February 26, 2021

Wait, Is That Backpack … Floating?

That is all high-quality and anything until eventually the human loses get hold of with the floor. At that level, there are only two forces on the human—the downward gravitational pressure and the downward spring drive from the pack. That yields a downward acceleration greater than what it would be from gravity by yourself. At the similar time, the pack is continue to currently being pushed up by the spring power. These two matters jointly trigger a vertical separation concerning the pack and the human.

Okay, just to make guaranteed every thing sinks in, how about a quick research question? What would transpire if you applied a backpack with a quite reduced mass? Would this alter the separation length in between the human and the pack? (You can use the code higher than to come across the solution.)

How to Conquer the Bounce

When we began you probably imagined, “Alright, the HoverGlide has a springlike shock absorber constructed into it—end of tale.” But now we have found that even a standard backpack has a form of springlike link in the harness. So the vital isn’t owning a spring for each se, it’s getting the proper spring.

Precisely, HoverGlide utilizes a spring with a significantly reduced spring frequent k. Due to the fact of that, the pack can take a much for a longer time time to accelerate upward, because the spring exerts a lesser power. By the time the human comes back again down, the pack truly has not even moved. Considering the fact that the pack scarcely moves, you never get that jarring impact when it collides with your shoulder.

Here’s a demonstration of this result with a 1-kg mass hanging from a rubber band.

Online video: Rhett Allain

See how my hand is going substantially extra than the hanging excess weight? That is the strategy. This is in fact a incredibly attention-grabbing physics challenge. Every single introductory textbook appears to be like at something similar but much more boring—a mass oscillating on a spring. But what if the attachment stage for the leading of the spring is also oscillating? I call this the “jiggle spring.”

You know what is tremendous great about this challenge? There are two strategies to product it. The initial uses Lagrangian mechanics to identify the movement by looking at the electrical power and the constraints on the procedure. That’s all I’m heading to say about Lagrangian. It is the ideal solution, but it would choose a little bit of clarification to get there.

In its place, I’m going to do what you know I like to do—a numerical calculation working with Python. The principal strategy of a numerical calculation is to break the problem into pretty little ways in time. At every phase, I make some simplifying assumptions to estimate the new posture and momentum. (If you want a far more detailed tutorial, below is how you would product an oscillating mass with a secure hanging point, not a jiggle spring.)

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