Lab 2 Uniform acceleration

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Indiana University, Bloomington *

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P221

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Physics

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Jan 9, 2024

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Lab 2: Uniform Acceleration Introduction In this lab, we investigate the physics of objects rolling on an incline due to gravity. We break down gravitational vectors to understand the cart's acceleration, aiming to calibrate by comparing our experimentally determined acceleration due to gravity ('g_final') with an accepted value ('g'). To account for friction, we calculate an average acceleration from both upward and downward motion, allowing us to examine the influence of friction on our results. This experiment provides insights into the complex forces at play during inclined motion. Procedure A. Calculating the Angle of the Track Preparation Check that the track is level: Visually inspect the track for levelness. Place the cart on the track and push it slightly to the right and left to ensure it rolls consistently. If the track is not level, adjust the leveling screws until it appears level. Measure sin(θ): Use a meter stick to measure the heights h1 and h2 of the ramp and the horizontal distance s between them. Estimate the uncertainty for each measurement. Record the measurements and uncertainties in a table. Calculate sin(θ): Use Equation 4 to calculate sin(θ): sin(θ) = (h2 - h1) / s Calculate the uncertainty for sin(θ) by combining the uncertainties for the length measurements. B. Measuring Acceleration Open the LoggerPro file: Log into the lab computer. Open the 'P201 Uniform Acceleration' file in LoggerPro. Record a run: Position the cart about 0.5 m away from the detector, aligned with the bumper.

Simultaneously release the cart and begin recording with LoggerPro. Adjust the vertical and horizontal scales of the graph to show one complete cycle of motion. Repeat this process for multiple runs until reasonably straight lines on the velocity graph are achieved. Measure the accelerations: The acceleration is determined from the slope of the velocity graph. Select and highlight the "going down" portion of the graph and use Analyze > Linear Fit to calculate adown. Repeat the same process for the "going up" portion of the graph to find aup. Record the values in a table. Complete at least 6 runs: Repeat steps 4-6 for a minimum of 6 runs. Take a screenshot or a picture of one representative run with the linear fits and include it as a figure in your report. Record all values of aup and adown in the table. Calculate the average accelerations: Calculate the average and uncertainties for both adown and aup separately. Include these values in the table. C. Gravitational Acceleration Calculating gdown Calculate g using only adown: Calculate gdown using Equation 5: gdown = adown / sin(θ) Record the value of gdown and its uncertainty, considering the uncertainties of adown and sin(θ). Calculating gfinal Calculate g using both aup and adown: Calculate afinal as the average of aup and adown. Use Equation 6 to calculate gfinal: gfinal = afinal / sin(θ) Calculate the uncertainties for afinal and gfinal by combining the uncertainties of both accelerations. Calculating Friction Calculate friction: Calculate the magnitude of the acceleration due to frictional force acting on the cart, considering the effect of friction.

Conclusion Analyze error in the experiment, considering sources of uncertainty and potential improvements to the experiment's accuracy. Analysis for (calculations check appendix) A. Calculating the Angle of the Track Measurements of h1, h2, and s with uncertainties. Calculation of sin(θ) and final value clearly reported. Calculation of the uncertainty of sin(θ). The uncertainty should be reported with the value for sin(θ). sin(θ)= 0.0523 +/- 0.0024 B. Measuring Acceleration Screenshot of one run with linear fits. Table of values from at least 6 runs with values of aup and adown. Average value and uncertainty for aup and adown, included in the table. Aup m/s^2 Adown m/s^2 Afinal m/s^2 1 0.61 0.48 0.545 2 0.6106 0.4836 0.5471 3 0.6091 0.4917 0.5504 4 0.6074 0.4914 0.5507 5 0.6019 0.4909 0.5464 6 0.6145 0.4911 0.5528 average 0.6089 0.4886 0.5487 Unc 0.00155 0.0018 0.0024

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Graph C. Gravitational Acceleration Calculating gdown Calculation of gdown and its final value clearly reported. Calculation of the uncertainty of gdown. The uncertainty should be reported with the value for gdown. gdown= 9.34 +/- 1.35 Question: What is the discrepancy between your calculated value for gdown and the expected value for g? The discrepancy between the calculated value and expected value is 0.46 m/s^2 Question: Does your experimentally determined value of gdown agree with the accepted value for g within your estimated uncertainty? Yes my experimentally determined value agree with accepted value for g within the estimated uncertainty Calculating gfinal Calculation of afinal and its final value clearly reported. Calculation of gfinal and its final value clearly reported.

Calculations of the uncertainties of afinal and gfinal. The uncertainty should be reported with the value for each, respectively. Question: Did your calculation for gfinal using both the up and down motions give a lower discrepancy than the calculation using just the down data? No, it gave a higher discrepancy than the calculation using just the down data gfinal= 10.49 +/- 1.35m/s^2 Question: Does your experimentally determined value of gdown agree with the accepted value for g within your estimated uncertainty? Yes, the experimentally determined value agrees with the accepted value of g within estimated uncertainty Calculating Friction Calculation of the acceleration due to frictional force. af= (aup-adown)/2 = 0.06015m/s^2 +/- 0.0012 Include answers to the following questions in the Conclusion of every formal lab report: Question: What were the largest sources of uncertainty? Question: Realistically, can anything more be done to significantly reduce the uncertainty in the experiment? Question: In general terms, how could this experiment be improved? Conclusion In conclusion my lab results is gfinal=10.49 +/- 1.35 m/s^2 even though it is off by 0.69 m/s^2 from the expected value, but since the expected value is within its uncertainty. I would argue that my results are valid;therefore, the lab is a success. I believe the largest sources of error in the lab would be how when the cart bounces back the trajectory is not completely straight and measurement error by myself when measuring data using the instrument as well as potential error of using the meter stick to measure the height and length of the setup. Realistically speaking I believe having a second team member making sure that the trajectory could decrease the uncertainty significantly. Generally the experiment could be improved by setting up a air track for the cart to slide up and down. It would eliminate the largest source of error I’ve had during the experiment.

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