phys 223 lab 6 report

February 27, 2024 PHYS 223-02 Experiment 6 Jasmine Warren, Mia Hardy, Ella Dozer Introductions and Objectives The objective of this experiment was to find the acceleration of a mass that is connected to another mass across a pulley. First, we had to set the pulley about 160 cm above the floor. Then we connected 50 g hangers on each end of a string that was then placed on the pulley with each hanger on each side of the pulley. We then added different sets of masses to each hanger according to the data table. We measured the distance from our starting to stopping point. Then we had one person release the heavier mass from the starting point, another person caught it before it hit the floor, and another person timed how long it took to reach the predetermined stopping point. We record the drop time for each set of masses 3 times and noted them in our data table. Lastly, we had to plot the calculated acceleration by (m 2 - m 1 ) and acceleration by [1 / (m 2 +m 1 )]. Data Sheets and Graphs m 1 (g) m 2 (g) m 2 -m 1 (g) t 1 (s) t 2 (s) t 3 (s) t ave (s) a = 2 d t 2 ( m / s 2 ) 125 145 20 1.88 1.71 1.60 1.73 0.72 120 150 30 1.35 1.37 1.56 1.43 1.05 115 155 40 1.41 1.16 1.16 1.24 1.38 110 160 50 1.09 1.13 1.06 1.09 1.79 105 165 60 0.94 1.00 1.03 0.99 2.18

100 170 70 0.81 0.96 0.84 0.87 2.83 Table 1: Data from when m 1 + m 2 = 270 g . m 1 (g) m 2 (g) 1 m 2 + m 1 ¿ t 1 (s) t 2 (s) t 3 (s) t ave (s) a = 2 d t 2 ( m / s 2 ) 120 150 0.0037 1.41 1.44 1.34 1.40 1.10 170 200 0.0027 1.56 1.69 1.63 1.63 0.81 220 250 0.0021 1.79 1.97 1.78 1.85 0.63 Table 2: Data from when m 2 − m 1 = 30 g . Graph 1: Plot of m 2 − m 1 vs acceleration.

from Table 2 vs 1 m 2 + m 1 (Graph 2). I applied the linear fit to get an equation that has a slope of 296.81 gm s 2 . The expected result was ( m 2 − m 1 ) g = ( 30 ) 9.81 = 294.3 gm s 2 . The percent error was | 296.81 − 294.3 | 294.3 ∗ 100 = 2.51 294.3 ∗ 100 = 0.0085 ∗ 100 = 0.85% . Some sources of error could be from us not releasing the mass from the exact same height each time which would adjust the time and affect when we calculate acceleration. Another source could be if the time wasn’t starting/stopping exactly when motion starts and when it reaches our stopping point. If there was any friction in the pulley or if the pulley wasn’t positioned could cause error. The weights also could have been inconsistent since they kept falling off the. Air friction is another thing that should be considered as a source of error. All of these would affect the acceleration we calculated which would in turn give us a different slope than what was expected. Discussion The toughest part of this lab was trying to get the weights to stay on the hangers which meant we had to replace them after each trial. The results we got showed that we had a 13.89% error from Activity 1 where m 1 + m 2 = 270 g and a 0.85% error from Activity 2 where m 2 − m 1 = 30 g . Clearly, we got better results with the second experimental setup than the first. I think we probably began to get the hang of the masses, positing, and timing as we went along. The reason the accelerations we got were different from the gravitational acceleration of 9.81 m/s 2 is because both blocks on each side of the pully

are experiencing that same force. Along with that force there is also the upward force from the tension in the string connecting the blocks. If the masses were equal, then there would be no net force on the blocks, and they would stay in place. But for our experiment we had one mass be heavier than the other so that it would accelerate downwards but with a reduced acceleration because of the other mass attached to it. Conclusion For this lab our objective was to find acceleration of a mass when it is connected to another mass by a string across a pully. We were able to calculate accelerations at different sets of masses and then plot them to find a slope. We noticed we did also have some error in our results from what would be expected.