Physics Mini Lab #7 (1)

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Texas A&M University *

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201

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Mechanical Engineering

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Dec 6, 2023

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Laboratory Report: Lab Date: October 24, 2023 Experiment’s Title: Work-Energy Theorem Course/Section #: PHYS 201-400 Station #: 11 Names of students (who performed the experiment): Natalie Hesterman & Holly Pawlowski & Alejandro Mapula Names of missing students: N/A TA’s Name: Mahmodul Maheen Lab Partners: Natalie Hesterman & Holly Pawlowski & Alejandro Mapula

Introduction: In this experiment, we familiarized ourselves with the Work-Energy Theorem. The idea behind this theorem is that the work being done by a net force on an object is equal to its change in kinetic energy. For this lab, we compared the work on an object versus the change in its kinetic energy. We continued to use the same equipment/setup as the previous two experiments. The tools we used included: the LabQuest Mini Interface, a force sensor, a photogate/pulley system, a string/hanger/various masses, and a dynamic cart and its track. We first took the mass of the pulley and hanging system which was 4.9g and then the mass of the car plus the friction sensor was 600g. Furthermore, we did seven total runs; the first three runs had a mass of 55g on the pulley system, for trial number four the pulley system weighed 105g, and trial number five had a mass of 205g. Lastly, trials six and seven had 205g on the pulley system and an additional 100g resting on the top of the cart. For this experiment, we used two equations: 1. W=F*d(cos theta) 2. W=(delta K)=Kf-Ki))=½ m*vf^2-½ m*vi^2 Results: Table 1: Run #1 Run #2 Run #3 Run #4 Run #5 Run #6 Run #7 Mass= Mh (hanger + hanging mass) 0.055g 0.055g 0.055g 0.105g 0.205g 0.205g 0.205g Mass= Mc (cart +sensor) 0.6g 0.6g 0.6g 0.6g 0.6g 0.7g 0.7g Initial Position (Xi) 0.03 0.045 0.06 0.045 0.03 0.045 0.12 Initial Velocity (Vi) 0.191 0.191 0.191 0.349 0.43 0.473 0.473 Initial Kinetic Energy= (Ki=1/2*Mc*Vi^2) 0.00109443 0.00109443 0.00109443 0.0365403 0.05547 0.07830515 0.07830515 Final Position (Xf) 0.375 0.405 0.465 0.6 0.51 0.51 0.525 Final Velocity (Vf) 0.796 0.796 0.796 1.252 1.571 1.489 1.489 Final Kinetic Energy= (Kf=1/2*Mc*Vf^2) 0.1900848 0.1900848 0.1900848 0.4702512 0.7404123 0.77599235 0.77599235 Displacement= (D=Xf-Xi) 0.345 0.36 0.405 0.555 0.48 0.465 0.405 Average Force= (Favg) 0.5014 0.5014 0.5014 0.8909 1.599 1.568 1.568 Work= (Favg*D) 0.172983 0.172983 0.172983 0.4944495 0.76752 0.72912 0.72912 Delta K= (Kf-Ki) 0.18899037 0.18899037 0.18899037 0.4337109 0.6849423 0.6976872 0.6976872 Table 1, highlights all of the data we collected during this experiment plus some equations we had to calculate in order to find our answers.

Discussions/Conclusions: 1. What is the percent difference between the work and the difference in kinetic energies |(Work-ΔK)/Work|? Table 2: Run #1 Run #2 Run #3 Run #4 Run #5 Run #6 Run #7 Work= (Favg*D) 0.172983 0.172983 0.172983 0.4944495 0.76752 0.72912 0.72912 Delta K= (Kf-Ki) 0.18899037 0.18899037 0.18899037 0.4337109 0.6849423 0.6976872 0.6976872 Difference= Work-Delta K -0.01600737 -0.01600737 -0.01600737 0.0607386 0.0825777 0.0314328 0.0314328 Percent Difference 90.74627565 90.74627565 90.74627565 87.71591437 89.24097092 95.68894009 95.68894009 2. Are the results from Table 2 expected and why? I would say the results from Table 2 are somewhat expected. This is because there is really no way our group could record the data wrong/do the calculations, however, the first three runs resulted in a negative difference of work subtracted by delta K. There are numerous reasons for how this could be due to errors in our experiment when running the cart on the dynamic track. The percent difference is mostly accurate, however, our accuracy strayed in trials four and five. 3. What is the conclusion you come up with, from the seven runs? After these seven runs, the conclusion I can come to is that increasing the weight on the hanging pulley will result in a higher force average and a higher velocity. This is proven in Table One. It became prevalent that the Work-Energy Theorem is in fact true and that when work is being performed it is equal to its change in momentum such as kinetic energy. 4. What are the possible reasons for the differences if there are any? Some possible reasons for the differences could ultimately be due to the fact of the system we used (LoggerQuest). Sometimes when my group would zero out the force it would not be as accurate and I feel that is why some of our data is different. Another possible reason for the differences/negative values in our data could be when letting the dynamic cart go and a group member stopping it, this could lead to strayed values. In conclusion, our lab on the Work-Energy Theorem proved to be an acceptable theory in physics. When doing this lab, we observed many variables that ultimately led to our findings. We were able to familiarize ourselves with two new equations that helped us to find work being done. Furthermore, we believe that the negative values in Table 2 could be due to an error in collecting our data, however, our percent differences were still pretty accurate.

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