How Catapults Work
A catapult is a device in which tension is accumulated and then suddenly released in order to hurl a projectile. The device works entirely on the collection of potential energy in the form of tension. Potential energy is the energy of a particle, or system, due to position or condition rather than motion. The potential energy is stored when the arm is brought back and tension increased. When the arm is released and then quickly brought to an abrupt stop, the projectile retains the kinetic energy from the motion of the arm and is launched at the target.
Newton's First Law
Newton's First Law helps us explain the launch of projectiles using catapults. Newton's First Law states that an object in motion tends to remain in motion unless acted upon by an outside force, so when the arm is stopped but not the projectile, the projectile keeps moving forward. The projectile eventually falls to the ground because of gravity, or the "outside force" in this situation. If we were in outer space, where there is no gravity, the projectile would keep on moving forever.
The Importance of Angles
When the tension from the spring or wire is released, the projectile goes flying. Let's say that x is horizontal velocity and y is vertical velocity. In order to gain maximum velocity in both x and y, I released my projectile at a 45 degree angle. Simple trigonometry tells us that when the sine or cosine of an angle is taken, the angle in which both the sines and cosines are equal is the 45 degree angle. Therefore, if released at a 45 degree angle, the projectile would have the exact same velocity in x as in y. This makes sure that it does not go too far upwards so that it does not get a lot of displacement in x, but also does not get so little displacement in y that it does not go far. If the figure below had had a 45 degree angle, then the velocities in x and y would've been equal.
Mousetrap Catapults
Mousetrap catapults use the tension collected from the spring in order to snap abruptly and swing forward. When a bar of some sort stops the arm's forward motion, the projectile keeps moving forward using the kinetic motion from the arm. This rapid snapping motion from the mousetrap arm causes the projectile to be launched forward quickly.
