Lab 7

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Oct 30, 2023

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Ravyn Solís Lab Partners (Brenna Ashley & Ayi-Lissa Dotson) Physics 1101 Conservation of Energy 10/10/22
Purpose When an object is compressed it gains elastic energy and a fraction of that elastic energy is contained within the spring. As a result, the purpose of this lab is to verify the Law of Conservation of Energy by investigating the compression of a spring. This is accomplished through the examination of spring potential energy, gravitational potential energy, and observation of how the energy is conserved. Equipment ● Assorted Slotted Masses ● (2) Bar Masses ● Dynamics Cart Track (ME-9430A) ● (3) Dynamics Cart Track Feet (ME-8972) ● Large Rod Stand (ME-8735) ● Mass Hanger ● Meter Stick ● Pasco Wireless Smart Car (ME-8972) ● Pulley ● (2) Rod Clamps ● String ● (3) Table Rods ● USB Bluetooth 4.0 Adapter P18295 (PS-3500) Procedure Determining Attach a foot to each end of the track and level it to where the cart does not roll The Spring around freely. Put the pulley on one end of the track and set the last foot on the Constant k track between the pulley and the cart. Record the mass of the cart in Table 1. Set the cart on the track with the spring plunger resting against the foot. Make note of this position and record in Table 1. Use the string to attach the cart to the mass hanger. Set the mass hanger to have a total mass of 300 g and let it hang off the table. You will see that the cart has been displaced. Measure this change in position and record it in Table 1. Calculate the force on the cart in dynes (g*cm/s²). Repeat until the table is filled. Potential Remove the leveling feet and use the Large Rod Stand and (3) Table Rods to Energy incline the track. Remove the string and masses from the cart and rest the cart against the end of the track with the spring plunger set on the second setting. Launch the cart up the track and record its maximum distance, d, up the track. Measure or calculate the angle of the track. Record this Table 2 under trial 1.
Repeat this until all trials are filled. Add 2 bar masses to the cart and repeat step 3. Change the angle of the track and repeat steps 2-5 until the table is filled. Data Analysis Using the data from Table 1, make a plot of force vs displacement and use a trendline to find the slope. The slope is equivalent to the spring force constant, k. Calculate the spring potential energy for each case and record the results into Table 3. Calculate the percent difference between the spring potential energy and the gravitational potential energy. Data Tables [Table 1 Data] [Table 2 Data] [Table 3 Data]
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[Table 4 Data] Graphs Mathematical Solutions Angle ℎ = 𝑑𝑠𝑖𝑛ϕ ϕ = 𝑠𝑖𝑛⁻¹(ℎ/𝑑) ϕ = 𝑠𝑖𝑛⁻¹(10/53. 7) = 10. 7° [ All data regarding angle measurements was collected in a similar manner for a total of 5 trials ] Spring PE k = slope According to the graph, k = 196000 Spring PE = x = 2.4 cm (1/2 𝑘𝑥²) Spring PE = (196000 × 2. 4) ÷ 2 = 115% [ All data regarding Spring Potential Energy was collected in a similar manner for a total of 5 trials ]
Gravitational PE Gravitational PE = mgh m = 271.6g g = 9.8 m/s² h = *varies based on trial 271. 6𝑔 × 9. 8 × 10 = 26617 [ All data regarding Gravitational PE was collected in a similar manner for a total of 5 trials ] Percent Difference |𝑃ₑ − 𝑃ₑ | ÷ (𝑃ₑ + 𝑃ₑ /2) × 100 |98000 − 26617| ÷ (98000 + 26617/2) × 100 = 115% [ All data regarding percent difference was collected in a similar manner for a total of 5 trials ] Q&A 1.) Which of the potential energies was larger? Where did the lost energy go? -The last potential energy of value 882000 was the largest. The potential energy lost was transformed into kinetic energy. 2.) When the mass of the cart was doubled, why did the gravitational potential energy remain about the same? -Gravitational potential energy has a proportional relationship to mass. As a result, when potential energy is doubled, mass is doubled and when mass is halved potential energy is halved. 3.) Suppose the mass of the cart is doubled, what is the distance d that the cart reaches? -If the mass of the cart were doubled ( 271.6g * 2 = 543.2g ) the cart would travel approximately 6.3 cm based on the data gathered from when the cart’s mass totaled 500g and 600g. Conclusion All in all, the objective of this lab was to reinforce the validity of the Law of Conservation of Energy in that energy is never created or destroyed, it merely changes form. Given the calculated percent difference blatant mistakes must have occurred throughout this experiment; nevertheless, a possible source of error lies within the established incline of the track not forming a perfect triangle. In spite of the high percent difference, this lab has served its purpose in allowing the investigation of the Law of Conservation of Energy.

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