Can someone please explain why the bottom of the slinky doesn’t fall to the floor until the top is finished falling down?
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So, a Slinky is nothing more than a loose spring with flexible material, like wire or plastic. The spring is strong enough that it tries to hold together, but weak enough that momentum can break that tendency.
So, when you flip over the top of a Slinky, the top part falls to gravity and the rest tries to balance out. But if the top falls underneath the bottom, then evening out those forces means dragging the rest of the toy with it.
The bottom of the spring wants to stay in place, but eventually it gets pulled up and away by the rest.
The slinky is a spring. The natural state is for it to be compressed in a tight coil, so it wants to return to that state.
When you hold the slinky up from the top, the slinky extends due to the weight of the bottom. It extends until the compressive force of the spring is enough to hold the bottom up; the force that a spring can exert is roughly tied to how far it has been stretched/compressed compared to its natural/rest state.
So at the moment before you drop the top, the slinky is completely stationary. The spring is exerting enough force to hold the bottom from falling further, with that force being exerted on the top. You feel that force as the weight of the slinky pulling your hand down, which you (easily) resist to hold it still.
When you drop the slinky, there’s nothing holding the top up anymore. But the bottom is still being held by the stretch of the slinky. That force is enough to hold the bottom roughly in place against weight/gravity (if you watch carefully, it’s not absolutely stationary while the top is falling) until the slinky closes up and the momentum of the top of the slinky coming down pushes the balance of forces all the way towards weight/gravity downwards.
The slinky is a spring. When you hold a slinky in one end it will stretch out. At each point, the upward force of it as spring will be equal to the gravitational force of everything below and the gravity on that point. The spring force that it up in that point will be the gravitational force of everything below for a point above.
That is for every point except where you hold it, the upward force from the spring is canceled out by a force from you hand
So when you start the slinky is at rest with forces equal at each point. When you release it the only thing that change is the top is no longer supported by your hand. Nothing has changed for the rest of it gravity pulls it down and spring tension pulls it up.
The result is that the top move down both from gravity and spring tension. The upward spring force in the other point that was previously transferred to your hand instead accelerated the top down faster. The point on the slinky only starts to move when the spring force at that point no longer accurate what is above, that will at the latest happens when two layers of the slinky collide
The top of the slinky will accelerate down faster the gravitational freefall. Is if you dropped a ball beside it the top of the slinky would move down faster.
It will be the center of mass of the slinky that accelerates down at freefall speed.
A way to think about it is what happens if you stretch out a slinky horizontally on the floor. The result is the end will accelerate to the center. So you can look at the drop as the slinky contracting itself like on the floor but at the same time, the center of mass is accelerating down. The net result is the bottom pulls itself towards the center of mass at the same rate as gravity pulls it down and the result is it remains stationary.
A slinky stretch out by gravity vertically is not identical to one stretch out on the floor. Each part is not equally stretched out it depends on the mass below. So the spring force at each point is equal to what is required for gravity to not accelerate it, this is why the contracting and center falling works out to the bottom being stationary.
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