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Design
Design
Our design was based on a trebuchet, consisting of a base measuring 8.75 in x 10 in, 2 legs measuring 3.25 in x 17 in, an axle measuring 8.5 inches across the legs, a stopper block measuring 12 inches, and a load-effort arm measuring 13 inches. Our individual pieces and entire trebuchet was held within 1 meter, allowing a medium-sized catapult to be made. Throughout this project, I incorporated two different models that held a few different keys. The origin model focused on a single variable, the position of the projectile, that we experimented on to conclude on the most optimal choice. Secondly, we utilized a number of variables that would be implemented into our trebuchet, allowing us to create an efficient, effective launching device.
Selling Points
Selling Points
Consistency: Our trebuchet can consistently launch the projectile to the same distance over multiple trials, which allows it to be used more often with similar results
Easy to Handle: Our trebuchet is small, simple, and easily usable, making it user-friendly and approachable to almost anyone. The mechanics of the machine are simple to understand and activate.
Effective/Efficient: Our trebuchet holds durable pieces and mechanisms, which allow it to perform a fluid release, which is efficient in its launch and effective in its resulting distance.
Powerful: Our trebuchet holds thick, strong rubber bands, which allow the machine to push more force onto the arm during the release. Alongside the stopper, the force applied to the projectile will be launched during its maximum point.
Single Variable Experiment
Single Variable Experiment
This experiment was presented in a powerpoint presentation, which showed a table of 4 different changes to the variable, each holding 3 trials. Additionally, we created a claim, saying that the most optimal position of the projectile would be at the top of the arm. This is supported by our graph that was created using the individual data points, while also having an analysis with more accurate reasonings based on physics concepts.
8 Variables of Change
8 Variables of Change
Number of Rubber Bands -- Rather than having a single rubber band, we attached 4 rubber bands to our trebuchet's arm, allowing my tension to be active, resulting in a greater force applied. When more tension was applied to the pull-back of the arm, the spring constant increases with the greater force and distance, which also increases the Spring Potential Energy in our launch.
Material of Axle -- We implemented a more rough axle into our design. This allowed a more balanced, consistent spin of the arm on the axle, which resulted in a more fluid release. Additionally, the ridged edges to our screw axle held a strong grip on the arm with the friction, which helped with the launch.
Moment of Release -- In order to obtain the most optimal height, the arm must release the projectile at the closest angle to 45 degrees, as this will launch it the furthest in a parabolic arc. For this to happen, we placed an additional block of wood at the end of our legs, which measures 12 inches. This allowed the arm to hit the block, causing it to stop and release the projectile at that point. This angle was 13.44 degrees off of the 90 degree point.
1:4 Arm Ratio -- Having a 1:4 arm ratio keeps a balance between the load and effort sides to the arm. As the total length of the arm is about 13 inches, the ratio between the axle and arm will be 2.6 inches to 10.4 inches. Knowing that Fd=Fd, we can see that the force applied to the force will be increased as the load as we apply a force of effort to the shorter side.
Position of Projectile -- Having the cup placed on the top of the arm will result in the furthest distance traveled. As the arm swings around following the release of the pull-back, the projectile will follow that motion and velocity. Once it reaches the point of release, the placement of the cup on the top will allow the projectile to exit the cup with a motion upward. Additionally, we can say that the cups higher height will result in a high maximum height and longer air time. Also, the higher position will result in an earlier release, which reduces the friction with the cup during the moment of release.
Position of Rubber Bands -- Having the rubber bands placed higher to the arm will result in a reduced stress on the rubber bands, allowing it to be used more consistently and effectively with similar results. Additionally, having the rubber bands higher allows us to connect it to the ground and the arm from the same point, which increases the tension within half the rubber band, causing more force to be applied to the arm on the effort side.
Thicker Rubber Band/Increased Pull-Back -- Having thicker rubber bands results in efficiency and effectiveness. This is because the rubber bands become more durable, which allows us to use it more often while avoiding the rubber ripping or becoming over-strained. Additionally, we added more pull-back distance to the effort, which adds more force to the arm. Using F=ma and the proportional relation between force and acceleration, we can say that the increased force due to the increased pull-back will result in an increased acceleration and further distance traveled.
Lighter Projectile Mass -- The lighter mass of the projectile allows it to travel further with the force applied during the release. Using F=ma, we can say that mass and acceleration are inversely proportional, meaning that the lower mass results in the higher acceleration in the force of the launch. This lowered mass and increased acceleration will allow the projectile to travel the further distance in a smaller amount of time.
CONTENT
Mass of Projectile -- the mass of the projectile is present in F=ma, causing the acceleration to increase or decrease when it is inversely proportional to the force
The mass of our projectile was taken from a small clay ball that covers the size of a quarter, meaning that the projectile had a mass of 0.01 kilograms.
Horizontal Distance -- the total distance traveled would be the horizontal distance, we is all dependent on the velocity and time during the fall
The horizontal distance varied between different positions of the trebuchet. Firstly, when the machine was placed at a height of 0.9 meters, the projectile traveled a total distance of 15 meters. However, when the catapult was placed at no added height, it traveled a distance of 6.56 meters.
Vertical Distance -- the vertical distance is the maximum height achieved, which can determine the factors of air resistance and air time during the projectile's arc
The maximum height achieved is the same as the initial height of the projectile since the projectile travels in a downward angle for our trebuchet. Knowing this, we can say that the maximum height is 0.7 meters, which is the height of the catapult itself. If we kept the machine at an additional height of 0.9 meters, then it would be held at a maximum height of 1.6 meters.
Time in air/Time of fall -- the total time in air can correlate to how far the projectile traveled and how fast it traveled that distance
Since our trebuchet launched the projectile downwards, its time in air is equivalent to the time of fall, being 0.4 seconds.
Horizontal Velocity -- the horizontal velocity determines how fast an object is traveling towards the destination directly, which can influence the time in air and distance traveled
We used our time in air (0.4 seconds) and the total distance traveled (6.56 meters) to get a horizontal velocity of 16.4 m/s.
Vertical Velocity -- the vertical velocity is the second component of speed that travels downward on our projectile during the launch, which is initiated by gravity
We used our time in air (0.4 seconds) and the acceleration due to gravity (9.8 meters per second squared) to get a vertical velocity of 3.92 m/s.
Total Velocity -- the total velocity is the velocity in the direction of travel by the projectile, which is determined by the vertical and horizontal velocities
Using the vertical velocity, horizontal velocity, and the Pythagorean Theorem, we found the total velocity to be 16.86 m/s.
Angle of Release -- the angle of release determines the direction at which the projectile will travel, which can be determined by using trig functions on the velocity vectors
Using the horizontal velocity, vertical velocity, and the unknown angle within, we can say that tan(x) = 3.94/16.4, meaning that the angle of release is 13.44 degrees off the 90 degree split.
Spring Constant -- the spring constant determines how strong and stiff the tension is within our rubber bands, which can add more force onto the arm when stretched
Using the force applied (20 Newtons) and the distance stretched from the rubber band (0.04 meters), we calculated the spring constant to be 500 N/m.
Spring Potential Energy -- the initial spring potential energy gives us the energy ready to be released through the stretch of the spring
Using the spring constant (500 N/m) and the distance of the rubber band's stretch, we calculated the spring potential energy to 8.1 Joules
Kinetic Energy -- the kinetic energy shares the energy built up during the travel of the projectile across the parabolic arc
Using the mass of the projectile and total velocity of the projectile, we calculated the kinetic energy to be 1.42 Joules
Percent of Energy Conversion -- the energy conversion determines how much of the energy is translated into the next form of energy
Using the kinetic energy and the spring potential energy, we can divide the two to get a percentage conversion of 18%.
REFLECTION
Throughout this project, I have improved on a number of concepts regarding communication, collaboration, and work ethic. Firstly, my communication and leadership skills have been challenged with the work I performed in this project. There were a number of instances where I was the active leader of the group, which required me to assign roles and communicate between each member of the group, telling them what they should and how they can do it. This also allowed me to take in more ideas from my members and organize them into a single concept for the machine. At the start of the project, I created a blueprint of the machine that could be used. Despite us not having enough time to follow the blueprint, I expressed my creativity and ideas through the concept of the machine.
Additionally, I was required to collaborate with my group members to give them roles and help them in each other there areas. This helped me understand my teammates perspectives and their own motives. While I improved on collaboration and communication, I also continued to show myself excelling in work ethic and determination. On the last day of our building day, our trebuchet broke. This required us to rebuild the entire machine, and despite my team members being discouraged by this, I continued to work with the most effort, which allowed us to create another trebuchet that launched our projectile a reasonable distance.
This project allowed me to improve on a number of things; however, I do believe that we could have done better on the design of our machine. If the original design did not break, we could have had larger, more stable materials, which would have improved our machines performance and result.
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