Energy of a Projectile
Another projectile energy measurement technique is to take a reasonable sized block of wood, weigh it, and suspend it as a pendulum in front of the coil gun.
The idea is to have the nail stick in the wood block when it is fired.
When you fire the gun, you should be able to observe, or at least estimate, the angle θ,from a vertical line, when the pendulum is deflected upward. Then use the formula for potential energy:
PE= WR(1-cos θ) units of your convenience ...
Where R is the length of the cord or string, and W is the weight of the object.
A little more accurate version would be to include the weight of the nail, along with the weight of the wood block, for the variable W.
Basically, you are converting the kinetic energy of the moving nail into potential energy ..... by raising the block vertically
n.b.: 1 ft-lbf=1.356 J
Maybe get a piece of balsa wood as the target ... a little easier to stick the nail.