Trebuchet Physics
Jason Hoisington
Phys 212
3/21/05
    The trebuchet is powered by means of a counterweight, which when allowed to fall rotates the arm and throws the projectile.  When the counterweight is lifted a height h above the ground, has a potential energy given by the equation
U=mcgh,
where mc is the mass of the counterwieght and g is the acceleration due to gravity.  This is converted to kinetic energy of the projectile, given by the equation
K=mpv2/2,
where mp is the mass of the projectile.  Once released, the projectile will have a range R given by the equation
R=v2sin2q/g,
where q is the angle from horizontal that the projectile is released at.  The maximum range is found at 45°, which makes the range
Rm=v2/g. 
Since the potential energy of the counterweight and the kinetic energy of the projectile are the same, the equations can be rearranged to
v2/g=2mch/mp. 
Since v2/g is the maximum range,
Rm=2mch/mp.

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