Have you ever wondered how a catapult works? We had to ask just that question when we were assigned a project. Where we had to create a functional catapult and graph the arc of the object shot from the catapult we created. In this essay I will discuss the history and mathematical concepts behind catapults. I will also include some fun facts.
There are many mathematical concepts behind a catapult. One big mathematical concept behind a catapult is a parabola. A parabola is defined as “a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.” A parabola is the shape of the arc made by the object launched. Sense the arc is a parabola not only will the curve of the object going up be same as it going down but, the arc can also be graphed.
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It depends on the angle it is shot at because if the angle to low or high it will have a very short range. It depends on force because the more force applied to shoot it the farther it will go and the less force you apply the less range you will have. Another thing that will affect the range of our catapult is the tightness of the rubber bands. If they are to tight won’t allow the catapult to be pulled back and spring forward. If the rubber bands are too loose they won’t hold it together and the catapult won’t be able to spring back like it’s supposed to. The angle also plays a crucial role in the range of a catapult. If the catapult is at to high of an angle it will shoot directly at the ground. If it is at to low of an angle it will shoot directly up into to the air. Both things will cause a drastic decrease in
To fire it, the spoke or arm was forced down, against the tension of twisted ropes or other springs, by a windlass, and then suddenly released. As the sling swung outwards, one end would release, as with a staff-sling, and the projectile would be hurled forward. The arm would then be caught by a padded beam or bed, when it could be winched back again. The Onager is usually the first type of catapult
Compared to the trebuchet, the designs of other siege weapons were lacking in many respects. The most important of these other siege engines included the Greek ballista, the catapult, and variations on the catapult design, such as the Roman onager and mangonel. The ballista's design was very similar to an extremely large crossbow with a guide chute to keep the projectile on path. A large ballista could launch an eight pound stone over 450 yards. It took two men to operate a ballista (Hamper). A standard catapult used the inconsistent strength and weight of men as a source of power. Groups of men had to work to pull down the catapult bar in order to launch the objects. Such catapults could typically throw as much as a fifty pound rock. An onager was type of a catapult with a short arm that would be launched forward by many twisted sinews. Both the onager and the ballista were limited in accuracy and range, because the tightly twisted sinews and ropes continually wore out and needed to be replaced. Likewise, the standard catapult lacked accuracy because of the inconsistent strength and weight of the men who fired it. While all of these siege machines were useful, none of them had the range, or were as powerful, accurate, and widely used as the trebuchet (Gurstelle 18-22).
A trebuchet is a siege weapon most commonly used in the middle ages. It uses gravity to propel an object. There are competitions held today called "Pumpkin Chunkin '" which use trebuchets to launch pumpkins as far as possible. The common question is what the dimensions should be when making it. Should the arm be longer or shorter? Should the counterweight be heavier or lighter? These questions have been asked by competitors in trebuchet competition as well as engineers. And this is why the project is in the field of mechanical engineering.
As the kicker steps forward and swings his/her leg back and then forward, contact with the football is made. The kicker kicks the football with the intention of the ball making it through the goal posts, which would result in either one (for an extra point) or three points (for a field goal). The kick is another example of a force. A great force is exerted on the football, causing it to accelerate and travel a distance (Newton’s first law of motion). Also, the football exerts the same force back on the kicker’s foot (Newton’s third law of motion). The kicker tries to kick the football about one-third of the way up the football (towards the bottom) so that the ball will travel high enough to get over the defense and high enough to maximize the distance. When the kicker hits the football, it is another example of an inelastic collision in which some of the energy is transformed into sound. The flight of the football can be described as projectile motion.
Trebuchets are most commonly known as medieval weapons used in the Middle Ages. Us three were to build a smaller scale of the trebuchet and had to make sure it hit the target two out of the five times. We had to build a hinged-counter weight type of trebuchet with wheels that could throw a ping pong or golf ball. Through the paper I will explain the history throughout trebuchets and why to have wheels and to have a hinged counter weight on the trebuchet. Also the calculations on the potential energy and velocity are through this report. Our trebuchet met all of the requirements that were to be made and it hit the target three out of the five times. This report will
Since the beginning of time, ancient civilizations have used technology for multiple purposes. It is known that Ancient Civilizations, like the Mongolian Empire, have created weapons to protect their empire. Guns, swords, and bows are some examples of weapons that have been used by major empires but it is also known that civilizations had other forms of technology that were not so advanced. Catapults are one of the oldest from of warfare weapons that have been used for the capture of territories. The greatest have taken part in the magnificents of a catapult. Throughout history, catapults have advanced through different empires and can be explained through multiple theories that were created by some of the most fascinating Scientist/ Physicist in the world.
The purpose of this experiment was to determine if rubber bands or bungee cord would put more force into the launch of the catapult. The experiment was designed to test the hypothesis if either a bungee cord or rubber bands would help an eraser to launch further, because of more force.
The physics concepts associated with them are projectile motion, energy, momentum, forces , speeds, and distances. The kinds of catapults all use the same theme of accumulated tension, but acquire that tension in their own way, their own design. The Mangonel catapult for instance, is what most of us think of as the traditional catapult. A large wooden device with four wheels and a spoon that launches fireballs. The Mangonel stores energy much like a spring would, therefore, we use the equation PEspring = 1/2kx^2. The tension in the ropes and arms of the catapult when pulling on its long arm stores potential energy which is transformed into kinetic energy when fired upon.
After all of the groups finished SketchUp we had to build a .33 scale model of the trebuchet we designed. Our group was way behind so there was not enough wood for us to build our model.
Altitude is another factor you have to be aware of. If there is a lot of wind the ball will travel to the side, reducing the distance the ball travels. If the wind is at a low speed the ball will travel much further. The higher the altitude there is less dense air. Density is the amount it weighs or how much mass is in it. If the air is denser the ball will have to struggle to travel through it. The less dense air allows the ball to travel further. When you are closer to sea level the ball will travel less of the distance.
The trebuchet catapult was one of the oldest catapults ever used in war. It's projectiles were mainly heavy rocks or sticks. When launched, this catapult could deal enough damage to knock down buildings, walls and other catapults. The trebuchet was designed on a T shaped frame with a long staff in the middle and another across the top. One end of the top shaft had a counterweight and at the other end was a basket that held the projectiles.
The purpose of the lab is to find a projectile’s horizontal velocity and make comparisons of the effects of different inclined planes with the projectile of a ball.
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
On October 31st, we finally shot up our rockets. Some of the rockets went well as we predicted; some others did not. Our rocket was launched three times in total, and out of all three, only one launch managed to get the parachute out when it was needed. In this report, I am going to write about what relationship the rockets have with Newton’s three laws we have been studying lately. I will connect each of Newton’s three laws with the rocket launches we had.
The Magonel is the most common catapult. It comes from the Latin word “manganon” meaning engine of war. It was invented in 400 B.C by the Romans. This catapult was extremely strong and accurate. It was capable of firing up to 1,300 ft. based on the angle it was placed. This catapult was easy to build and travel because wheels were added to the