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Introduction ☼ Method ☼ Results ☼ Discussion
Introduction
Designed to figure out how the trajectory of the slingshot must be changed to compensate for the different weights of the objects to reach the same distances.
The most common use for a trebuchet today is for entertainment, from pumpkin throwing contests to human projection. The original intent of the trebuchet stems from warfare. The main purpose of heavy siege machines was to hurl missiles over the walls of cities or castles. Trebuchets employ a strong yet lightweight arm with a sling full of ammunition, with a heavy counterweight. Along with the traditional stones being tossed, they also used “beehives, small stones burned into clay balls which would explode on impact like grapeshot bullets, casks of tar and oil on fire, dead animals introducing plagues and diseases, and finally prisoners of war and spies” (Hansen, 1998). The first recorded historical reference to siege weapons occurred “in A.D. 339 when a biographer states that Dionysus I, Tyrant of Syracuse, brought together engineers from all over the Mediterranean for the purpose of developing an engine of war powered by a large bow – requiring more power than one man could muster” (Hansen). There were many devices that were created and they can be divided into three main groups: ballistas, catapults, and trebuchets. As the successor of the catapult, the trebuchet was more accurate than previous machines. The effectiveness is evident as, “the first weapons using gunpowder were introduced to the theaters of war in Europe during the 14th century but it took another 200 years before they replaced the old engines of war completely” (Hansen). There are several important background pieces of information in the areas of conservation of energy, torque, and Newton’s laws of motion. The trebuchet operates changing potential energy into kinetic energy rapidly. By using torque, the counter weight is put up in the air with the projectile attached to the side on the ground with a string and pouch. After the trebuchets arm is release, the lighter side with the “missile” will rotate up into the air and the string will come off the pin and release the projectile.
Statement of the Problem:
The purpose of this experiment is to find the relationship between the mass of an object and its horizontal velocity when it is flung from a trebuchet.
Review of Literature:
Since there are so many different variable involved with trebuchets, we limited our research to those topics that pertain directly to the effect the mass has on the velocity of the missile. This, however, encompasses a wide range of issues. Firstly, there are two values that affect the horizontal velocity of a missile launched from a trebuchet: the horizontal displacement of the object and the time it takes to travel that distance. Therefore we will need to use the conservation of energy theorem, which states that the initial energy will equal the final energy. The kinetic energy of the missile at the point of release can be calculated from the initial potential energy of the counterweight, taking friction into account (Motz and Weaver, 1989). Another useful piece of information, pointed out by Gardner (1990), is that the ratio of force to acceleration measures the mass of an object. He also points out that since all masses accelerate down at a constant rate (due to gravity), the gravitational force on an object is proportional to its mass. Getting more specific, Miners (2004) points out on his website about trebuchets that since a heavier tends to pull the loop of the sling off of the pin sooner than a light projectile does, the heavier projectile will have a more arched flight than a lighter projectile if the same pin angle is used. On another website Radlinski (1996) lists the mass of the counterweight, the length of the counterweight arm, the length of the projectile arm, the starting angle, the angular acceleration, and the angular speed as other variable besides the mass that affect the performance of trebuchets. We will have to ensure that these remain constant throughout our experiment to secure valid results.
Hypothesis:
We believe that graphically (with mass as the independent variable and velocity as the dependent variable) our results will resemble a bell curve, with the extremely heavy and the extremely light missiles traveling the shortest distances. This is because the lighter masses will be influenced by air friction, and the heavier masses will be simply too heavy to throw. We will strive to find a medium in which the missile will travel the furthest. Mass is defined as the measure of the missile’s inertia. The velocity is defined as the velocity at the point of release.
Bibliography:
Gardner, Robert. Famous Experiments You Can Do. New York: Franklin Watts, 1990.
Hansen, Peter V. “War Engines of the Middle Ages.” Middelaldercentret 1998.
Miners, Russell. “How Do Trebuchets Work?.” The Grey Company Trebuchet Page.
2004 <http://members.iinet.net.au/~rmine/gctrebs.html>
Motz, Lloyd and Jefferson Hane Weaver. The Story of Physics. New York: Plenum Press, 1989.
Radlinski, Filip. “The Physics of the Trebuchet.” 1996.
<http://www.geocities.com/SiliconValley/Park/6461/>
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Method
Method:
When creating our ballista we created a unique feature in the front of it to allow for easy manipulation of the angle of trajectory that we were shooting at. When we began to collect our data we took the ballista to a large patch of grass at the high school so we could have accurate results with as little outside interference as possible. What we did was we set up the ballista to the specific angle that we wanted to test out for our 3 differently massed objects. We then did 3 trials at each weight to provide our data with enough stability to try and minimize our uncertainty and false data. Once each of the objects were shot at that set angle, we then readjusted the angle and began to once again take down data relating to the distance traveled of the objects. The below photograph shows our ballista that we used for measurement. If you look at the peak where the two sides meet you can see a hinge, this was used to change the angle of trajectory and give us an easy way of recording data.
Once the angle was set and the bungee cords had been retracted we released the cords and the ball was sent off the ramp and down the field. Before doing the trials we set up predetermined distances along the field that allowed us to more easily and accurately judge the distance that each object traveled. We felt that our methods of gathering the data were very efficient because we were able to simplify each process so that it had the least possibility for mechanical and human error.
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Results:
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Discussion
First and foremost, our hypothesis was only halfway correct. We predicted that a 45degree angle of trajectory would have the furthest launch distance of objects, regardless of mass. However, our data shows that the launches at 30degress went further than the other two angels. We figure that part of this could be due to wind resistance. When launched at 45degrees, the objects spent more time in air, therefore being pushed by wind longer. Judging by the fact that the distances for the 30 and 45 degree launches were similar, I would say that wind resistance is what kept the 45 degree launches from reaching further distances. The launches at the 60 degree angle went the shortest horizontal distance, as was expected. However, had our sling shot been more powerful, the 60 degree launches might have gone further, assuming the wind resistance was minimal.
Judging by the data we collected, upon further research, we would hypothesize that there exists an angle less than 30 degrees, which will launch a projectile a greater distance at that angle, than it could at 30 degrees. Some factors that we would need to be more aware of, and weren’t aware of in our experiment, upon further research, is that anything made by teenagers cant be that durable – and our project sure wasn’t 100% tough. It ended up launching lacrosse balls directly up, and a tennis ball directly backward towards the end of our time with it. This was due to the fact that our ‘sling’ was being weakened with every launch, and our launch arms were becoming unstable. A more sturdy structure would be necessary for a second research with a new hypothesis as discussed above.
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