Questions from elevator ride

Question

I like to play inside the lift (elevator). For instance, there are bars attached at the side of the lift, and I like to hold my body up using my two hands on the bar. I realised that I actually feel lighter when the lift is decelerating and heavier when it is accelerating. Takes the upward motion as positive.

Also, I tried weighing myself inside the lift using a balance ;D As most people know, my weight increases as the lift is accelerating, and vice versa. Does this mean that when I am holding an object inside the lift, the object will actually feel heavier when the lift is accelerating?

Lastly, and this question is quite stupid. My friend once told me that if you want to survive an elevator crash, just jump the moment it hit the floor. I told him that's a stupid idea, but I can't really explain why it wouldn't work! Please help me.

Answer 1

Yes, exactly. However, Albert Einstein beat you to this discovery by about 100 years with the equivalence principle. The key idea is the equivalence between a downward gravitational acceleration and downward force due to an acceleration upward. There is no experiment you can locally perform that will tell you whether you feel heavier because the elevator is accelerating upward or because the gravitational field below you just got stronger. Since weight is just the force due to gravity, then you can use Newton's second law to calculate your weight in the elevator as $F = m(a+g)$, where $g$ is the acceleration due to gravity on the surface of the earth, 9.81 m/s^2.

So yes, everything in the elevator feel heavier when it's accelerating upward. When it's accelerating downward, everything gets lighter (unless of course it's accelerating you faster than gravity would, in which case you'll feel pulled to the ceiling. You'd need a cable pulling the elevator down for this to happen.). In fact, if the acceleration downward perfectly matches the acceleration due to gravity, you'll be weightless. This is the second piece of the equivalence principle - an elevator accelerating downward at the same rate as gravity is indistinguishable from floating in empty space with no gravitational field at all.

For some more about the equivalence principle, see here:

http://www.einstein-online.info/spotlights/equivalence_principle

The reason jumping won't work is because you'd need to time it perfectly - the chances of you doing this are impossibly small. I'm not 100% sure, but I've always heard the thing to due in a falling elevator is to lie flat on the floor as to distribute your weight to spread the force of impact out across your entire body.

Answer 2

The reason jumping at the end doesn't work is because you are not actually counteracting your downward speed significantly. Though it may appear, relative to the elevator before it hits the bottom, that you moved upward, in fact you are still moving downward. You'll notice this when the elevator stops moving (i.e. it hits the ground) and you hit the elevator with the approximately the same speed as if you hadn't jumped it all. It's just the frame of reference of being in an elevator makes this somewhat confusing to picture.

Answer 3

Jumping would not help, as you are still falling at the same rate when you hit the ground, regardless if you hit at the same time as the elevator or not.

Answer 4

I think jumping at the last moment will help. Imagine that when the elevator starts falling you held on to the side rails so as to be able to have your feet planted on the floor. Now, say the elevator is in a free fall and you are thus falling with acceleration of 'g'. Just before it hits the ground, you push on the elevator floor and jump up. this means you are accelerating in a direction opposite to that of g or effectively reducing the effect of it.

So you will be able to 'slow' down only if you jump up with an acceleration greater than 9.8m/sec2. Anything less than that will reduce the rate at which you are picking up speed every second.

Hope this helps.