How to improve the mechanical advantage of a catapult

[mastoll]

I have a catapult that is a class 1 lever i.e. a rubber band pulls down on the beem on one side of the fulcrum; the load is launched from the end of the beem on the other side of the fulcrum.

I want to increase the throwing distance of the catapult. I recognize that one option is to increase the throwing arm - the length of the side with the load. According to the Law of the Lever, classical equation, I should also be able to shorten the rubber-band arm and see improvement.

Now, I'm trying to explain this to 6th graders in terms of the Actual Mechanical Advantage and the Law of the Lever equation - and convince them that it really works that way. They intuitively want to LENGTHEN the rubber-band arm as they recognize that this would stretch the rubber band further and thus increase the force. Yes, it would increase the force, but it would reduce the mechanical advantage. But would it decreate the length of the throw?

You see, now I've gotten myself confused too! 'Trying to use theory to support experience . . .

What am I doing wrong?

 

[Andrew Mason]

I have a catapult that is a class 1 lever i.e. a rubber band pulls down on the beem on one side of the fulcrum; the load is launched from the end of the beem on the other side of the fulcrum.

I want to increase the throwing distance of the catapult. I recognize that one option is to increase the throwing arm - the length of the side with the load. According to the Law of the Lever, classical equation, I should also be able to shorten the rubber-band arm and see improvement.

Now, I'm trying to explain this to 6th graders in terms of the Actual Mechanical Advantage and the Law of the Lever equation - and convince them that it really works that way. They intuitively want to LENGTHEN the rubber-band arm as they recognize that this would stretch the rubber band further and thus increase the force. Yes, it would increase the force, but it would reduce the mechanical advantage.

Your 6th grade kids are pretty smart - they are right.

The force of the elastic band is proportional to d where d is the the stretched length minus the initial (unstretched or equilibrium) length. The energy it contains is proportional to this distance^2. What you want is energy.

What you want to do is arrange it so that the elastic stretches as much as possible (without breaking) when you pull the projectile back the full distance. The way to do this for a given length of elastic band is to move the end of the elastic arm further from the fulcrum.

AM

 

[rayjohn01]

Catapult site

I don't want to get into details cause I am not sure what your kids may understand -- but there is tremendous interest in catapults by amateur
builders and there are a couple of good sites on the web with complete calcs and simulations -- you may get some ideas there. Use Yahoo search.
Ray