The Cannon Of Doom Trace Thompson Josh Wilson University Property Bush Library

Description The basic design was a 2” PVC pipe with a 3” PVC combustion chamber added on. An electric starter from a gas barbeque grill was used to ignite the propellant, which was hairspray. The choice of projectiles were 3 regular size potatoes and 3 granny smith apples. Using basic knowledge of kinematics, we attempted to calculate some theoretical distances, based on data gained from a sample firing. This sample firing was done at zero degrees of inclination, and based on that result values were calculated for varying degrees of the cannon’s barrel (above the horizontal). Trajectories were then measured at the different angles of inclination. Obviously our calculations are using simplified assumptions, ie: no wind resistance, no friction in the cannon tube, and full combustion of propellent. Our longest launch was 304 feet 9 inches. Our longest flight time was 6.31 seconds.

Calculations For our calculations we began with the data obtained from our zero angle shots. We were able to use the time and the distance to determine the muzzle velocity. Using the following: ∆x=v 0 t By setting the muzzle velocity as our final velocity, we were able to determine the acceleration of the projectile over the distance of the barrel by using the formula: v f 2 =v o 2 + 2a∆x We were also able to determine the force produced on our projectile by using the known mass of the object as well as the calculated acceleration and inputting those values into Newton’s Second Equation of motion. By using simple trigonometric relations, we determined our three different barrel angles. We then calculated the theoretical distances that each of our projectiles should have traveled using our barrel angle, our measured initial velocities, and our measured time. We related these three values through the formula: ∆x=v ox t+1/2at 2 (of course setting the final term to zero) By using these relationships we were able to determine the velocity of the projectile at the end of the barrel, the acceleration of the object over the distance of the barrel, as well as the theoretical distances that the projectiles would have traveled in an ideal environment.

Results Table Horizontal Distances Traveled by Projectile ShotTypeBarrel AngleMeasured Distance [m]Calculated Distance [m] 1Potato Potato Potato Apple Apple Apple

Conclusion It was in mutual agreement that the experiment was a fairly successful one, especially considering the lack of supplies and budget available. Our average percent error was %, which is fairly reasonable considering the simplifying assumptions that were made as well as some of the variables that we were not able to control. Some things that would have made this experiment more accurate would have been: more precise timing, more accurate measurements, and a more controlled way of dispensing the propellant. Given more time, supplies, budget, and minimizing the simplifying assumptions, and we both feel like we could do this experiment again and the results would be much closer to the calculated data.