Essay about Physics of Catapults

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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.
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 towns.

Ballista Design

The design of the ballista was fairly simplistic. The arms were mounted into twisted ropes, which provided the tension. The ratchet was used to pull the arms back, increasing the tension. A spear or rock was loaded onto the ballista, and the release pin was pulled. The tension on the arms pulled them forward, and the spear or rock was propelled forward by the rope in between the arms.

Ballista Physics

The design of the ballista is such that the force applied from the projectile comes from the tension of the twisted ropes. The ropes, when the tension is released, tend to return to their rest state with minimum tension, much like a spring would expand after being compressed. Using this similarity, the assumption can be made that the forces act in a similar way, and that Hooke's Law can be applied to give at least a general idea of the nature of the force applied by the bal...

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...en by the equation
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
where mp is the mass of the projectile. Once released, the projectile will have a range R given by the equation
where q is the angle from horizontal that the projectile is released at. The maximum range is found at 45°, which makes the range
Since the potential energy of the counterweight and the kinetic energy of the projectile are the same, the equations can be rearranged to
Since v2/g is the maximum range,


Serway, Raymond, and Jewett, John. Physics for Scientists and Engineers. Belmont: Brooks/Cole, 2004.

Macaulay, David. The Way Things Work. Boston: Houghton Mifflin Company, 1988

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