Fire Away!
Trebuchet is a machine built consisting of two arms, base, lever, axle, spring constant, projectile and screws that connect the spring constant from lever to base. Push the side that's up down, there's a nail at the tip where the string with projectile is at and will fling off. It'll fling off once it was let go of pushing down.
.
Trebuchet Physics; Calculations for my group's machine (each machine is different, so this is just what we got):
Mass of projectile is 0.011 kg. Horizontal distance is 12 m. Time in air is 0.44 seconds. To calculate vertical distance, need equation d= ½ a t ^2. Then plug in numbers and solve. d= ½(9.8 m/s^2)(0.44s)^2 ---> 0.94864 meters. To find horizontal velocity, use the equation v=d/t.Plug in numbers known and solve for the unknown variable. v=12m/0.44s----> 27.3 m/s. To find vertical velocity, the equation used was v=at. Then we plugged in numbers, v= (9.8 m/s^2)(0.44s) ---> 4.312 m/s. Calculating total velocity, equation used was a^2+b^2= c^2.Plug in numbers, (27.3m/s)^2+ (4.312 m/s)^2 to get total velocity as 27.638 m/s. Angle of release is 35* (*=degrees). The spring constant formula is k=F/d. We had to find force of rubber bands, we did two steps. F=ma=1kg(9.8m/s^2)=9.8N. Then we plugged in for force. k=9.8N/0.105m= 93.34 N/m. The initial spring PE is PE spring=1/2kx^2; 1/2(93.34 N/m)(0.21m)^2=2.058 J. The kinetic energy of ball is KE= 1/2mv^2; 1/2(0.011kg)(27.638m/s)=4.20122J. The percent converted is (KE/ PE; 4.201J/ 2.058J=2.04)= 204%.
Modifications
We changed the arms because previously it was shorter than the lever and it affected projectile being thrown because lever would hit base and not really get the projectile to land a good distance. We also moved the position of the arms to the top of the base and not on the sides. We changed the lever so it could be longer and a bit more thicker at width. We changed the string length to something a bit longer because we did it with something too short and it wouldn't fling off. So we got an 8" string. We also changed number of Rubber bands to two chains of two that way it would work better because with too much tension it will not work and with too little it will not work. The projectile positioned was changed, we realized after a while that it worked better with projectile in center of two arms before releasing and it getting flung. The projectile mass was modified to something light, but not too light so it could be easily swung. Height of axle on arms was moved a bit higher so lever will not hit base. Axle positioning on lever was in the center of lever so it would not hit base because before the modifications it would hit the base. Then it wouldn't get a good release angle that would work for our trebuchet so we modified it. We got the projectile to go a further distance after modifications.
Each team solved for one variable to fix/ study the best way to get it fixed, to help others and us so they could apply information to their trebuchet. We choose to see if shape of projectile matters, which is what the paragraph below is about.
CLEAR paragraph: Does shape of projectile matter?
In short distances the shape of the projectile/ object being thrown does not matter. We were testing if the shape of the projectile matters, we tested this by using a trebuchet that we built in two days. It did not launch far, so air resistance or any other factors did not have the chance to kick in. We tested by getting results from testing the distance traveled by the projectile in different shapes and comparing them. The shapes was a sphere out of clay and a cube out of clay, both shapes were around the same size. The results that we gathered for the sphere’s trials distances were 0.5 meters, 0.48 meters, and 0.5 meters. For the cube’s results we got similar results, the distances traveled were 0.54 meters, 0.46 meters, and 0.5 meters. We did 3 trials and got those results, the results are so similar leading to how come the shape of projectile in short distance does not matter. What is happening is that other factors have not really affected the shape of projectile yet because it has not traveled far for other factors to affect it like air resistance.
We made it in 2 days, we tested to find solution to one variable. Then we modified machine. Our design has been modified to work better and get projectile at further distance. We managed to get it (projectile) at further distance (by a good amount) after the modifications were done.
Reflection
We did really well, but I think we should have managed time more carefully. One downfall is that we found many ways that made the trebuchet not work as well as we would have hoped. The good part is we noticed our mistakes and fixed it in our modifications. We did really well, one thing is that if we needed help we should've asked sooner. We did ask, and it did help. We just should've asked for help on a few calculations. In the end, all was fine. The other downfall is that the video of the trebuchet working was somehow deleted so it was hard to find the angle of release and the distance it went with that.