Physics Application: Energy

A: The counterweight has all Gravitational Potential energy at this point. It is not moving, but has a lot of mass and is being suspended above the ground. Giving it a chance to move downward. As it does the Gpe turns into kinetic energy as the counterweight speeds up, and the Gpe diminishes because there is less and less space to travel as the weight is moving down.

B: The projectile at this point has no Gpe, no kinetic energy, it is all regular potential energy as the sling is taught to the arm. But as the arm flies up it gains kinetic energy and starts losing its potential energy as the arm moves, as it rises in elevation it also gains Gravitational potential energy. Once it reaches the top and the projectile is released, the kinetic energy is still climbing, the original potential energy is gone, but the gravitational potential energy is now at its peak. As the projectile flies in the air and comes back down its kinetic energy is still gaining energy due to the dwindling gravitational potential energy as the projectile lowers elevation. Finally once it hits the ground all potential energy is lost and the rest of the kinetic energy falls due to friction.

Modifications to increase range would be to increase the gravity potential energy in the counterweight as much as possible without exceeding structural capacity. This way the most energy can be transferred to the arm which gives the arm the best chance to release the projectile with as much energy as possible letting it go the farthest distance possible.