# TREBUCHET PHYSICS

Some physics concepts applicable
to our trebuchet lab:

Projectile motion- applicable to movement
of Christmas ball in air

Forces- a major factor
in launching the projectile, the best ratio between applied force, air resistance, machine resistance must be determined to
achieve best performance.

Kinematics- used to calculate projectile
motion

The trebuchet is a first class
lever. The force is applied to one end, the load is on the other end and the fulcrum sits between the two. Children playing
on the see-saw is an example of the lever. If a child on one end is allowed to
fall from a high place all the way to the bottom through circular motion, the other child will be launched into midair (provided
the first child is heavier than the second). This is basically how a simple counterweight
trebuchet works. With the lever type trebuchet, the fulcrum can be adjusted to
change the performance of the trebuchet. If it is close to the weight and far
from the projectile, it will require heavier weights, but it will also give great projectile distances.

The sling is another application of physics. It is basically
a piece of string tied to the projectile and attached to the arm, this gives the projectile extra hurling power coming off
the arm. The length of the sling can also be changed to maximize the performance. The length of the sling forms the radius of the circle that the projectile travels
through when the arm swings up and forward. The formula v = 2πr/T says that
velocity of an object traveling in a circle equals 2π multiplied by the radius divided by the time it takes to complete
one revolution. Therefore, if the period is the same, a larger radius will give
a greater velocity, meaning the projectile will travel further.

Physics can also be implemented in calculation of the projectile’s speed and height during flight. There are 5 equations that are used in the calculations:

D = ½ (V_{2} + V_{1}) t

D = V_{1}t + ½ at^{2}

^{ }

D = V_{2}t – ½ at^{2}

V_{2} = V_{1} + at

**V**_{2}^{2}
= V_{1}^{2} + 2ad

Given enough information, the maximum speed, height, and distance of the projectile can be calculated.

Newton’s famous 2^{nd} law states F = ma.

This basically says that force of an object = mass of object * its acceleration. This formula is also applicable to the launch of the projectile.
For instance, knowing the velocity change of the projectile in air, we can calculate the acceleration (or deceleration)
of the projectile as a result of air resistance. If we use this along with the
mass in Newton’s formula, we can see how much, in terms
of force, the air resistance is.