Tonight’s episode (actually there are two episodes tonight) looks at the famous slinky drop problem. Let’s start with the first place I saw this—from Derek Muller (Veritasium) even though he didn’t invent this either.
That’s pretty awesome, right? Of course the first thing I want to do is to make a model of a falling slinky. Here is that first post.
Some important comments.
- It’s important that the slinky itself has mass. You can’t use the normal assumption of a massless spring.
- The best way to model a spring with mass is to have a bunch of smaller masses connected by massless springs.
- When the slinky is dropped, the center of mass falls with a downward acceleration of -9.8 m/s^2.
- However, since the slinky is contracting this makes the bottom of the slinky motionless.
Here is an animation of my python model.
Sorry—this code is older and I don’t have it on some online platform (I will try to update that soon). But here is the important plot. What if you look at the vertical position of the top, bottom and center of mass for this “slinky”? Here’s what that looks like.
The red curve is the bottom mass. Notice how it “hangs” there? Awesome.
But can you just put a mass (like a car) on the end of a spring and drop it? Yes, but it won’t look very cool. The key is the center of mass. You want the center of mass to fall such that the bottom mass stays in place. With a car and a spring, there is no top mass moving down faster than the acceleration due to gravity to make the bottom mass (the car) move up relative to the center of mass.
In the end, you need some type of mass at the top of the spring too. So, that could work. Two large masses separated by a spring. When you hang and then drop, the bottom mass will be stationary.
But wait! You can try this yourself. Get two masses and connect them with rubber bands (even though rubber bands aren’t ideal springs). Hold one mass and let the other hang below. Now drop.
Here’s what that looks like in slow motion. Sorry about the vertical video, when I recorded this I didn’t think I would post it.
But wait! What if you want to make something like the slinky? In that case you can get a bunch of masses and connect them with rubber bands. It will be just like the python animation above, but in real life.
I should have recorded this in slow motion. Oh well.
Just for fun, here are some of my original notes in which I estimate what kind of spring you would need to do this drop thing with two cars.
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