Fire Away!

Evidence of Work:

In this project our goal was to make a trebuchet of some sort and launch a projectile (clay ball) as far as possible. After launched with the distances and trials recorded and put into a data table, we were also asked to make some calculations. So my group and I took on this project and made a trebutchet, and although we did have some troubles when building the project, we ended up some descent results in our data. When we thought our project was finished we actually found out it was just beginning. We all as a class made a list of things that might improve our trebuchet's launches and each group tested out certain parts and changes. Our group had to change the positions of our arm length.

We tested at our arm length's at 3, 6, and 9 inches. Sadly the 9 inch one was a bit hard for us to test, because it was too big to wrap rubber bands around, but it worked just enough for us so that we could record our data. Our data ended up showing that the average for the 3 inches was 5.63 meters. The average for 6 inches was 11.88. And the average for 9 inches was 3.04 meters. So we concluded that our six inch mark was the best spot for our trebutchet. But noting that everyone's trebutchets are all different in size we converted our arm length's distance to a fraction, we told other groups to figure out where the 2/5 mark is on their arm and make their axle's there.

Content:

Our calculations are shown here:

Vertical distance: amount of covered distance in a vertical velocity. The equation for vertical distance is 1/2 times acceleration due to gravity times time to the power of 2.

d = 1/2 a t^2

D = ½ (9.81 m/s) (0.835 s)^2

d= 3.419888625 meters

d= 3.42 meters

Horizontal velocity: rate of covered distance in a horizontal direction. The equation for horizontal velocity is distance divided by time, and the unit is meters per second. We solved for the velocity of the projectile.

v= d/t

v= 11.8 m / 1.67 s

v= 7.065868263 m/s

v= 7.07 m/s

Vertical velocity: rate of covered distance in a vertical direction. This type of velocity is different because it relies on the acceleration due to gravity. The equation for vertical velocity is the acceleration due to gravity times time it took for the ball to reach its peak height (Ag (t)). The units are also meters per second. Like horizontal velocity, we solved for the velocity of the projectile.

v= at

V = 9.81 m/s (0.835 s)

V = 8.19135 m/s/s

v= 8.19 m/s/s

Total velocity: hypotenuse of the horizontal and vertical velocities. To solve for total velocity, you need to use pythagorean theorem. Pythagorean theorem is "a" squared plus "b" squared equals "c" squared. The units for total velocity are also meters per second.

a^2 + b^2 = c^2

(7.07 m/s)^2 + (8.19 m/s)^2 = c^2

49.9849 m/s + 67.0761 m/s = c^2

117.061 m/s = c^2

√117.061 = √c^2

c = 10.81947318 m/s

Total velocity = 10.82 m/s

Spring constant: measure of how rigid an object is or strength of spring. In our case, the spring was the rubber bands.

k= F/d

k = 9.81 N / 0.26 m d= 34 cm - 8 cm = 26 cm = 0.26 m

K = 2.5506 N/m

k= 2.5506 N/m (5)

k= 12.753 N/m

Initial spring PE: PE measured in the compression or the expansion of a spring

PEspring = 1/2 k x^2

PEspring = ½ (12.753 N/m) (0.26 m)^2

PEspring = 0.4310514 J

KE of ball: The energy due to motion. The unit for KE is joules (J), and this concept is closely related to PE because is the energy an object has before it falls, and KE is the energy an object has after it falls, so PE is transferred to KE. To solve for KE, you need mass and velocity, and the equation looks like this: KE=1/2 m (v v), or Kinetic Energy equation one half time mass times velocity squared. Once you plug your real numbers in, you can solve the equation.

KE = 1/2 m v^2

KE = ½ (0.0173 kg) (7.07 m/s)^2

KE = 0.432369385 J

Percent energy converted:

KE/PE

0.432369385 J / 0.4310514 J

1.003057605

Reflection:

I really enjoyed this project. Building was a little hard at times but it was still fun to do. Surprisingly in my last building project I didn't get to built most of it, so I was new to the building process in a way which made it a bit hard for me to do some of it, but I tried my best. So building was one of my struggles, and I also think another struggle I had was leadership in this project. I listened more to my other teammates. Specifically I wished I contributed to more ideas. But I think I did do well on other things during this project too. I think I contributed a fair amount and I cooperated. I also think I was good at being positive and keeping my team going. Overall this was a fun project and I learned a lot from it.