MadSci Network: Physics

Re: how works a sling of dave?

Date: Wed Nov 1 19:42:22 2000
Posted By: Benjamin Monreal, Grad student, Physics, MIT
Area of science: Physics
ID: 972417100.Ph

Bonjour Dirk,

In the Biblical story of David & Goliath, David uses a sling to throw a small pebble hard enough to kill Goliath. Now, I've never killed a giant, but when I was younger I used a sling to throw rocks 100 meters across my back yard.

It is not a complicated device at all; the idea is to throw something by swinging it around really fast and letting go. But there's some physics behind that which of course I will talk about first. :)

You can think of a sling as a way of storing energy from your muscles. To throw something really fast, you want to put as much energy into it as possible. But your arm, while it's perfectly happy lifting twenty kilograms fairly slowly, can only deliver small amounts of power during the half-second exertion of throwing a baseball. You'd get that ball going faster if, somehow, you could put energy into it slowly - the way your muscles work best - and have the energy converted into forwards motion all at once.

There are lots of ways to store up energy like this; a bow and arrow is an example. You draw the bow very slowly, storing energy in the springy bending of the bow, and all of that energy is released quickly into the arrow. A crossbow allows you to store up even more energy, if you use a crank to draw it. Imagine if you build a super-stiff crossbow, you might spend half an hour cranking it back, but that half-hour's worth of effort all goes into the arrow at once. A golf club is another approach; when accelerating a golf club, you have a long, long stroke - much longer than the "stroke" of throwing a baseball - during which to accelerate the club head, so it's going very fast when it hits the ball. Meanwhile, your arm and shoulder muscles didn't have to move very fast at all.

Anyway, a sling is a simple way of putting lots of energy into a rock and then letting it go all at once. You basically use your arm to accelerate the rock, but keep it on a string so it stays near you, going in a circle - so you can accelerate it again and again, speeding it up, and then releasing it when you've gotten it going very fast.

Here's very simple design!

                          cloth cloth cloth cloth
string string string strinloth cloth cloth cloth string string string strin
                          oth cloth cloth cloth c                  (tie a 
                          th cloth cloth cloth cl                  loop in
                                                                   one end)
Use about 75 cm of string on each end, and maybe 25x8 cm of cloth in the middle. One string's end gets tied onto your finger, the other is held in your hand. When holding the two strings, the cloth hangs below and makes a little basket. Put your rock securely in the basket. Now, go to a WIDE OPEN SPACE, swing the rock-in-basket around above your head until you get it going really fast, and let go of the free string! The basket opens up, the rock flies out and sails away!

Yes, it's really that simple. And yes, a rock thrown like this can seriously injure someone. The only thing limiting the speed of the rock, now, is air resistance. When you're spinning it really fast, the amount of energy you put in with your arm is about equal to the amount taken out by drag forces - you'll be able to feel this. It'll feel like the rock just can't go any faster. That's all I'll say about physics, and I'll end with a safety notice (I work with NASA; we make a big deal of safety).

WARNING - not only is the rock going very very fast, but it's also terribly hard to aim, until you've practiced a lot. I mean, REALLY REALLY hard to aim; be prepared to deal with the consequences if the rock goes completely behind you, or sideways, instead of forwards. Not only is it hard to decide when to let go of the string, but also sometimes the rock will fall out of the basket on its own. So start with small projectiles (small pebbles, crabapples) and stay far away from people, and windows, and Goliaths!

Have fun, and be careful!

-Ben Monreal

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