From: ronwong@unleashed.net
Message-Id: <l03102801afcde9768bc5@[156.1.196.12]>
Date: Wed, 18 Jun 1997 13:11:58 -0800
To: pinhole@exploratorium.edu
Subject: Re: catapults - Why the 1/2??
Kim Greco asked:
>Why , for the catapult, is work = 1/2 force X distance??? Why the 1/2??
The formula for work, Work = Force X Distance, assumes the Force is
constant over the Distance.
When it comes to the Dog-Dish Catapult, the Force is NOT constant. It
ranges from a maximum value, which occurs when the catapult is about to be
released and the elastic tubing stretched to its maximum, down to zero when
the dish has traveled the prescribed Distance and the tubing is no longer
stretched.
Under these circumstances, the value of the Force in the Work equation
would be the average force over this Distance. If we assume the strength of
the force acting on the dish is a linear function of the distance that the
tubing has been stretched then an acceptable value for the average force
would be 1/2 the Force at the moment of release. Thus, Work = (1/2) X Force
X Distance.
Actually, you should check to see whether the force acting on the dish in
the Dog-Dish Catapult really is a linear function of the amount of
stretching of the tubing. If it isn't, you have more "work" to do in order
to determine the Work done. It just adds to the fun.
ron