PHYS 1100 Group 6 Lab Report 2

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Physics

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Feb 20, 2024

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Group 6 PHYS 1100 - Prof. Karl Sandeman Lab 2: Projectile Motion Date Performed: 9/5/2023 Brief Description:
The objective of this lab is to understand the principles of projectile motion. This lab shows how we can use two dimensions, horizontal and vertical, to describe motion. To achieve this objective, we used an inclined plane apparatus with a photogate detector attached to it, which measured the time of a steel ball as it passed through, thus allowing us to calculate the initial speed along with the diameter of the ball measured using a Caliper. Additionally, using the measurements of the distance of the ball from when it left the inclined plane (vertical y), the angle of inclination, and the initial speed, we were able to calculate and predict the horizontal distance x, to be used to compare to the measured horizontal distance. Moreover, we learned how to use the data measured in the experiment to understand factors that influence projectile motion, assuming that gravity is the only force acting on the steel ball and two-dimensional motion. Tabulated Results: Diameter of ball: 19mm, or 0.019m Trials X (Measured cm) Time (s) Speed Values (m/s) X (Calculated cm) % Error 1 63.9 0.01039 1.83 70.4 9.23% 2 64.4 0.01041 1.83 70.4 8.52% 3 64.7 0.01041 1.83 70.4 8.10% 4 65.9 0.01039 1.83 70.4 6.40% 5 63.5 0.01040 1.83 70.4 9.80% 6 63.5 0.01050 1.81 70.0 9.29%
7 66.6 0.01040 1.83 70.4 5.40% 8 64.4 0.01039 1.83 70.4 8.52% 9 62.3 0.01038 1.83 70.4 11.5% 10 64.2 0.01041 1.83 70.4 8.81% Mean of speed values: 1.83 m/s Standard deviation of speed values: 6.30 x 10^-3 m/s Mean of measured horizontal displacement ( X ): 64.3 Standard deviation of measured horizontal displacement ( X ): 1.22 Calculations: Inclined plane angle calculation
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* Since the times taken as the ball passed the photogate detector are similar, they maintain the same horizontal displacement. Additionally, all the work in calculating the horizontal displacement used m as the unit to coincide with 9.8 m/s^2, and the final product was converted to cm (9.8 is positive due to deciding that the downward direction is positive).
Percent error:
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*In calculating the percent error of each of the ten trials, the measured X is compared to the calculated X . Most percentages fell below 10%, but none of them went below 5%. The discrepancies in the X values are further discussed below. Original Data Sheets:
Graphs:
Discussion:
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In this experiment, we measured the distance a steel ball bearing would travel off a ramp onto the floor. We used materials such as a ramp and photogate and additionally, a piece of paper with a piece of carbon paper on top. Our percent errors averaged 8.5% error for all ten trials. Our highest error was during trial 9, with 11.5%, and our lowest was in trial 7 with 5.40%. Our measurements were only somewhat precise, ranging from a 0.5cm to 4.3cm difference, with none being 5 cm or more apart, our accuracy was further off, ranging from 3.8cm to 8.1cm difference. Such a large difference in error percentages could have had numerous reasons. For example, during the ten trials, we were unable to tape the paper to the floor, so the location of the blank paper constantly changed, which could be a reason for the discrepancies in our X values, calculated and measured. Another issue that could have caused these errors, was that our ramp did not completely stop at the edge of the rounded table, one edge of it was off and the other was on. This could have overall affected our Y measurement. Our measurement for X was done using a meter stick that we placed at the edge of the ramp and then we would lean it down. During the process of leaning the stick down, it could have shifted or even not come down in a straight line. To mitigate discrepancies like this in the future, we can take steps to fix these problems. Such as making sure the ramp is truly at the edge of the table, pre-measuring a distance on the floor so we can make better measurements of where the ball landed, and by measuring the distance multiple times. A final step we could take to avoid discrepancies is to make sure we have as little as possible initial velocity on the ball as we can. We can attempt to do this by putting a type of “starting gate” at the start of the ramp, so we can try to avoid accidentally pushing the ball bearing down the ramp.
Conclusion: We learned how to use calipers to measure the diameter of the ball and how to use the measurement and the photogate detector to calculate the speed of the ball when it goes off the inclined plane. With all the information gathered, we were able to find the predicted horizontal distance and compare it to our tested horizontal distance to find our percent error, revealing potential errors that could have affected the trajectory, such as air resistance, though negligible in our calculations. Our experiment had a few potential errors that we did our best to prevent and limit any chance we could. One error that all the other groups also probably had was the fact that we can never guarantee we’re dropping the ball from the same spot on the ramp every time with absolutely no initial velocity on the ball. But we tried our best to make sure we were doing it the same every time, and for any reason it wasn’t the same we’d redo it to make sure we got it as close as possible. Another error that all the other groups probably had to deal with too was measuring the distance from the bottom of the ramp to the black dot on the paper where the ball hit. It wasn’t easy to place the ruler very well straight down from where the bottom of the ramp was but we tried our best and even measured a few multiple times to make sure we were getting the most accurate measurement we could get every time. Furthermore, as seen by the considerably low percent error, we can conclude that we were successful in predicting the range of the projectile’s trajectory through our calculations.