The basis for elevator problems is the same for ALL of our forces problems:

• If an object experiences unbalanced forces in the "x" or "horizontal" direction, it will accelerate in the direction of the unbalanced force.

• If an object experiences unbalanced forces in the "y" or " vertical" direction, it will accelerate in the direction of the unbalanced force.

• If an object is at rest in the "x" or "horizontal" direction the forces in that direction MUST be balanced or absent.

• If an object is at rest in the "y" or "vertical" direction the forces in that direction MUST be balanced or absent.

Mathematically we express those situations as:

∑F_x = ma_x

∑F_y= ma_y

 

THEREFORE--

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.

 

TO WIT:

ELEVATOR PROBLEMS REVIEW

Elevator problems can be nasty beasts to conceptualize... nonetheless, let's give it a try:

An object's weight is determined by how much gravity accelerates that object's mass. Mathematically we express that as:

W = mg

which is just a specialized version of Newton's 2nd Law:

F = ma

Let's consider the case of Ms Spock riding in an elevator.

• When the elevator is a rest, she feels the floor pushing up on her with the same force she pushes down on the floor: mg

• When the elevator accelerates upwards, she feels the floor pushing up on her with the same force she pushes down on the floor (mg). She also feels the additional mechanical force of the elevator pushing up on her (F_el). The two forces combine and she feels heavier as her mass is accelerated upwards.

• When the elevator accelerates downwards, she feels the floor pushing up on her with the same force she pushes down on the floor (mg). She also feels less mechanical force of the elevator pushing up on her (F_el). We can think of this situation as either:

The elevator is pulling her downwards

or

The elevator is pushing up on her with insufficient force to support her weight

 

In either case she accelerates downwards and feels lighter... her weight decreases.

For an annotated, step-by-step solution to an elevator accelerating up problem try HERE: (if the link doesn't take you to the bottom of the page, scroll down)

For an annotated, step-by-step solution to several different elevator problems try HERE:

For a basic elevator-going-up problem that we did on Friday (11/21/17) see below:

 

See if you can follow that same logic to show that if the passenger is accelerating downward that her weight decreases:

m(A_el - g)

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

=

560 N

And if the person is at rest her weight is simply mg:

(95.5kg)(9.81 m/s/s) = 937 N

Try to make it make sense.... accelerating upwards adds to your weigh, accelerating downwards takes weight away and being at rest keeps your weight the same