Mangonel Physics
Jason Hoisington
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 w2=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=v2sin2q/g,
where g is the acceleration due to gravity and q is the angle from horizontal at which the projectile is released.
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