Our main task was to create a trebuchet that launched a 10 gram projectile as far as it could.

Pictures of final project

Proof of Efficacy Document for Trebuchet

By Natalie Davila

Our project was to create a trebuchet/catapult to latch a projectile the farthest distance we can.

Our measurements/design

Base Board: 11x12 inches

Cup: 7cmx3cm

Legs: 34.5cmx9cm

Axle: 6inx0.5cm

Arm: 31inx.3.5in

Our 8 modifications we decided to do

Modification 1- Number of rubber bands

We wanted to see how many rubber bands worked the best. We found that 4 rubber bands were the most efficient for us. We found that having more rubber bands (PE) would make our trebuchet go a shorter distance.

Modification 2- Stopper VS No Stopper

We tested and came to the conclusion that having stopper made our trebuchet more efficient. Having a stopper creates more momentum and allows our projectile to go a farther distance. The stopper we chose was rubber band rather than wood because wood made our leg stop right away while the rubberband stopper lets us stretch it more.

Modification 3- Rubber Band placement

We changed the rubber band placement and placed the rubber bands in front and between the legs was the most efficient than placing them in the front of both if the legs because it allowed us the pull out our arms farther creating more momentum.

Modification 4- Mass of projectile

We decided to make our projectile 10 grams because according to class data 10 grams worked the best. 10 grams worked the best because it was light but not to light that the air resistance slowed it down.

Modification 5- Cup size

We found that using a cup that is 7 cm worked the best because it was not too big but not to small. The cup we used put the right amount of force on our projectile as it launches.

Modification 6- Leg Placement

According to class data the leg placement did not make a difference. We put our legs closer together because of the size of our axle.

Modification 7- Cup VS String

According to class data the cup was more efficient. We decided to use the cup as well because it worked the best for us.

Modification 8- Projectile Shape

We decided to use a sphere because a sphere is the most efficient because it has less surface area than a cube and the rectangle.

Calculations

Mass of our projectile: 10 grams

Time in the air : 0.79 seconds

Horizontal Distance: 18 meters

Horizontal Velocity:

Dh/T

18/0.79= 22.7 m/s

Vertical Velocity

Agtfall

(9.8m/s)(0.34s)= 3.32m/s

Vertical Distance

1/2at2

1/29.8(0.34s) 2

4.9 x 0.1154 = 0.567 m/s

Total Velocity

Vv2+ hv2

3.32(2)+ 22.7(2)

11.0224+ 515.29= 526.3124

23m/s

Spring Force

For 1 rubberband= 75.4n/m

For all 4 rubber bands= 301.6n/m

PE Spring= 7.3 J

Kinetic Energy: 27 J

Percent Of energy transferred: 37%

Release Angle: 15 degrees

Main selling Points of our design

• Our trebuchet stays in a 1 meter bubble

• Our trebuchet always goes over 10 meters

• Our greatest distance was 18

Trebuchet Calculations:

Vertical Distance: 0.57 meters or 1foot and 10.441 inches

dv = ½ at fall²

dv= ½ (9.8)(0.34²)

dv=0.56644 or 0.57 m

Horizontal Velocity: 22.78 m/s or 50.957 mph

Vh= dh/Tair

Vh= 18m/0.79 s

Vh= 22.78 m/s

Vertical Velocity: 3.33 m/s or 7.449 mph

Vv= agtfall

Vv= 9.8(0.34²)

Vv= 3.33 m/s

Total velocity: 23 m/s or 51.45 mph

Vt= a²+b²=c²

22.78+3.33 m/s=c²

518.9+11.1=c²

530 square root = c² square root

c= 23 m/s

Angle Release: 15 Degrees

Tan 0= Vv/Vh

Tan 0= 3.33/22.78

Tan 0= 0.146

<)= 15 Degrees

Spring Force (k): 75.4 N/M or total is 301.6 N/M

Number of Rubber Bands

Single rubber band from trebuchet:

K=F/d

K=4.9/0.065 9.5 cm to 16cm

6.5 cm to 0.065

K=75.4 N/M

75.4(4)

Total Rubber Bands= 301.6 N/M

PE Springs:7.3 J

PE spring= ½ Kx²

PE= ½ (301.6 N/M) (0.22m²)

PE= 7.3 J or 7.29 J

KE= 27 J

KE= ½ m ballVtotal²

KE= ½ (0.001kg) (23²)

KE= 2.645 J

KE= 2.7 J

% efficiency= 37%

% efficiency= KE/PE

% efficiency= 0.7/ 7.3

% efficiency= 0.369

% efficiency= 37%

Reflection

Two things I did well in this project was that I listened to my group and I was very open to new ideas. Something I did very well was that listened to my team and their ideas. Even though I had a different approach to the project, my group and I worked together to combine our ideas to create our final project. I also made sure to not let down any of my teammates ideas and made sure to make their ideas feel included. Something I want to work is leadership in the group and getting more hands on with the project. I feel like I let one of my teammates take over the building process and I did not really touch the project till it was finished and time to take calculations. I also want to have more of a voice in the group and make sure all of my ideas are heard. Overall I really enjoyed this part of our 2 part project.