PHYS 223 - Lab Report 4 (The Atwood Machine and Newton’s Second Law)

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Mechanical Engineering

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Feb 20, 2024

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PHYS 223 The Atwood Machine and Newton’s Second Law Megan Cousins Tuesday-Thursday Objective Our goal for this lab was to use an Atwood Machine to prove Newton’s Second Law of Motion and to subsequently prove that gravitational acceleration is approximately 9.8 through additional calculations. Introduction For this experiment we used a pulley system similar to that of an Atwood Machine which helps us understand Newton’s Second Law of Motion better. According to Newton's Second Law of Motion, if a force is applied to a body or system, the body or system acquires acceleration in the direction in which the force acts and is proportional in magnitude to it. If the acceleration is proportional to the resultant force acting upon it then F=ma. There are two parts to this experiment, one with the difference in masses increasing proportionally while simultaneously keeping the total mass the same, and the other where the total mass changes but the proportionality of the two masses stays the same. 1. Plot the graph of acceleration versus (m2 – m1), using the average acceleration of each set of three trials. If the graph is a straight line then the first proportionality is proved. Determine the slope of the curve and compare it with the total mass. Figure 1. Our slope for this graph is 28.024, this correlates to the linear increase in the difference in masses seeing as our plotted data is approximately a straight line. 2. Plot a graph of the acceleration versus the reciprocal of the total mass, 1 / m1 + m2 using the average acceleration of each set of three trials. Determine the slope of the curve and compare it with the resultant force (m2 – m1) g. The slope for this graph is 0.6051 with our resultant being 0.294 3. What are some sources of error in this experiment? Some pretty prominent sources of error in this experiment are timing, making sure that the pulley is directly vertical, keeping the rope clear of knots, the fact that with our particular pulley the friction is not negligible, and
4. Consider the relative importance of each source of error upon the accuracy of your results. Everything would throw off the final gravitational acceleration, either a faster or slower acceleration can be calculated at the end of the calculation. 5. Calculate the percentage error for the value of the total mass obtained from the slope of the graph in Part 1. Our average percent error is approximately 30.75% 6. Calculate the percentage error for the value of resultant force obtained from the slope of the graph in part 2. Our average percent error is approximately 66.17% Discussion During this lab, we worked in only the y direction as we were letting gravity take effect onto different masses on hangers off of a pulley system. Our main goal was to observe acceleration of two different parts to the experiment, one with the difference in masses increasing proportionally while simultaneously keeping the total mass the same, and the other where the total mass changes but the proportionality of the two masses stays the same. For the first part of the experiment, the total mass was .270 kg with the difference between the two masses increasing by 0.01 with each new trial. For the second part of the experiment, the proportionality was a difference of 0.03 with the mass on each side increasing by 0.1 kg each time In both parts of this experiment, we started with the heavier mass at the top of the pulley system and allowed it to drop as it was time. The distance between this mass that was higher positionally was measured and our acceleration was calculated. For the first part, our true acceleration and calculated acceleration increased as the proportion increased, our average percent error was approximately 30.75%. For the second part, our true acceleration and calculated acceleration decreased as the proportion increased, our average percent error was approximately 66.17%. Our error can be related to a lot of different reasons, but our main one was accuracy with timing and that in our pulley system we treated the friction as negligible but it was not really. Appendix
Figure1. Figure 2.
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