# Physics of Catapults Essay

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The ballista, or "shield piercer," was first developed by the Greeks using the same principles as a bow and arrow. Its primary use was to, as the name suggests, pierce enemy shields, since normal bows lacked the power to do so. Early versions of the ballista include the gastrophetes, which is nothing more than an enlarged bow that can be braced against the users body. http://members.lycos.nl/onager/GastrophetesPic.jpg
As time went on ballistas were improved to become larger and more powerful, eventually becoming mounted mechanisms that could be operated by two or more people. The Romans eventually modified them to throw stones, making them more effective in seiges against walled
Using this relationship assumes that the force constant is constant, or that moving the arms back 2 meters gives twice the force that moving them back 1 meter would do, which is most likely not correct, but close enough for a general assumption of the force to be made. When the force is applied, the projectile is accelerated to the end of the ballista, at which point it released with a velocity v and an angle q from the horizontal. The velocity can be found using the kinematic equation v2=2ax, where a is the acceleration and x is the length of the ballista that the projectile is accelerated upon. Since F=ma and F in this case is -kd, the equation can be simplified into v2=2-kdx/m. After it is released, the projectile obeys the laws of projectile motion, disregarding air resistance. Therefore, the range of the ballista can be given by the equation
R=v2sin2q/g,
where g is the accleration due to gravity.

Mangonel History

The Romans, finding the ballista difficult to construct, simplified the design and created the onager. It had one arm instead of two, and is what is most commonly identified as a catapult today. http://members.lycos.nl/onager/OnagerPic.jpg
During the Dark Ages, the French were able to re-invent the onager, and they called it the mangonneau, and it became known in England as the mangonel.

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