Overview
The idea for this project was to create a trebuchet that could launch a projectile 5 meters or farther. Also the trebuchet could not be larger than one meter in length and width. The first thing we did in this project is to make a functioning trebuchet that could shoot at least a meter. Then afterward everyone got to choose one modification to their project in order to make it better. We had to record the results of the one modification and present it to the class. Afterwards, everyone chose eight modification that they were going made to their project. But if you’re project already had one of the modifications listed then it counts as one of your eight. Then after my group did that we did all the calculations for our trebuchet.
Calculations
Time in air: 1.34 seconds
Mass of projectile: 10.7 grams
Horizontal distance: The horizontal distance of our project is 20 meters and we got that answer by seeing where the ball landed and measuring how far it went.
Vertical distance: I used this equation to find the vertical distance. I plugged in .67 sec for t which is the half of the total time the ball took to hit the ground. For a which is acceleration I plugged in 9.8m/s^2. Then I solved for vertical distance and got 2.19 meters for the vertical distance.
Horizontal Velocity: So to solve for horizontal velocity I used the equation shown above. For the distance I plugged in 20 meters and for the time I plugged in 1.34 seconds and then I divided. After I divided I got Velocity Horizontal is equal to 14.92m/s.
Vertical Velocity: So to solve for this velocity I use the equation above to solve. Since acceleration due to gravity is 9.8m/s^2 I plug that in for that part of the equation. Then since I am finding the vertical velocity I use half of the total time for the time part of the equation which is .67 seconds. Then when I solved for velocity I got 6.56m/s.
Total Velocity: So to solve for the total velocity of the projectile I need to use pythagoras's theorem. For pythagoras’s theorem I plugged in the horizontal and vertical velocity for a and b. Then I just solved for c which is the total velocity. What I got for the total velocity is 16.32m/s.
Spring Constant: To find the spring constant we used the force of 9.8N because I used a 1 kilogram weight to find the spring constant. For the distance I used .045m for solving for k. Then I solved for k by dividing the force by the distance which is 217.7N/M.
Initial Potential Energy of Spring: To find the potential energy of the spring I used the equation above. For k I used the answer I got for spring constant and plugged it in. For the variable x I used the distance the spring stretched which was 33 cm or .33m. Then I just solved for the potential energy and I got 11.84 Joules.
Kinetic Energy of Projectile: To find the kinetic energy of the projectile I used the equation above. The variable which means mass is m. The mass of our projectile is 10.7 grams which converts to 0.0107kg. Then for v I plugged in the total velocity and solved for Kinetic energy. For kinetic energy I got 1.43 Joules.
Percent of Energy Converted: To find the percent of energy converted from kinetic energy to potential energy I just divided the kinetic by the potential. What I got for my answer was that only 12% of my potential energy was converted into kinetic energy.
Mass of projectile: 10.7 grams
Horizontal distance: The horizontal distance of our project is 20 meters and we got that answer by seeing where the ball landed and measuring how far it went.
Vertical distance: I used this equation to find the vertical distance. I plugged in .67 sec for t which is the half of the total time the ball took to hit the ground. For a which is acceleration I plugged in 9.8m/s^2. Then I solved for vertical distance and got 2.19 meters for the vertical distance.
Horizontal Velocity: So to solve for horizontal velocity I used the equation shown above. For the distance I plugged in 20 meters and for the time I plugged in 1.34 seconds and then I divided. After I divided I got Velocity Horizontal is equal to 14.92m/s.
Vertical Velocity: So to solve for this velocity I use the equation above to solve. Since acceleration due to gravity is 9.8m/s^2 I plug that in for that part of the equation. Then since I am finding the vertical velocity I use half of the total time for the time part of the equation which is .67 seconds. Then when I solved for velocity I got 6.56m/s.
Total Velocity: So to solve for the total velocity of the projectile I need to use pythagoras's theorem. For pythagoras’s theorem I plugged in the horizontal and vertical velocity for a and b. Then I just solved for c which is the total velocity. What I got for the total velocity is 16.32m/s.
Spring Constant: To find the spring constant we used the force of 9.8N because I used a 1 kilogram weight to find the spring constant. For the distance I used .045m for solving for k. Then I solved for k by dividing the force by the distance which is 217.7N/M.
Initial Potential Energy of Spring: To find the potential energy of the spring I used the equation above. For k I used the answer I got for spring constant and plugged it in. For the variable x I used the distance the spring stretched which was 33 cm or .33m. Then I just solved for the potential energy and I got 11.84 Joules.
Kinetic Energy of Projectile: To find the kinetic energy of the projectile I used the equation above. The variable which means mass is m. The mass of our projectile is 10.7 grams which converts to 0.0107kg. Then for v I plugged in the total velocity and solved for Kinetic energy. For kinetic energy I got 1.43 Joules.
Percent of Energy Converted: To find the percent of energy converted from kinetic energy to potential energy I just divided the kinetic by the potential. What I got for my answer was that only 12% of my potential energy was converted into kinetic energy.
Reflection
Even though building a catapult may seem pretty easy my group and I had some difficulty with making ours go some distances. At first my group and I we're thinking about using weights to pull down the catapult then fire it. But when we actually got to the building phase we changed from weights to rubber bands. When we were building it we were also having trouble with making the projectile go anywhere in our project. Then after that we had to make modifications to our trebuchet. But in the end we got our trebuchet to work so it was all ok.