Chain Drop Answer 2

2m read

·Nov 10, 2024

All right, are you ready for the moment of truth? Let's drop these two objects at exactly the same time and see which one hits the ground first. Ready? 3, 2, 1. Wow! Did you see that? The one connected to the chain landed just before the other free weight. I'd like to show this in slow motion so you can see that the weights are accelerating at just slightly different rates.

[Music] Go! Oh, why did that happen? I mean, most people, most students of physics, would know that all objects on Earth's surface should accelerate down at the same rate: 9.8 m/s squared. But in this case, what happens is the chain actually whips the weight around, so it accelerates at a rate greater than the acceleration of objects when in free fall. That's a pretty remarkable result.

I want you to think about the bend in the chain as the weight descends. The chain goes from falling to becoming stationary, so it's accelerating up. The tension required to accelerate the chain up actually pulls down on the weight, accelerating it at a rate greater than the acceleration due to gravity, and that's why it hits the ground first.

Now, this actually happens to bungee jumpers. If the weight of the rope is appreciable, they will actually accelerate down at a rate faster than free fall, faster than 9.8 m/s squared. When I went bungee jumping, I was aware of this. What is actually true is that as you fall, your acceleration will be greater than free fall, and that's due to some, uh, effects of the way the rope pulls on you.

So I'll do an explanation of that later when I'm not scared out of my mind. Oh my God! I couldn't figure out what the acceleration was as I was going down, but you know, it fell high. It fell very fast—very great increase in your rate of speed. So, oh my God, that was fast! Loved it!

Worked examples: Definite integral properties 2 | AP Calculus AB | Khan Academy

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Chain Drop Answer 2

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