Physics Lab 6

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Massachusetts Institute of Technology *

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8.02

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Mechanical Engineering

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Oct 30, 2023

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Work and Energy Lab Number and Title: 6a1 Work and Energy Name: Aaron Hsu Group Id: 6 Date of Experiment: 3/2/22 Date of Submission: 3/9/22 Course and Section Number: PHYS 111A006 Instructor’s Name: Bhairavi Apte Partners’ Names: John Pryce IV and Lucas Velerio Mala 1. Introduction: The goals and objectives of this lab are to clearly and completely understand how the total amount of work done on an object would change the energy of that object. To use and show the work-energy theorem by measuring the work that is done on an object with a constant force as well as the kinetic energy of that object. 2. Experimental Procedure: The equipment that we used for this lab is a wooden block, short rod, computer with capstone software installed, 850 universal interface, protractor, single sheave pulley, rotary motion sensor, electronic balance on the lab counter, air supply with a hose, right-angle clamp, force sensor, glider set that includes a glider, 4 50-g weights, a hook, and a string, L-shape aluminum rod, air-track, and 1-m stick in front on the lab counter. To set this experiment up, we would set up both the force and rotary motion sensors towards the end of the air-track and the table using straight and L-shaped rods as well as a right-angle clamp. Then we put the hook on the glider and placed it on the air track and connected one end of the string to the hook that we just put on the glider. We then would take the other end of the string and connect it to the force sensor after we have put the single sheave pulley with the weights already on it. We would then make sure that the string is on the rim of the hanging pulley and the largest pulley of the rotary motion sensor. In order to meet the horizontal condition we would have to level the air track. We would then make sure to connect both the force sensor and the rotary motion sensor to the 850 universal interface. We would then take the weight of the glider with the hook and the 50 g weights and find the inclined angle. Then we would turn on the air supply to the max in order to make it frictionless. We would then click record on the computer and release the glider. The data would then show up on the computer with what was recorded from the run. For the second part, we would slide the wooden block

under one end of the air track to create an inclined angle. Then we would keep the glider with the same mass as in part 1 and make sure to use a protractor to measure the inclined angle. We would then do the same procedure to record the data as in part 1. (see attached photos below) 3. Results: Position x i [m] v i [m/s] Tension, T i [N] Net Force, F i [N] 1 9.4e-2 4.68e-1 2.98e-1 2.33e-1 2 3.26e-1 8.49e-1 2.38e-1 2.38e-1 3 7.30e-1 1.342 2.68e-1 2.68e-1 4 1.089 1.650 3.27e-1 3.27e-1 Position change ( 𝑖 → ? ) 𝑠 = 𝑥 ? − 𝑥 [m] 𝑊 = 𝑇 · 𝑠 [J] 𝐾𝐸 𝑖 = 1 2 ?𝑣 𝑖 2 [J] 𝐾𝐸 ? = 1 2 ?𝑣 ? 2 [J] ∆𝐾𝐸 = 𝐾𝐸 ? − 𝐾𝐸 𝑖 [J] % Difference 𝑊−∆𝐸 | | (𝑊+∆𝐸) × 100 1 → 2 2.32e-1 6. 91? − 2 2. 08? − 2 7. 66? − 2 5. 58? − 2 21. 29% 2 → 3 4.01e-1 9. 54? − 2 7. 66? − 2 1. 71? − 1 9. 44? − 2 1. 054% 3 → 4 3.59e-1 9. 62? − 2 1. 71? − 1 2. 58? − 1 8. 70? − 2 10. 04% 1 → 4 9.95e-1 3. 25? − 1 2. 08? − 2 2. 58? − 1 2. 37? − 1 39. 05%

Position x i [m] v i [m/s] Tension, T i [N] Net Force, F i [N] 1 9.4e-2 4.68e-1 2.98e-1 2.33e-1 2 3.26e-1 8.49e-1 2.38e-1 2.38e-1 3 7.30e-1 1.342 2.68e-1 2.68e-1 4 1.089 1.650 3.27e-1 3.27e-1 Position change ( 𝑖 → ? ) 𝑠 = 𝑥 ? − 𝑥 [m] 𝑊 = 𝑇 · 𝑠 [J] ∆𝐾𝐸 = 𝐾𝐸 ? − 𝐾𝐸 𝑖 [J] ∆𝑃𝐸 = 𝑀?∆ℎ (∆ℎ = 𝑠 · 𝑠𝑖?θ) [J] ∆𝐸 = ∆𝐾𝐸 + ∆𝑃𝐸 [J] % Difference 𝑊−∆𝐸 | | (𝑊+∆𝐸) × 100 1 → 2 1.84e-1 4.38e-2 1. 84? − 1 2. 978? − 2 4. 88? − 2 10.87% 2 → 3 4.04e-1 1. 18? − 1 2. 8? − 2 6. 54? − 2 9. 34? − 2 23.21% 3 → 4 2.14e-1 4. 45? − 2 2. 2? − 2 3. 47? − 2 5. 67? − 2 24.11% 1 → 4 6.59e-1 1. 57? − 1 6. 7? − 2 1. 07? − 1 1. 74? − 1 10.27% These are our equations and calculations that we did: 𝑊 = 𝑇 · 𝑠 𝐾𝐸 𝑖 = 1 2 ? 𝑖 2 𝐾𝐸 ? = 1 2 ? 𝑣 2 ∆𝐾𝐸 = 𝐾𝐸 ? − 𝐾𝐸 𝑖 ∆𝑃𝐸 = 𝑀?∆ℎ ∆𝐸 = ∆𝐾𝐸 + ∆𝑃𝐸 𝑊−∆𝐸 | | (𝑊+∆𝐸) × 100 Table 1-2 0. 298 · 0. 232 = 0. 0691 = 6. 91? − 2 0. 238 · 0. 401 = 0. 0954 = 9. 54? − 2 0. 268 · 0. 359 = 0. 0962 = 9. 62? − 2 0. 327 · 0. 995 = 0. 3250 = 3. 25? − 1 1 2 (0. 18959)(0. 468) 2 = 0. 0207 = 2. 08? − 2 1 2 (0. 18959)(0. 899) 2 = 0. 0766 = 7. 66? − 2 1 2 (0. 18959)(1. 342) 2 = 0. 171 = 1. 71? − 1 1 2 (0. 18959)(1. 650) 2 = 0. 258 = 2. 58? − 1 0. 0766 − 0. 0208 = 0. 0558 = 5. 58? − 2 0. 171 − 0. 0766 = 0. 0944 = 9. 44? − 2 0. 258 − 0. 171 = 0. 087 = 8. 70? − 2 0. 258 − 0. 0208 = 0. 237 = 2. 37? − 1

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0.0691−0.0558 | | (0.0691+0.0558)/2 × 100 = 21. 29% 0.0954−0.0944 | | (0.0954+0.0944)/2 × 100 = 1. 054% 0.0962−0.0870 | | (0.0962+0.0870)/2 × 100 = 10. 04% 0.352−0.237 | | (0.352+0.237)/2 × 100 = 39. 05% Table 2-2 0. 371 − 0. 187 = 0. 184 = 1. 84? − 1 0. 632 − 0. 371 = 0. 361 = 3. 61? − 1 0. 846 −0. 632 = 0. 214 = 2. 14? − 1 0. 846 − 0. 187 = 0. 659 = 6. 59? − 1 0. 238 · 0. 184 = 0. 438 = 4. 38? − 2 0. 327 · 0. 361 = 0. 118 = 1. 18? − 1 0. 208 · 0. 214 = 0. 045 = 4. 45? − 2 0. 238 · 0. 659 = 0. 157 = 1. 57? − 1 1 2 (0. 18959)(0. 634) 2 − 1 2 (0. 18959)(0. 450) 2 = 0. 038 − 0. 019 = 0. 019 = 1. 9? − 2 1 2 (0. 18959)(0. 832) 2 − 1 2 (0. 18959)(0. 634) 2 = 0. 066 − 0. 038 = 0. 028 = 2. 8? − 2 1 2 (0. 18959)(0. 955) 2 − 1 2 (0. 18959)(0. 823) 2 = 0. 086 − 0. 64 = 0. 022 = 2. 2? − 2 1 2 (0. 18959)(0. 955) 2 − 1 2 (0. 18959)(0. 450) 2 = 0. 086 − 0. 019 = 0. 067 = 6. 7? − 2 (0. 18959)(9. 8)((0. 184)𝑠𝑖?(5)) = 0. 0298 = 2. 978? − 2 (0. 18959)(9. 8)((0. 404)𝑠𝑖?(5)) = 0. 0654 = 6. 54? − 2 (0. 18959)(9. 8)((0. 214)𝑠𝑖?(5)) = 0. 0347 = 3. 47? − 2 (0. 18959)(9. 8)((0. 659)𝑠𝑖?(5)) = 0. 107 = 1. 07? − 1 0. 0190 + 0. 0298 = 0. 0488 = 4. 88? − 2 0. 028 + 0. 0654 = 0. 0934 = 9. 34? − 2 0. 022 + 0. 0347 = 0. 0567 = 5. 67? − 2 0. 067 + 0. 107 = 0. 174 = 1. 74? − 1 0.0438−0.0488 | | (0.0438+0.0488) × 100 = 10. 87% 0.118−0.0567 | | (0.118+0.0934) × 100 = 23. 21% 0.0445−0.0567 | | (0.0445+0.0567) × 100 = 24. 11% 0.157−0.174 | | (0.157+0.174) × 100 = 10. 27% 4. Analysis and Discussion: This experiment has a lot of errors that could be produced and many different pieces that could cause an error. It can be from human error which takes place when we release the glider all the way to the computational error that takes place when we work with the lab computer and the capstone software. 5. Conclusion: This experiment gives us a better understanding of how to use the work-energy theorem as well as how it works. The air track that we used in this experiment is a representation of a frictionless surface with the air supply hose that gives us little to none friction coefficient against the track so that we can calculate changes in work and energy without having to eal with any amount of friction. We were also able to learn from this experiment about the ability to change the total energy where total energy in this experiment would be within the gravitational energy and the kinetic energy. 6. Raw Data: