Mangonel
Physics

Jason
Hoisington

Phys 212

3/21/05

Phys 212

3/21/05

The mangonel works on
similar principles to the ballista, but since the projectile is
accelerated through a circular path rather than a straight one, the
laws of angular motion must be used. The tension in the ropes,
rather than applying a force, will apply a torque t
to the arm of the catapult, which will result in an angular
acceleration. This relationship can be given by the equation

t=Ia,

where I
is the moment of inertia for the catapult arm and projectile.
This accleration, when taken over the range of motion of the catapult
arm when firing, will result in an angular velocity w that can
be found with the equation w^{2}=2aq,

where q
is the
range of motion of the catapult arm. Once the projectile is
released, the velocity of the projectile is tangent to the circular
path it was traveling at the point it was released, and is equal to the
angular velocity times the length of the catapult arm, or v=rw,

where r
is the length of the catapult arm. Once released, the projectile
obeys the laws of projectile motion, which, desregarding air
resistance, give the range as

R=v^{2}sin2q/g,

where g
is the acceleration due to gravity and q is the
angle from horizontal at which the projectile is released.