Acceleration - Lab Report, Received Letter

Acceleration My measurement of g d oes agree with my expected value of 9.81m/s^2 within my uncertainty. After measuring the distance D, which is the distance between the bottom of the lowest black striped to the bottom of the highest black stripe, and N, which are segments and these segments are pairs of black and white stripes that are on the ‘picket fence’, we calculated the length of a single segment d  by dividing D, 0.35 m, by N, 7 segments and got 0.050 m for d.  T  hen, we dropped the ‘picket fence’ through the Photogate five times and got the best fit line for each Velocity vs. Time plot and analyzed the linear fit and it output five slopes for each trial. After determining these five slopes, we found the average of all of the trials’ slopes. Lastly, we were able to find our measurement of g b y multiplying d, 0.050 m by the average slope, 195.4 segments/s^2 and got 9.79 m/s^2. Including our uncertainty propagation, which can be seen on the attached excel sheet, of 0.063 m/s^2 we can agree that our measurement of g i s very close to the expected value of 9.81 m/s^2 within the uncertainty measured. As for part II, we measure g b y dropping the ‘picket fence’ from varying heights of 0.02 m, 0.04  hich did not have physical units m , all the way to 0.10 m (5 trials). We calculated velocity, v, w so we multiplied each velocity by d  which is what we calculated earlier in part I and got 1.24 m/s, 1.37 m/s, 1.47 m/s, 1.63 m/s, and 1.74 m/s respectively to the varying heights. We squared each velocity to get m^2/s^2 and plotted v^2 vs. h as you can see above. We were able to determine the slope 19.05 v^2/h and to calculate g we divided that value by 2. Along with calculating all of these values, we also found the uncertainty, which was only 0.47 m/s^2 and our measurement of g does agree with the expected value of 9.81 m/s^2 within the uncertainty. Error Analysis: If we were to measure the length from one corner to the opposite corner, we would overestimate the length of D. Now, if we were to drop the ‘picket fence’ straight down and measure the time it would take to pass through, we would determine that the overestimated distance D p assed through time t instead of the actual distance which should have been straight across. Therefore, we would calculate a larger velocity of D/t and a larger acceleration so we overestimated g. If we released it with a consistent nonzero velocity, it would be more accurate and velocities would have been more similar to each other. It would impact the look of our plot by making it more steady and straight with less errors. It would impact our measurement of g by just making it correspond to the consistent nonzero velocities. It does matter if the initial velocity went up or down because if it went up it will have a higher height and have a faster speed as it is going down, thus lowering the time. If we were to drop it with an initial velocity of zero on average but varies from height to height, it would not alter our g because it starts at the same initial velocity. This implies that our measurements might be off by human error of not dropping it at an initial velocity of 0. If it were rotated slightly in any of those axes it would have altered g . If it were by the x-axis it would have messed up the longer length and it would take longer time so it would underestimate the value of g . If it were to drop by the y-axis it would take shorter time to go through, thus resulting in a larger g v alue. For the z-axis, it would be altered in both time and length so the g would just be altered completely. Conclusion: In this lab, we were studying the vertical motion of a ‘picket fence’ that had black and clear stripes at regular intervals. We had measured the distance travelled, the time that it took for the ‘picket fence’ to pass through the Photogate and calculated average velocities from these measurements. We determined these measurements in order to be able to compute the acceleration of the object which would determine the value of v ( acceleration due to gravity) and get the value g. As explained in the results, we did receive very close values to the expected value of 9.81 m/s^2 within the uncertainty and believe we did really well. To improve this lab, I would have a set ruler on top of the photogate that doesn’t move so we can accurately drop it from the given heights we were supposed to drop.