The Procedure of Making Our Cannon

 We first obtained the materials needed to build the cannon properly. These materials consisted of

o    2 Tennis ball canisters

o   A 18 inch pair of tape

o   A pair of scissors

o   Ruler

o   Protractor

o   Compass

o   Permanent marker

·         After we had done this we sketched out multiple designs of what we may use as the design for the cannon. We based the decision of the final design by what would have a minimized volume which would lead us to hopefully result in a greater pressure according to Gay-Lussac’s Law.

·         We outlined the final cannon design with a sharpie pen in order for us to get a better picture of what we have planned.

·          After this we took pictures of our materials and our final and previous designs that way we would be able to put them on our blogs later on.

·          We then measured the tennis canisters and we went and saw what we thought what would be a better angle for the cannon to be at. We chose that it would be best for us to cut one canister to be taller by half an inch that way it would be able to give us the pieces that we needed to construct the cannon. The longer piece of the cannon was 4.5 inches while the shorter piece is 4.0 inches. 

·         In order to make sure we cut this accordingly we drew a circle with a sharpie pen making sure it was clear enough for us to make sure we didn’t go off of our directed course.  We did this for both of the tennis canisters and when they were both cut to their right sizes, we began to poke a hole in the bottom of the 4.5 inch canister in order for us to get a higher pressure in it from the 4.0 inch canister that will attached to it also.

·         For us to be able to make the hole in the bottom of the canister we used a pen, thumbtack and a compass (which we broke the tip off of), and scissors. It took us approximately ten minutes in order to get a hole the size of a tack but when of our colleagues helped us he was able to make it the size of a pencil eraser in only a few seconds.

·         After all this was over with we inserted it into the 4.0 inch canister and we moved it into a 27 degree angle using the protractor to make sure we stayed on target. This will be the entire barrel.

·         We then traced the 27 degree angle onto the sheet of paper we took what was left of the 4.5 inch canister and traced a dip with a marker before cutting it. This will be the base and it will be holding our cannon at the angle that will be needed in order to make this thing succeed.

Planning stage

The first thing we did before actually designing the cannon was to find the things of what we didn’t want the cannon to do. This is so that we will be able to get the best possibly distance that our cannon can actually shoot the tennis ball.

What we had listed was that we didn't want it to have a great chance of misfiring and we didn’t want it possibly break our cannon. The things that we did want for us to do, was that we wanted it to have a sturdy structure and that it had an airtight seal allowing us to increase the pressure.

After this we split our team of four into two teams of two. One team researched the formula that we would need in order to find the correct angle to tilt it at, and the other team starting the design of what the cannon will look like. We knew that we wanted to have as much pressure as possible to be built up inside the cannon.  In order to do this we made the bottom half an inch smaller to increase the pressure. (This is Boyle’s Law which is when temperature and pressure are indirectly related)  We would also poke a pencil-size hole in the bottom of the top half in order to create even more pressure. Because of part of our group working on this the other part found two equations that would help us. The two equations are listed below

·         y = ax²+bx+c

·         x = vt(cos)Ө

o    x = the distance the ball would travel

o    v = velocity

o    t = time the ball was in the air

o    (cos) = co-sign

o    Ө = angle of the cannon

We soon realized that we would have to guess at some of our numbers that are needed, such as the velocity and the number of seconds that the ball was in the air, in order to find out how far it would be able to go.

We plugged the numbers into the equation and got x=(1ft/sec)(5 sec)(cos)( angle of cannon) the only thing we had left to fill in was the correct angle of which the cannon would be at. We started at an angle of 25 ^o then later worked our way up. We tested the range of angles to tilt our cannons at then narrowed it down depending whether or not the final value would be the largest number or not. The angles we chose were 25 ^o, 26 ^o, 40 ^o, 35 ^o, 30 ^o, and 28 ^o. Though later we realized that the best angle would be at 27 ^o, at this angle our cannon would be able to launch the ball a distance of about 4.45 meters or about 14.49 feet.

Science Component

In this group project we had the opportunity to learn many things about the gas laws and how they worked in many situations. For our group design we used a 27 degree angle for the cannon, this is because after inputting it into two formulas we found out that the 27 degree angle should give us our best distance out of the other angles that were previously mentioned. This project relates to the gas laws because during it we use Gay-Lussac's Law, where volume is constant and the pressure of the gas proportional to the temperature. When we light the ethanol the temperature will increase along with the pressure that is inside of the cannon. When this happens it be holding enough pressure inside so that when it does have enough pressure it will push the ball out and fire it into the air. When ethanol combusts and turns into carbon dioxide and water it will be the formula of C₂H₅OH + 3O₂ => 2CO₂ + 3H₂O this will be the balanced equation. The only difficulties that we had with building the actual cannon was when we had to poke the hole in the bottom of the canister. It proved to take up much our time and if we could I would have changed that maybe we could have just cut off the bottom of the canister and replace it with the lid instead.

For the results of the actual cannon shooting, come back and check this blog in spring!

Math Component of Cannon

Cannon Blog: Math Component

Initial velocity equation: (speed (ft/sec))cos(launch angle)

Use the quadratic model h = -16t²+v₀t+h₀ to solve the following problem.

Blog about the steps you took to solve these problems.

A cannonball is shot upward from the upper deck of a fort with an initial velocity of 192 feet per second.  The deck is 32 feet above the ground. 

Quadratic Model: h = -16t²+192t+32 

1.     How high does the cannonball go? 607.9 feet

2.     How long is the cannonball in the air? 12.16 seconds

Calculations
-192√ (192)²-(4)(-16)(32)   =      12.16           
                   2(-16)
12.16/2= 6.08
-16(6.08)²+192(6.08)+32= 607.9 feet

Procedure to find this answer

•  In order to the this part of the project I plugged the formula into the y=. The formula is listed above and when i went over to the table I saw the highest part of the parabola, the x coordinate is 6 while the y coordinate is 608.
•  Once I found this I used the number 608 as the highest that the cannonball goes because it is the vertext of the parabola.
•  Afterwards I went back to the table and scrolled down until I reached zero or at least near it. I got to the x coordinate of 12 and the y coordinate of 32. If I went to 13 it would have been to the negatives so I assumed it was between 12-13 seconds of time.