Janna+and+Cassie's+Trebuchet

=**Design Project:Trebuchet **= __ **Purpose**  __ To build an effective trebuchet using a counterweight that can obtain the highest score possible when placed in the equation P=d/ml. This assignment teaches us the applicable physics principles, and gives us hands on experience, which allows us to better understand these principles.

__**Applicable Physics Principles** __ A trebuchet is essentially a complex teeter totter that uses a counterweight, throwing arm and sling to project objects forwards. This involves too many physics principles to name, but a few of the major ones are outlined below.

** Newto ns Laws of Motion-  **An object in motion stays in motion, and object at rest stays at rest unless acted upon by an outside force. This is demonstrated by the counterweight acting on the arm which acts on the sling to begin the motion of the projectile. Once the projectile is released, there is no more propelling force acting on it. Gravity and air resistance are the force which brings it to a stop. F=ma is demonstrated by the acceleration upon the projectile, which can be changed depending on the mass and the force used to propel. For every action there is an equal and opposite reaction. This is demonstrated when the counterweight falls, and the opposite end of the arm is propelled upwards. This law explains the "teeter totter effect".
 * Centr ipetal Force- **  This is the force that holds the projectile in the sling until the moment that the sling is released.


 * Gravity **- This is what causes the counterweights downwards acceleration. The projectiles decline in height also is caused by gravity pulling it downwards.


 * Air Resistance - ** This acts against the projectiles motion, slowing it down, eventually to a stop.


 * Kinematics  -** This is the study of motion, so can be applied to our trebuchet to find the motion of the projectile.


 * Projectile Motion **<span style="font-family: Tahoma,Geneva,sans-serif;">- Occurs on an object with only the force of gravity acting upon it. In our trebuchet, the projectile is experiencing projectile motion upon release.

<span style="color: #420585; display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;"> __**<span style="color: #420585; display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Materials **__<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;"> Wood pieces of the dimensions (cm): 1 of 10.5x2x1.5 2 of 14.5x2x1.5 2 of 50.5x4x2 2 of 70x2x2 2 of 36x4x2 2 of 23x4x2 2 of 9.5x2x2 2 of 38.5x7.5x2 2 of 24.5x4x2 2 of 9x10.5x2 Fishing Line Nail Gun Cassie's Dad Wood Glue Metal tape 2 Metal hooks (end of arm) 2 Metal rods (hang the counter-weight) <span style="font-family: Tahoma,Geneva,sans-serif;">

__<span style="color: #420585; font-family: Tahoma,Geneva,sans-serif;">**Procedure** __<span style="font-family: Tahoma,Geneva,sans-serif;">

1. The first thing we did was built the arm. We put two blocks on each side of the arm to help keep it steady and screwed the hooks into the end. For our second model we sanded down the arm quite a bit to make it as light as possible. The blocks on each side of the arm are glued together. 2. Then we drilled a hole through the entire arm and put the metal bolt through it. We also drilled a hole in the opposite side of the arm and inserted a bolt to hang the counter-weight off of. 3. Next we measured all of the wooden pieces and cut them out with the help of Cassie's dad. 4. We built the base of the trebuchet with twelve pieces all angled in and connected them to the main two side pieces. 5. We used a nail gun and glue in some cases to attach all of the pieces together. 6. We sanded out the holes in the top of the side pieces for the metal rod in the arm to sit and to act as our pivot point. 7. We made the first sling out of jean and string. For our second sling we used metal tape folded around fishing line instead, as we thought that it would hold much better and be much lighter. 8. For our counter-weight we used an old soup can filled with weighed out pennies. Bent metal rods were used to hang it from the arm. 9. In our second model we sanded each piece down as much as possible. <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="color: #1c27e9; font-family: Tahoma,Geneva,sans-serif; font-size: 130%;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> //**<span style="color: #1c27e9; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 150%; text-align: right;">Modified Trebuchet **// //<span style="color: #1c27e9; font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">**Original Trebuchet** // <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="color: #008080; display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Length: .7 m Width: .67 m (all not including throwing arm) Height: .405 m Weight of counterweight: 890 grams <span style="font-family: Tahoma,Geneva,sans-serif;">

__<span style="color: #420585; font-family: Tahoma,Geneva,sans-serif;">**Procedure Used to Test and Analysis of Changes** __<span style="font-family: Tahoma,Geneva,sans-serif;"> We began testing our first trebuchet by throwing various items such as ping pong balls, socks and christmas balls. We were able to reach a distance of around 7 m. We then changed from a sling made of denim and ribbon, to one made of fishing line and metal tape. In addition to this change we greatly reduced the weight of our trebuchet by cutting down the wood pieces and removing any unnecessary additions. This gave us a greater distance of up to 7.7 m as well as a smaller mass. We continually launched a Christmas ball and tried modifying it different ways for better effectiveness.

We made many modifications to maximize the trebuchets efficiency. These included: 1. Changing our sling made of denim and ribbon to one made of fishing line and metal tape. This was much stronger, since our first sling broke multiple times. 2. Changing the length of the sling (We found that 104 cm worked the best). We needed to balance the hang time and horizontal velocity. 3. Reducing the size and weight by removing unnecessary elements and cutting down existing boards. It originally weighed 5.6 kg, but we reduced it to 4.5 kg. 4. Changing the weight of the counterweight. We had originally found that the counterweight should by 133 times the weight of your projectile. This would make our counterweight equal to 665 g. Then we found that the distance increased when we added more weight. We hypothesize this is because you also need weight to balance the weight of the arm. 890 g is the weight we found to be the best. 5. Holding the projectile in the sling at different heights upon release. Holding it up higher caused it to become tangled and not project in a straight path. Releasing from rest on the ground was the best way. 6. Changing the angle of the sling release hook. With test trials we found that since the hook was so flexible, it changed angles due to the force pulling on it during every trial. For maximum efficiency we had to readjust the angle of the hook before every trial.

__<span style="color: #420585; font-family: Tahoma,Geneva,sans-serif;">**Test Trials** __ <span style="font-family: Tahoma,Geneva,sans-serif;"> __<span style="color: #420585; font-family: Tahoma,Geneva,sans-serif;">**Conclusion** __<span style="font-family: Tahoma,Geneva,sans-serif;"> We have found the model of trebuchet containing a hanging counterweight (opposed to a fixed counterweight) and an "A" shaped frame to be an effective model. A counterweight of 133 times that of the projectile, plus the weight needed to balance the throwing arm, was the weight needed to provide the greatest distance. For us, that was 890 grams. The projectile does best when released at an angle of 45 degrees, which we came close to by adjusting our sling release hook. Also, we designed our trebuchet to be easily transferable, with a removable arm and counterweight.
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">Trial || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">Mass (kgs) || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">Arm Length (m) || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">Distance (m) || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">P=d/ml ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">6.55 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.09 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">2 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7.30 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.21 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">3 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">6.12 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.02 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7.70 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.28 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">5 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">6.54 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.09 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 110%; text-align: center;">6 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7.45 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.24 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7.23 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.20 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">8 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7.68 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.27 ||
 * <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">9 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">4.1 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.47 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">7.10 || <span style="color: #1ba77b; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">1.18 ||
 * = <span style="color: #1ba77b; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">Average ||= <span style="color: #1ba77b; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">4.1 ||= <span style="color: #1ba77b; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">1.47 ||= <span style="color: #1ba77b; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">7.07 ||= <span style="color: #1ba77b; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">1.18 ||

Although we are content with our trebuchet, there are some aspects that we could improve on. In retrospect we have found that although our distance is far (up to 7.7 m), our trebuchet is so heavy and has such a long arm length that it almost cancels the distance when placed into the equation P=d/ml. Next time we would build a smaller model, possibly in a lighter material, that would decrease our mass. Also, wheels would help the counter weight to fall straighter, since all objects have a spherical falling path. The momentum of the release would move the trebuchet forward on the wheels, allowing the counter weight to fall directly below its starting point. This would cause our projectile to travel a farther distance. A shorter arm length would also be beneficial, since it was our major downfall. Although a longer arm provided a larger distance, that distance was canceled out by the long arm length.