Fire Away
The goal of this project was to design a trebuchet that could launch a clay ball as many meters possible. Our “client” was looking for a projecting device that will stay in one place and be reusable regardless of how many times you use it. It must have a base that sits on the ground, two legs that hold up an axle, and a lever arm with both a load and an effort end. The device must be easily portable by one person and have no dimension that is larger than 1 meter. During building everyone had to keep making modifications to make the ball go farther so every group in the class took one main restriction to see if the ball would go further or closer by testing different angles or lengths of the materials being used.
The original model had to have an arm, pivot point, counterweight, projectile holder, string trigger, hook, and a sturdy base. The modifications we made on our project were the angle of the nail holding the effort between 0-10 degrees backwards. We did this because the lower angle degree that the nail was the further the ball will fly, the lowest angle we tested gave us the farthest distance of 5.95 meters. We also changed from using weights to rubber bands for projecting the ball. The science shows using weights and rubber bands should have the same results since they are both equal to 10N (newton's.) The rubber bands are also much smaller and easier to attach to the arm because you can’t fit over 3 1kg weights on. We moved the placement of our nail that held the load to the side of the board for more force that would launch the ball even farther. The last thing we changed was the bar in between the 2 arms. We used to have 4 different sized sticks but we changed it to one wood bar because the multiple ones broke under too much tension from the rubber bands. To make sure the axle is even more study and it wouldn’t snap under pressure we wrapped rubber bands around the outside of the 2 arms which the axle is in between. We also modified the size of the ball from 4g-7g and the length of the string to 35cm-40cm. We did this because the air resistance is more effective on smaller masses, therefore it wouldn’t travel as far. But when the mass is larger, inertia is involved so it can’t travel as far either.
We had to find all the calculations of the ball like distance horizontal, time in air, velocity horizontal, velocity vertical, velocity total, release angle of projectile, spring constant, spring potential energy, kinetic energy of the projectile, and distance vertical. The ball’s distance horizontally was 28 meters and the time in air was 5 seconds. To find velocity horizontal you would divide 5 seconds from 28 meters to get 5.6m/s because the equation is distance over time. To get velocity vertical you multiply 9.8m/s by 2.5 seconds because the equation is at and the acceleration is always 9.8m/s and the half the time the ball was in the air was 2.5 seconds. The velocity total was 25.1m/s because the equation a(2)+b(2)=c(2). a= 5.6(2)+b=(24.5)(2)=c(2). 31.36+600.25=c(2). 631.61square root(2). c=25.1m/s. We used all these numbers from previous equations and calculations, for example a is from velocity horizontal, b from velocity vertical, and c is velocity total. We found that the release angle of the projectile was 77 degrees after measuring it and by doing the same with the spring constant with the spring measuring tool which came to 80N/m. To find spring potential energy you would use the equation ½(kx(2)), then you would plug in the numbers and multiply so it would come to ½(80N/m)(0.4m)(2). It would be 80N/m because that’s the spring constant and 0.4m because the tension of the arm was 40 cm. Then the equation comes to ½(80N/m)(0.16), multiply those two numbers= ½(12.8N/m) and half of 12.8 is 6.4J. To find the kinetic energy the equation is ½(mv)(2) m=mass v=velocity =½(0.007kg)(25.1m/s)(2) = 2.21kgm/s or J. The last calculation we had to find was the distance vertical. The equation was ½(ag)(t)(2), then plug in all the numbers= (9.8m/s)(2)(2.5s)(2) 9.8 is always the acceleration and 2.5 is half the time the ball was in the air. The distance vertical then comes out to 30.625m.
For our experiment we tried to figure out if rubber bands or weights was more efficient to launch the projectile from the trebuchet. We added numbers of rubber bands and weights and recorded our data to see which went farther and was more consistent. The rubber bands made the ball go alot further distance than the 1 kg weights. The rubber bands had more tension so the projectile snapped faster than it did with the weights. We couldn’t even test more than 3 of the 1 kg masses because they were so big. The results on how far the ball traveled with each were inconsistent due to other factors and some errors made in the building process. The rubber bands traveled 4m with one rubber band, 10m with two, 11m with three, and 15m with four. The weights didn’t travel as far and the results were very inconsistent but close to each other. With one 1 kg mass the ball traveled at 1m, with two it traveled 5m, and with three it went 4m. We could not test more than three because of the size of the masses. Overall the rubber bands distance consistently increased over time, unlike the weights was inconsistent but increased after more than one weight was added. The weights slowed it down by pulling the arm because they had a big mass. The science shows that using the rubber bands and weights should have the same results, since they both are equal to 10 newtons. In practicality that is not the case. The rubber bands are much smaller and easier to attach than the 1 kg masses and went at least 10m farther. We concluded that the rubber bands are more efficient way to set off the trebuchet.
The original model had to have an arm, pivot point, counterweight, projectile holder, string trigger, hook, and a sturdy base. The modifications we made on our project were the angle of the nail holding the effort between 0-10 degrees backwards. We did this because the lower angle degree that the nail was the further the ball will fly, the lowest angle we tested gave us the farthest distance of 5.95 meters. We also changed from using weights to rubber bands for projecting the ball. The science shows using weights and rubber bands should have the same results since they are both equal to 10N (newton's.) The rubber bands are also much smaller and easier to attach to the arm because you can’t fit over 3 1kg weights on. We moved the placement of our nail that held the load to the side of the board for more force that would launch the ball even farther. The last thing we changed was the bar in between the 2 arms. We used to have 4 different sized sticks but we changed it to one wood bar because the multiple ones broke under too much tension from the rubber bands. To make sure the axle is even more study and it wouldn’t snap under pressure we wrapped rubber bands around the outside of the 2 arms which the axle is in between. We also modified the size of the ball from 4g-7g and the length of the string to 35cm-40cm. We did this because the air resistance is more effective on smaller masses, therefore it wouldn’t travel as far. But when the mass is larger, inertia is involved so it can’t travel as far either.
We had to find all the calculations of the ball like distance horizontal, time in air, velocity horizontal, velocity vertical, velocity total, release angle of projectile, spring constant, spring potential energy, kinetic energy of the projectile, and distance vertical. The ball’s distance horizontally was 28 meters and the time in air was 5 seconds. To find velocity horizontal you would divide 5 seconds from 28 meters to get 5.6m/s because the equation is distance over time. To get velocity vertical you multiply 9.8m/s by 2.5 seconds because the equation is at and the acceleration is always 9.8m/s and the half the time the ball was in the air was 2.5 seconds. The velocity total was 25.1m/s because the equation a(2)+b(2)=c(2). a= 5.6(2)+b=(24.5)(2)=c(2). 31.36+600.25=c(2). 631.61square root(2). c=25.1m/s. We used all these numbers from previous equations and calculations, for example a is from velocity horizontal, b from velocity vertical, and c is velocity total. We found that the release angle of the projectile was 77 degrees after measuring it and by doing the same with the spring constant with the spring measuring tool which came to 80N/m. To find spring potential energy you would use the equation ½(kx(2)), then you would plug in the numbers and multiply so it would come to ½(80N/m)(0.4m)(2). It would be 80N/m because that’s the spring constant and 0.4m because the tension of the arm was 40 cm. Then the equation comes to ½(80N/m)(0.16), multiply those two numbers= ½(12.8N/m) and half of 12.8 is 6.4J. To find the kinetic energy the equation is ½(mv)(2) m=mass v=velocity =½(0.007kg)(25.1m/s)(2) = 2.21kgm/s or J. The last calculation we had to find was the distance vertical. The equation was ½(ag)(t)(2), then plug in all the numbers= (9.8m/s)(2)(2.5s)(2) 9.8 is always the acceleration and 2.5 is half the time the ball was in the air. The distance vertical then comes out to 30.625m.
For our experiment we tried to figure out if rubber bands or weights was more efficient to launch the projectile from the trebuchet. We added numbers of rubber bands and weights and recorded our data to see which went farther and was more consistent. The rubber bands made the ball go alot further distance than the 1 kg weights. The rubber bands had more tension so the projectile snapped faster than it did with the weights. We couldn’t even test more than 3 of the 1 kg masses because they were so big. The results on how far the ball traveled with each were inconsistent due to other factors and some errors made in the building process. The rubber bands traveled 4m with one rubber band, 10m with two, 11m with three, and 15m with four. The weights didn’t travel as far and the results were very inconsistent but close to each other. With one 1 kg mass the ball traveled at 1m, with two it traveled 5m, and with three it went 4m. We could not test more than three because of the size of the masses. Overall the rubber bands distance consistently increased over time, unlike the weights was inconsistent but increased after more than one weight was added. The weights slowed it down by pulling the arm because they had a big mass. The science shows that using the rubber bands and weights should have the same results, since they both are equal to 10 newtons. In practicality that is not the case. The rubber bands are much smaller and easier to attach than the 1 kg masses and went at least 10m farther. We concluded that the rubber bands are more efficient way to set off the trebuchet.