Purpose: To find the initial velocity of a projectile based on the mass of the projectile, the mass of the catcher, the length of the strings that the catcher swings on and the angle that the strings make after the collision. By propagating the uncertainty for the measurements the uncertainty of the initial velocity can be calculated. From this the quality of the initial velocity can be derived.
Procedure: The mass of the ball and catcher had previously been measured so that the experiment would progress quickly for each of the groups that needed to use the apparatus. These values were recorded. The shooter was cocked and the ball loaded. The needle that measures the angle was moved to a position less than the max angle that was expected to be reached. The release was triggered and the ball was fired at the catcher. The first 2 attempts were unsuccessful as the ball was not trapped in the catcher and any data was not correct. The 3rd. attempt was successful as the ball was caught inside the catcher. The maximum angle was recorded.
Data Analysis: Since the ball was stopped inside the catcher the collision was modeled as a completely inelastic collision. This meant that in the collision momentum was conserved but kinetic energy was not conserved as some of the kinetic energy was dissipated as heat and sound. The angle of the needle was used with the length of the strings to calculate the change in gravitational potential energy. This equaled the kinetic energy just after the collision. Using the velocity just after the collision, the momentum can be calculated This is equal to the momentum before the collision. Using the mass of the ball, the initial velocity can be found. The initial velocity of the ball was found to be 4.87m/s.
Results: The initial velocity of the ball was found to be 4.87m/s +- 6.49x10^-2 m/s. Therefor that the initial velocity is within +- 1.33% of the actual initial velocity. Since the initial velocity was not a known true value or measured using another, more accurate means, it is impossible to say that this result is accurate. The result is precise and am effective way to measure the velocity of a projectile using simple and easily available equipment.
