For example, I want to figure out the impact force on a person inside a free falling elevator.
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>For example, I want to figure out the impact force on a person inside a free falling elevator.
If an object is in free fall then it is in free fall. Whether there are other objects in free fall in or around the first object doesn’t matter.
Unfortunately it doesn’t quite apply to your specific scenario though, because an elevator will never be in free fall and so neither will its occupants. It will always be slowed down significantly by its various frictional braking- and security features and by the air cushion underneath it. By **how much** depends on the model, materials, shape and condition of the elevator, the air pressure within the building, the distance traveled by the dropping elevator, the total weight (or precisely the *density* of the whole elevator cabin including occupants), on how air-tight the elevator shaft is, the temperature within the elevator shaft and probably a number of other different things I’ve forgotten.
What I’m saying here is that you’re tackling a very tricky engineering problem and won’t just be able to model an elevator as a box dropping from a plane.
Assuming you mean the impact forces on the person when the elevator hits bottom:
It will be almost the same as if the person fell down the elevator shaft without the elevator. The main difference is the air resistance/terminal velocity of the elevator car is likely to be different than that of the person. If you remove the air resistance from the problem the force becomes exactly the same as if the person fell without the elevator car (minus the minor fall distance to account for the thickness of the elevator bottom). Both the person and the elevator are in the same gravity field, so they are accelerated at the same rate. When they hit the bottom the person will have accelerated to the same velocity they would have if the elevator was gone.
One thing you have to appreciate is that when another object, such as an elevator, is moving with other objects the elevator is pushing up on the individual. This is the same with a car, you are being pushed along by the car – you are strapped in to make you a part of the movement as opposed to feeling like your being pushed.
So how do we work out what will happen to the object inside?
In all situations including moving and crashing their is always a conservation of momentum, crashing is literally just “a rapid, unexpected deceleration”.
As such following this principle, unless you are strapped into the body of the elevator the elevator will crash into the ground at the set speed, and then you will crash into the elevator at the set speed. Your phone in your pocket will then crash into you, at the set speed, and that speck of dust on your phone screen, will crash into your phone at that set speed.
If you are not strapped in, your force will always attempt to go into and through the blocking object. If it does not overpower it, you will crumple.
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