Projectile Motion Lab
Name: Kyle Collins
Lab Partner: Parker Fairchild
Date: 2 October 2014
Purpose: This lab's purpose is to predict the range at which a projectile will land based on measurements taken in class.
Lab Partner: Parker Fairchild
Date: 2 October 2014
Purpose: This lab's purpose is to predict the range at which a projectile will land based on measurements taken in class.
Theory: To estimate the range, an equation first needs to be derived. Since time cannot be accurately measured here, an equation is necessary to find the range. In order to find this, use the third kinematic equation and solve for time (below left). Then, substitute the equation for t in the range equation (below mid). In addition, Voy and Vox must be written as functions of theta (below right).
Experimental Technique: First, the launcher was set to a 45 degree angle. The initial velocity was found by averaging ten shots from the launcher. Next, a plumb line was used to mark a spot on the floor correspondent to where the ball would launch from, which would be utilized as a start point for the range. Lastly, the change in height, or delta y, was measured with a measuring tape. Ten shots were then fired at the paper covered by a sheet of carbon paper with the predicted range marked with a line, and the distance away from the line was measured. Then, the uncertainty and percent difference were calculated.
Data And Analysis: To start, delta y was measured to be .936 meters. The average velocity of the launcher set at a 45 degree angle on the second setting was calculated to be 3.80 m/s; this was an average from a total of ten shots. Using this information and the derived equations above, the predicted range for the projectile was estimated to be 2.12 meters. When the shots were completed, it was clear that it was not hitting exactly where it was to predicted to.
Data And Analysis: To start, delta y was measured to be .936 meters. The average velocity of the launcher set at a 45 degree angle on the second setting was calculated to be 3.80 m/s; this was an average from a total of ten shots. Using this information and the derived equations above, the predicted range for the projectile was estimated to be 2.12 meters. When the shots were completed, it was clear that it was not hitting exactly where it was to predicted to.
Next, the uncertainty was calculated to be 2.75%, which is calculated by subtracting the shortest launch (2.175m) from the longest (2.230m), dividing the difference by 2, and multiplying the quotient by 100.
Conclusion
In summary, this lab was successful. Having said that, there were many measurements taking place, and thus many sources for error. The first could be that the starting point for measuring range was not directly beneath the launcher, perhaps caused by a slight slant in the plumb bob. The paper which the ball was to hit was also not exactly 2.12m away from the launch point. These would make the range inaccurate. Second, the paper was also picked up after launching the balls, making it necessary to use a ruler to measure the distance from the predicted value, compounding error by adding parallax error. While wind resistance may have played a part in other trial of the experiments, it likely did not in this one. One would expect wind resistance to shorten the actual range from the predicted, but the range in this trial increased. In addition, there is no way to observe or calculate the resistance, and so it must be ruled out of calculations.
In summary, this lab was successful. Having said that, there were many measurements taking place, and thus many sources for error. The first could be that the starting point for measuring range was not directly beneath the launcher, perhaps caused by a slight slant in the plumb bob. The paper which the ball was to hit was also not exactly 2.12m away from the launch point. These would make the range inaccurate. Second, the paper was also picked up after launching the balls, making it necessary to use a ruler to measure the distance from the predicted value, compounding error by adding parallax error. While wind resistance may have played a part in other trial of the experiments, it likely did not in this one. One would expect wind resistance to shorten the actual range from the predicted, but the range in this trial increased. In addition, there is no way to observe or calculate the resistance, and so it must be ruled out of calculations.