Physics Applications: Energy

Energy

The two forms of mechanical energy, Kinetic and Potential, come into play every time a catapult's trigger is pulled. Before we begin, let's quickly observe the difference between the two forms of energy:

KE = 0.5mv²

PE = mgh

while KE and PE are kinetic and potential energy,

m is the mass,

v is the velocity,

g is the gravitational constant,

and h is the height above ground

Kinetic energy is the energy of an object due to its movement, and potential energy is the energy of an object due to its position or arrangement of components.

Here's a diagram of our catapult at rest.

One might say that M1, or the counterweight, has a lot of potential energy just before launch because not only does it contain large quantities of mass, it is also fairly above ground. In contrast, the projectile's end of the arm has no potential energy, since it's on the ground. At the moment, we lack kinetic energy because nothing is moving.

Keep in mind, however, that probably the most important part of a catapult is its energy transfer. Take a look at the diagram below---of the same catapult, except just fractions of a second after being set off:

Now that things are moving, kinetic energy exists by feeding off of the potential energy in the counterweight. Even though the counterweight has a bit of kinetic energy itself due to its mass and slow movement, the projectile possesses a lot more because of the proportion of the length of L2 to that of L1, squared. Now that a significant amount of energy transferred from M1 to M2, the projectile can now jettison itself across whatever it's aiming at.

With that being said, a more massive counterweight and/or a longer L2 are both ideal for catapulting our projectile across large distances, for M1 could translate more potential energy to kinetic energy while the disproportionately high L2 further multiplies and squares the kinetic energy that fuels the projectile's travel.