Force

During the catapult launch Newton's three laws occur. Newton's first law applies as the arm of the catapult swings and launches the balloon. As the arm continues to move back it is stopped by the retaining bar. This explains how an object in motion will stay in motion until an outside force acts upon it. The smaller the mass of the balloon, the more force will be needed to accelerate the balloon. This relates to Newton's second law which states that the acceleration of an object is proportional to the force acting on the object, and is inversely proportional to the mass of the object. As the balloon sits in the arm of the catapult it exerts a force. Then the arm launches the balloon, exerting a force on the balloon. This process uses Newton's third law which states whenever an object exerts a force on another object, the second object exerts an equal/opposite force on the first object.

To increase the Range:
Some modifications that would increase the range would be to add a more heavier weight which would cause the arm to exert more force on the balloon. Also the length of the arm can affect the range. If we were to increase to length of the arm, then the balloon would launch farther and higher. The higher the balloon goes, the longer it will take for gravity to pull it down.  

The Energy Behind a Trebuchet

To put a trebuchet into its "cocked" position, a team of people use their energy to hoist the counterweight. When the counterweight is raised, it gains this energy as potential energy. In this case, the potential energy is gravitational potential energy-energy that results from the position of an object in a gravitational field. The amount of gravitational potential is dependent on both the weight of the object and its position. Since the counterweight in a trebuchet is very heavy, it has a great deal of potential energy. While energy cannot be created or destroyed it can change forms. The potential energy from the raised counterweight is released and begins to fall. The downward motion of the counterweight then causes the sling to swing and the projectile to be released. The potential energy that was stored in the form of kinetic energy, to the projectile, which is released at a high velocity.

To increase the range of the trebuchet, one would have to increase the mass of the object in order to create more potential and kinetic energy within the catapult. After building up more potential and kinetic energy, it will increase the velocity which will, in effect, increase the range of where the projectile will fall.