontal ("x") direction. Objects (and people!) inside an elevator are not subject to side-to-side acceleration so we ignore that.

(2) determine if the forces acting in the vertical ("y") direction are *balanced* or unbalanced.

If the object (or person!) inside an elevator accelerates upwards they feel heavier because there is more upward force acting on them than if they were at rest.

If the object (or person!) inside an elevator accelerates downwards, they feel *lighter* because there is* less upward force* acting on them than if they were at rest.

Elevator problems can be a wee bit nasty beasts to conceptualize at first, but if we work the steps, they get a WHOLE lot easier a whole lot quicker.

To wit:

Let's consider the case of a person riding in an elevator standing on a bathroom scale to measure their weight.

(We keep in mind that a bathroom scale actually measures how much the springs inside are pushing up on the person standing on the scale)

w = mg

EXAMPLE:

Now let's step through the opposite situation -- which is to say when the elevator accelerates downwards.

We start by summing the forces as usual:

~~∑F~~_{x} = ma_{x} (no motion in x)

∑F_{y}= ma_{y}

Now we list the forces in Y (remember, we'll deal with +/- when we do our substitutions in a moment).

Also, a key to understanding these beasties is to realize that the floor is ALWAYS pushing *up on us* (F_{el}), and we imagine we are standing on a bathroom scale showing us just HOW much the floor is pushing up on us:

F_{el} + weight = ma

Now let's substitute the mathematical equation for the passenger's weight (mg):

F_{el} + mg = ma

Now let's isolate for the force the elevator floor is pushing up on the passenger:

F_{el} = ma - mg

Factor out the passenger's mass:

F_{el} = m(a - g)

Substitute using negative values for the passenger's acceleration (*the passenger *is* accelerating downwards after all!*) and gravity is ALWAYS negative:

95.5kg(-3.945 m/s/s - (-9.81 m/s/s))

Solve:

= 560 N

Therefore if passenger was standing on a bathroom scale as the elevator accelerated downwards at 3.945 m/s/s the passenger would feel lighter!