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Title: Hooke's Law Credit: https://phet.colorado.edu/sims/html/hoo ... aw_en.html Objective: Through this virtual lab assignment/simulation, Hooke's law for linear springs will be verified. Series and parallel spring combinations will be analyzed and overall displacements or deformation for these combinations will be determined /verified. Theory For linear springs, the applied force and the elongation of the spring from the equilibrium (un- stretched) position are proportional to each other, and the proportionality constant is called the spring constant. FA= KAX For two springs (with spring constants ki and k₂) in a parallel combination, the equivalent spring constant can be found using the equation: kea= k1+k2 (for parallel configuration) For two springs (with spring constants ki and k₂) in a series combination, the equivalent spring constant can be found using the equation: 1/keq = (1/k1) + (1/k₂) (for series configuration)
Lab Narrative Part 1: "Intro" tab 1. Copy and paste the following URL in your browser: https://phet.colorado.edu/sims/html/hoo ... aw_en.html 2. Click on the "Intro" tab. 3. Check all options in the top right corner ("Applied Force", "Spring Force", "Displacement", "Equilibrium Position", and "Values"). Also, check the two springs options right below these options. Now the screen should have two springs. 4. Set the "Spring Constant 1" value to 200 N/m, and "Spring Constant 2" value to 400 N/m. 5. Gradually increase the "Applied Force 1" value from 0 N to 100 N, and record the displacement values corresponding to the following forces: 0 N, 20 N, 40 N, 60 N, 80 N, and 100 N.
6. Gradually increase the "Applied Force 2" value from O N to 100 N, and record the displacement values corresponding to the following forces: 0 N, 20 N, 40 N, 60 N, 80 N, and 100 N. 7. Complete the following table (Table 1): Table 1. Two individual springs Spring 1 Applied Force 1, FA1 (N) Spring Force 1, Fs1 (N) Displacement 1, Ax: (m) 0 K₁= 200 N/m 20 40 60 80 100 Spring 2 Applied Force 2, FA2 (N) Spring Force 2, Fsz (N) Displacement 2, Ax₂ (m) 0 K₂= 400 N/m 20 40 60 80 100 8. Plot displacement (Ax) vs. applied force (FA) for both springs in one graph. Plot Ax in x axis and FA in y axis. Confirm that the slope of such a line represents the spring constant.
Part 2a: "Systems" tab Parallel configuration 1. Click on the "Systems" tab. 2. Check all options in the top right corner ("Applied Force", "Spring Force", "Components", "Displacement", "Equilibrium Position", and "Values"). Also, check the two parallel spring options right below these options. Now the screen should have two parallel springs. 3. Set the following values: Top spring: spring constant, k₁= 200 N/m Bottom spring: spring constant, k₂= 400 N/m Applied force, FA = 100 N 4. Record component forces (i.e., the individual spring forces), and the displacement. Complete the following table (Table 2)
Table 2: Two springs: parallel configuration Top spring, k₁ F, (N) Top spring Bottom spring, k₂ (N/m) Bottom spring Displacement, force, F2 (N) Ax (m) (N/m) force, FS: (N) 200 400 100 5. Verify the simulation results (Fs1, FS2, and Ax values) through theoretical calculations. Show all calculations. Part 2b: "Systems" tab Series configuration 1. Click on the "Systems" tab. 2. Check all options in the top right corner ("Applied Force", "Spring Force", "Components", "Displacement", "Equilibrium Position", and "Values"). Also, check the two springs in series option right below these options. Now the screen should have two springs in series. 3. Set the following values: Left spring: spring constant, k₁= 200 N/m Right spring: spring constant, k₂= 400 N/m Applied force, FA= 100 N 4. Record component forces (i.e., the individual spring forces), and the displacement. Complete the following table (Table 3) O
4. Record component forces (i.e., the individual spring forces), and the displacement. Complete the following table (Table 3) Table 3: Two springs: series configuration Left spring, k₁ Right spring, k₂ FA (N) (N/m) (N/m) Left spring force, Fst (N) Right spring force, Fsz (N) Total Displacement, Ax (m) 200 400 100 5. Verify the simulation results (Fs1, Fsz, and total displacement (Ax) values) through theoretical calculations. Show all calculations.