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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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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