Lab Report 6

Physics Laboratory Report Lab number and Title: Lab 125: Conservation of Energy in Spring-Mass System Name: Sami Choudhury Group ID: N/A Date of Experiment: _ 10 /_ 31 _/__ 22 ___ Date of Report Submission: 8 __/_ 5 __/__ 22 Course & Section Number: Physics 111A Lab Instructor’s Name: Professor Dieonna George Partners’ Names: Nick, Gulam, Alexis, Sahil 1. INTRODUCTION 1.1 Objectives: - 1.1.1 This experiment's purpose will be to demonstrate that mechanical energy is conserved in an oscillating spring-mass system. 1.2 Theoretical Background: - 1.2.1 The law of conservation of energy is KEi + PEi = KEF + PEF, as we are aware from the prior lab. where the end mechanical energy equals the starting mechanical energy (the sum of the initial potential and kinetic energy). The application of the law of conservation of energy is different in a spring mass system, though. Using our motion sensors and software, we will conduct an experiment using a body of mass M suspended on a coil spring with constant spring constant K to track how the object's KE and PE vary with displacement. The increase in mass will reveal the various displacements. We'll carry out our experiment and assess the answers to the equations from the lab manual. We shall contrast the results of the experiment.

EXPERIMENTAL PROCEDURE

3.) Results: - 3.1 Experimental data: - Table I M M+100g M+200g M+300g M+400g M+500g Mass (g) 50.3 150.4 251.4 350.4 450.4 550.4 Mass (kg) .0503 0.1504 0.2514 0.3504 0.4504 0.5504 Weight (N) 0.493 1.4739 2.4639 3.4339 4.4139 5.3939 Position h0 h1 h2 h3 h4 h5 Position, (m) .44 .417 .3901 .3492 .3086 .27 Displacement (m) 0 .013 .05 .0908 .1314 .17 - 3.1.2 - Table II Point # Displacement (m) Velocity, v (m/s) 𝐾𝐸 = 1/2 ?𝑣 2 (J) PE=1/2kx^2 + (mg)^2 / 2k E mech 1 .049 .0230 .0000129 1.44256 1.4425 2 .0565 .5260 .007816 1.663 1.6639 3 .1295 .0291 .000054831 3.81248 3.8125

3.2) Calculation: 3.2.1.1 Fg = M *g (Mass #1) = 0.503 * 9.81 = 0.493 N (Mass #2) = (0.0507+ 0.1) * 9.81 = 1.4739 N (Mass #3) = (0.0507+0.2) * 9.81 = 2.4639 N (Mass #4) = (0.0507+0.3) * 9.81 = 3.43 N (Mass #5) = (0.0507 +0.4) * 9.81 = 4.414 N (Mass #6) = (0.0507+0.5) * 9.81 = 5.39 N 3.2.2 Spring Constant for each Mass K1 = (Fg)/Displacement K2 = Fg (Mass #1) / (h1-h0) = 1.47/ (0.44-0.417) = 63.91 K3 = Fg (Mass #2) / (h2-h0) = 2.46 / (0.44-0.3901) = 49.2 K4 = Fg (Mass #3) / (h3-h0) = 3.43/ (0.44-0.3492) = 37.78 K5 = Fg (Mass #4) / (h4-h0) = 4.41/ (0.44-0.3086) =33.56 K6 = Fg (Mass #5) / (h5-h0) = 5.39/ (0.44-0.27) = 31.71

3.2.4 Spring Constant Error 𝑀𝐸 𝑀𝑎𝑥 −𝑀𝐸 𝑀𝑖? 𝑀𝐸 𝑀𝑎𝑥 +𝑀𝐸 𝑀𝑖? /2 | | | | | | *100 = 22.4% 3.81−1.44 3.81+1.44 /2 | | | | 4 ANALYSIS and DISCUSSION As the data portrays above, ME can vary with displacement, as it continues to stay in oscillating motion. The variation could be the probable cause for the percent error experienced as well.Our results for KE and PE will vary because we are taking three measurements of the object's oscillation in relation to its maximum, minimum position, and maximum velocity. Additionally, with the differing velocities in each different displacement, the kinetic energy will be different as a result as well. Similarly for potential energy, since we used differing displacements, the potential energy will be different. As a result, each point's mechanical energy, which is the total of the potential and kinetic energy, will likewise vary. The mechanical energy at each point is still fairly near, therefore our experiment still achieves our goal of confirming Hooke's rule of conservation of mechanical energy. Energy is conserved in oscillations, according to Hooke's rule, even though there is a slight difference of around 22% between each mechanical energy. 5 CONCLUSIONS In conclusion, this lab helped me solidify concepts in conservation of energy to verify work energy theorems. Since some of the concepts were fairly similar to the previous lab, Lab 6a1: Work and Energy. It has helped me grow a familiarity with the use of work and energy concepts in physics. This lab has helped me understand concepts of the kinetic and potential energy in a spring-mass system and how a spring does in fact conserve mechanical energy as it becomes compressed. The visualization of the spring-mass system in the works alongside the computer software showing the values has also brought about understanding in the many different equations we utilized to find the mechanical energy, kinetic energy, and potential energy. The only question I had during the experiment was how different would the numbers be if we took wind resistance into account as the mass was oscillating up and down, would that significantly reduce the percent error?

Attachment of Raw Data (5 points)