The Physics of Slingshots 2 | Smarter Every Day 57

Hey, it's me Destin. Welcome back to Smarter Every Day. So, if you want to become smart in any particular field, you have to go talk to the experts. This is why I went to Germany to a guy named Jörg Sprave. [thunder] Now today we're gonna learn about the physics of slingshots, but before we do that, let's just have some fun shooting. You're getting Smarter Every Day.

So today we are in Germany at a 300-year-old dairy farm in a small village. Jörg, so what are we gonna do?

• Well, we're gonna see Tobias shooting, and Tobias is actually the current world record holder for the strongest handheld slingshot, so getting more than a hundred joules with the handheld slingshot. So we're gonna try to kill this good German beer. We've been shaking this a bit. Let's hope for the best. [cheering]

Oh man. [laughing] Ja. That's the way. [music] [laughing] Oh man.

(Jörg) It's really dark red; I love the color.
(Destin) Arrgh, it looks like a skull. It's pretty wild.
(Destin) It is dark red.

(Destin) Awesome. High five! We give high fives in America. [laughs] High five Jörg. Nice.

Elastic is a pretty interesting material. Alright, so here's our graph. So if we want to add energy to the system, meaning increase the potential energy on the bands of the slingshot, all you have to do is pull back the bands, obviously. But the thing about this is when you pull the bands back, the further you pull the more difficult it gets to pull.

Let me show you. If you look at this force gauge, the further I pull, the more difficult it becomes. If I were to plot the potential energy going into the system versus the displacement as I pull back, because it gets harder, it's not a linear graph; it's actually a curved function.

So here's something else. As I release the projectile and then it begins to accelerate out of the pouch down towards the fork, it's going to also have this curved function because of the material properties there, but here's the interesting part. If you were to add up the potential energy still left in the band, and the kinetic energy of the projectile going towards the fork at any point along the displacement going back towards the fork, they would equal approximately the total energy that I put into the system.

OK, the last property of elastic I didn't understand until I saw some of Jörg's experiments. As you pull the bands back, they heat up. But if you hold them there and allow them to cool off, you're losing energy. So what this means is the total potential energy in the system is going to go down, so your projectile will be slower if you sit there and wait and let your bands cool off.

Why do you think that happens? Jörg, you want to explain it a little bit?

(Jörg) Yes. Tobias' record shot was shooting a 20mm steel ball at 83m/s which is 115 joules.

(Destin) OK, ready.

(Jörg) How he achieves that is by drawing out and firing immediately without any kind of break, so that the rubber is still at full force and it doesn't lose power through the hysteresis that otherwise happens.

Oooh! [laughing]

(Destin) Good grief. How thick is this? Oh yeah.

This is a frustum. A frustum is when you try to distribute a stress throughout a material. OK, here I have two bands and they're C-clamped to the barn, and as I go down the length of the band, you can see the one on the left is tapered to a smaller width than the one on the right.

So clearly, if I put weight on each of them, then the one on the left you would assume would stretch more because it has less material resisting the stretch, right?

OK, yeah, that makes sense. So if we were to fire a slingshot with both a tapered band and an untapered band, I would assume that the one on the right, the untapered band would accelerate the projectile faster, right?

No. That's not what happens at all. And the slingshot community has known this for years, but they never had the rock-solid evidence. So that's what Jörg and I did with the Phantom high-speed camera. We fired two different slingshots at 1000 frames per second. The one on the top here is an untapered band; the one on the bottom is a tapered band.

The top band is clearly accelerating slower than the bottom band. My theory is pretty simple. Every solid material has what is called a stress-strain curve. Stress is the force per unit cross-sectional area on the material as you pull it. Strain is the percentage that it elongates as you pull it.

You are probably putting more strain energy into the system.

OK, in summary, we went to two different continents, I learned two things, and I'm gonna ask you two questions.

First thing I learned. The potential energy in a stretched rubber band is conserved; however, it is rapidly dissipated in the form of heat.

The second thing, for slingshots, a tapered band is more efficient or effective at converting potential energy into kinetic energy.

Here's a little bonus. In 1660, a guy named Robert Hooke discovered the law of elasticity, or Hooke's Law. Here's the interesting thing. The rubber in a rubber band does not obey the law of elasticity.

I'll leave a link in the description so you can read about that, but spoiler alert, some of your physics books might be wrong.

Anyway, here's the two questions for you. Number one. Why does rubber lose energy when it cools off? I.e., I can shoot a rubber band farther if I just pull it back and let it go.

And the second thing, why are tapered bands more efficient? Help me figure this out.

I'm Destin. Thank you very much for watching. Enjoy the outtakes.

Jörg's really good, and I wanted to go from a superficial knowledge about how elastic works to a deep understanding. But before we look into the physics of slingshots... let's just shoot.

I just messed that up. Even though I hit it. Blah!

We're using less reactive material to fire something faster. [goat bleating] Come on in. Come on in.

...talk about slingshots.

I wanted to learn... [whispered] oh no.

When I first saw you, I thought you were kind of a sissy, so I'm glad to see that you're not. [laugh]

I'm only talking like this because his hand is hurt, and he can't punch me.

...so I wanted to go from a deep... I'm killing myself here. I can't talk.

...tapered one actually deflects more. But here's the interesting part. It... goat... really.

...I wanted to learn about the elasticity of...

Aah!

...Jörg Sprave. [thunder] Now today we're gonna learn about the physics of slingshots, but before we do that, let's just have some fun shooting.

You're getting Smarter Every Day.

I finally said my words right! Now that the lightning's here. [laugh]

[Captions by Andrew Jackson] captionsbyandrew.wordpress.com