Proof of Efficacy Document

Our design of our trebuchet consisted of

• Two 40cm long legs on each side.

• A base of 25 cm by 36 cm (total area base of 900 cm square).

• An axle of 30 cm long, with a diameter of 1.1 cm.

• An arm length of 59 cm.

• 9 rubber bands used to pull down the arm.

• A screw 2 cm long, halfway screwed in to the base, used to hold the rubber bands.

• A screw 2 cm long, used to hold the projectile (the ball we launched).

• The projectile: a ball with a diameter of 3.5 cm and a string attached around it that is 11.5 cm. The clay ball has a mass of 35.15g.

For our assignment we had to try and make it the trebuchet the best we possibly could. Each group experimented on a certain part of their trebuchet (arm ratio, amount of rubber bands, mass of ball, etc.) to see which one worked the most efficiently. We then had to make eight changes to our trebuchet that other groups had said worked the best.

Our seven changes are listed below:

1. MORE RUBBER BANDS: We decided to add 9 rubber bands to our trebuchet instead of one. The ball launched with nine rubber bands had a much higher average distance than the ball launched with only one rubber bands. We added more rubber bands because more rubber bands have more PE, and more PE means more KE is transferred into the clay ball. This means that more distance is covered, when the ball is launched.

2. 7:5 ARM RATIO: A 7:5 arm ratio ended up going the farthest distance after trying a 2:1 and 1:1 arm ratio. When using a 7:5 arm ratio the rubber bands had the max amount of PE, which created the max amount of KE. The more KE the farther the ball goes, which is why the ball went the farthest with a 7:5 ratio.

3. USING COPPER: We changed our arm from wood to copper because it is lighter which allows all the PE to be transferred to the ball. This lets the ball go the farthest, but when we tried it our group got different results. The ball did not go nearly as far as it did with the wood as an arm. In the end we ended up changing it back to wood because that worked better for our machine.

4. HORIZONTAL AXIS: When the axis is tilted the arm will hit the sides which causes tension. That slows down the speed and distance of the ball. We changed out axes to make sure it was almost perfectly horizontal. This allowed the arm to have a clean launch every time, meaning it would not hit the sides and get slowed down.

5. RUBBER BANDS UNDER AXIS: We moved the rubber bands from the end of the base to right under the axle. This would create more tension in the rubber bands which means more PE. The more PE the farther distance the ball travels. When we tested this our ball ended up not going as far as it went before and we changed it back to the end of the base.

6. 30cm STRING: We changed our once about 10cm string to 30cm around the ball. This should have created the most amount of force but ended up throwing the ball up high and a short distance. After a couple of tests, we changed it back to a 12cm string because the ball went farther a farther distance with that string length.

7. STOPPER: We added a stopper to stop the arm from throwing the ball down towards the floor. Though the more we watched our trebuchet launch, it become clear that the ball was launched before hitting the stopper. Therefor, the stopper had no effect on the machine and was not useful, so we took it off.

Here is my Clear Paragraph explaining in detail about why a 7:5 arm ratio works the best.

For a trebuchet, we discovered that the ball goes the farthest with a 7:5 arm ratio. We created a trebuchet and then tested what the best arm ratio would be. We tested three ratios, 2:1, 7:5, and 1:1. For each ratio we held three tests to see how far the the clay ball was launched. The average trial numbers of the 2:1 and 1:1 ball were both less than the average distance of the 7:5 ratio. This show that the 7:5 ratio works the best, because with this arm ratio the ball’s average distance traveled was the highest. For the 2:1 ratio the trial numbers were 26m, 28.75m, and 24.5m, with an average distance of 26.4m. The 1:1 ratio has three trial numbers of 25m, 25m, and 21.5m, with an average distance of 23.8m. The 7:5 had three trial numbers of 26.6m, 33m,and 25m, with an average distance of 28.3m. This shows that the arm ratio 7:5 will result in the farthest distance because it had the highest average distance. With a 7:5 ratio the PE of the rubber hands is the highest, which maximizes the KE, allowing the ball o go the farthest. Overall for a trebuchet the ball will go the farthest when using a 7:5 arm ratio.

Technical Specifications:

• Mass of Projectile: 0.035kg

--> This is the weight of the projectile we used to launch in our project.

• Horizontal Distance: 26 meters

--> The total distance the projectile traveled after we launched it. We tested it a couple times but ended up getting a final average of 26 meters.

• Time In Air: 1.8 seconds

--> The total time the projectile stayed in the air from the second it was released till when it hit the ground.

• Vertical Distance: 16 meters

--> To solve for the vertical distance we used the formula (d = 1/2 a t^2). We then plugged in the values of the acceleration due to gravity and time to get (d=½(9.8m/s^2). Giving us a total of 16 meters. Our vertical distance showed that our projectile got launched higher in the air rather than farther horizontally.

• Horizontal Velocity: 14.4m/s

--> The formula for horizontal velocity is (v = d/t). When you plug in our numbers you get (v=26m/1.8s). This then gives a total velocity of 14.4m/s. The horizontal velocity showed us how quickly the ball moved horizontally though the air.

• Vertical Velocity: 17.6m/s

--> The formula for vertical velocity is (v=at). We took the acceleration due to gravity then multiplied it by the time the projectile was in the air to get (v=9.8m/s^2(1.8s).That ends up being 17.6 m/s. This shows us how far our ball rises and the speed it rises at.

• Total Velocity: 22.7m/s

--> We used the pythagorean theorem to find the total velocity. Using (a^2 + b^2 = c^2) we plugged in our numbers to get (14.4^2+17.6^2=c^2). Then took the square root of both sides. (√517.12=c^2). We got a total velocity of 22.7m/s. This is 49 miles per hour.

• Release Angle: 51 degrees

--> Using the formula (tan x = vvert/vhoriz) we were able to plug in our numbers

(x= tan^-1(17.6m/s/14.4m/s) to get a release angle of 51 degrees. The release angle is the angle the arm is at when the projectile is released.

• Spring Constant: 420 N/m

-->We used the formula (k=F/d). Taking the force of 4.9N and mass of 0.105kg to get

(k= 4.9N/0.105m). We then took that number multiplied by 9 because we had nine of the same rubber bands (k=46.7N/m(9). This gave us a final spring constant of 420N/m.

• Initial Spring Potential Energy: 11.10J

--> Using the formula (PEspring = ½ k x^2)we were able to calculate the spring potential energy. Plugging in the spring constant and the distance changed of the rubber bands while pulling them we got (PEspring= ½(420N/m)0.23m^2). To get the distance of the rubber band we measure the length of the rubber bands when just hanging from the trebuchet, then the length of the rubber bands when the arm is stretching them. Then subtracted the two lengths from each other to find the distance changed. This gave us a final spring constant of 11.10J.

• Kinetic Energy of the Ball: 9J

--> The formula for kinetic energy of the ball is (KE = ½ m v^2)> plugging in the mass of 0.035kg multiplied by the total velocity of 22.7m/s we got (KE=½ (0.035kg) 22.7m/s^2). Which ends up equaling 9J.

• Percent Energy Converted: 81%

--> We used the formula (KE/PE) to find the amount of energy converted. With the numbers plugged in we got (9J/11.10J) which equals 81%. This seems high but because our arm was so light that caused most of the energy to be converted to the ball, rather to other energy such as friction.

Main Points of Design:

• Our trebuchet launches the ball a good distance of about 25 to 30 meters.

• The energy transfer is high which shows we did a good job converting most of our energy to the ball being launched.

• The trebuchet has been modified to work the most effectively it can and keep firing at a consistent distance.

• It is easy to use and does not take a lot of time to set up.

Overall our trebuchet has been changed to work the most efficiently it could and stays consistent. It is easy to set up and fires a good distance distance every time. If I had to change something else I would probably make the ball smaller to increase the distance. Overall everything else worked pretty well and consistent each launch.

Reflection

Overall this project was more difficult than the others. A lot of our time our ideas did not work and we were constantly having to redo our work. Especially when we made our trebuchet worse when trying to make it better. This often caused all to get a little frustrated with ourselves and teammates. If I had to do something better it would be to stay positive and not get frustrated, even when things do not go our way. This would have helped my teammates and me get more work done because we would have been working on fixing the problem rather than being frustrated with the problem.

Looking at the positive side, all these problems helped our team get very creative and learn to work through issues. I think our ability to be able to think of new ideas and apply them to a project in a short period of time was a strength of our team. When something did not work, we all came together to create something that did. If that did not work we would keep going until we found something that did. This helped bring out our creative mindsets and how we work well under pressure.