Physics of a Trebuchet

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Trebuchet

A trebuchet is a medieval war machine that makes use of two simple machines: a lever and a sling. A lever was used because once on a pivot point it was able to throw projectiles with the most efficiency and accuracy. It performed consistently because of the counterweight which allowed it to deliver the same amount of energy. The sling was introduced to the trebuchet because it was able to double the speed of the projectile as it moves in a parabolic arc. Important factors to consider when building a trebuchet are the weight of the projectile, the weight of the counterweight, and the length of the arm.

The ideal trebuchet, in order to launch the projectile with the most energy would turn all of the initial potential energy into kinetic energy. This feat is impossible because of friction in the axle, the slide, the air resistance experienced by the projectile, rotational energy of the beam, and kinetic energy that is left over in the arm as it swings towards the ground after releasing the projectile.

Projectile Motion

The idea behind a trebuchet is to give a projectile energy without creating an explosion. Therefore to make an effective trebuchet, potential energy and kinetic energy must be calculated. The goal is to transform as much potential energy into kinetic energy as possible.

Potential Energy: PE=mgh

·         M= mass of counterweight (where the energy is stored)

·         G = force of gravity

·         H = height of the swing

Kinetic Energy: KE=½mv²

·         V=velocity of swing

·         M= mass of counterweight

To determine how efficient a trebuchet is, one must determine how much of the potential energy was converted to kinetic energy since this is the goal of the trebuchet. To determine the percentage, kinetic energy should be divided by potential energy and then multiplied by 100.

Gravity

The trebuchet functions due to the force of gravity. Gravity is needed to find both the velocity and potential energy because gravitation force is constantly pulling down on the projectile. This initially gives the projectile potential energy as it is raised off of the ground. Once the object is launched, it ultimately affects the distance the projectile travels as it acts to pull it closer to the ground.

Energy

            Potential energy is the amount of energy the object may produce depending on it position (often the position above the ground) and is therefore affected by height. While the water balloon sits in the swing and has yet to be fired, it possesses potential energy.

Kinetic Energy is the energy an object has because of motion. The water balloon will have kinetic energy after it is launched.

In a trebuchet, speed is gained as the arm loses height. Before a projectile is launched, the trebuchet has the maximum amount of potential energy and very little kinetic energy. When the arm is released it will reach a point at which it will experience maximum kinetic energy and low potential energy and will at this point launch the projectile. As the arm swings towards the ground, it experiences low potential energy but high kinetic energy.

According to the Law of Conservation of Energy, neither potential energy nor kinetic energy is lost. The trebuchet retains the same amount of energy while shifting its balance between kinetic and potential.

To measure efficiency in a trebuchet is to calculate how much potential energy is retained as the object gains kinetic energy. The more kinetic energy experienced by the projectile, the farther and faster it will go and therefore the more efficient the trebuchet (in its goal of inflicting mass destruction).  Other forces such as air resistance act to decrease the distance and speed of the object and therefore decrease the trebuchet’s efficiency. To make a trebuchet more efficient, one must decrease frictional forces by constructing the machine with materials that hold a low friction coefficient.

The sling of a trebuchet works almost like a pulley. In a pulley, less work is needed to lift an object if the distance is increased. A sling works in the same way by increasing the distance and therefore making it easier for the trebuchet to throw an object.

Momentum

Momentum is a mass in motion and depends on mass and velocity. It has both magnitude and direction making it a vector quantity. In a trebuchet, the momentum is conserved from the beginning of the swing to the throw of the balloon. The counterweight acts with a force equal and opposite of the arm and water balloon.

P = mv

Because increasing mass will produce greater momentum, using a heavier counterweight will be able transfer more momentum to the projectile and make it travel faster and farther.

Sources

"Unit 6: Trebuchet - SimoPhysics!" Web log post. Unit 6: Trebuchet - SimoPhysics! N.p., n.d.       Web. 13 May 2013.

 "Physics of the Trebuchet." Thinkquest.com. N.p., n.d. Web.