Help in calculating efficiency of a catapult

[pcgmks]

Help with a catapult

Homework Statement

Hi all I have design a prac to investigate the efficiency of a catapult, was wondering if anyone could shed some light into this area

Homework Equations

Ee=0.5kx^2 (hookes law)

The Attempt at a Solution

I was thinking that my independent variable for the experiment is to change the length of the catapult arm thus changing the distance (x) in which the rubber band is stretched each time, while the dependent is how far the projectile is launched, from this can i determine the efficiency of the catapult?
was thinking that i collect how far the weight is projected each time- from the same angle of 45*? - then do i then need a formula to find out the force used and then compare to potential elastic energy?
so i am not sure how to piece this together fully from here
was told efficiency = output work/energy used, but what does that mean exactly and would it be helpful in this situation,

if anyone could help, it would be much appreciated,
thanks

 

[jbsteele]

The efficiency of a catapult can be determined by measuring the potential elastic energy stored in the rubber band of the catapult and comparing it to the kinetic energy of the projectile after it has been launched. To do this, you will need to measure the distance that the projectile is launched, as well as the amount of force used to stretch the rubber band. Using Hooke's law (Ee=0.5kx^2), you can calculate the potential elastic energy stored in the rubber band. The distance (x) in this equation is the distance that the rubber band is stretched, which can be determined by changing the length of the catapult arm each time. To determine the kinetic energy of the projectile, you will need to measure the speed at which it is launched, as well as its mass. The kinetic energy of the projectile is equal to 0.5mv^2, where m is the mass of the projectile and v is its speed. Once you have determined both the potential elastic energy and the kinetic energy of the projectile, you can then calculate the efficiency of the catapult by dividing the kinetic energy of the projectile by the potential elastic energy. This will give you a percentage value which indicates how efficient your catapult is.