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Graph 1: Force versus Displacement + 0.199 0.98 0.296 1.47 0.988 4.9 1.085 5.39 1.182 5.88 1.279 6.37 Force Vs Displacemnt y.= 4.9809x - 0.0098-- R 31.... Force (N) 0.2 0.4 0.6 0.8 12 114 Distance/Displacemnt (m)Data Table 1: Measuring the Spring Constant of a Spring Mass Displacement (m) Weight (N) k = slope (N/m) (kg) 0.100 0. 199m 0.98N 4.98N/m 0. 150 0.296m 1.47N 0.500 0.988m 4.9N 0.550 1.085m 5.39N 0.600 1. 182n 5.88N 0.650 1.279m 6.37NData Table 2: Potential Energy for m = 0.500 kg Push Up Y1- Yo Y1 (m) Y2 (m) Ugi ( J ) Ug2 ( J ) Us1 ( J ) Us2 ( J) Aug ( J ) AUs (J) % Diff. (m 0.010 0. 15 m 13 m 1.029 J 1.274 J 0.246 J 1849.705 J 1.259 J 1849.489 J 99% 0.020 0.25 m 14 m 4.018 J 2.744 J 0.684 J 2145.220J 2.695 J 2144.536 J 100% 0.030 0.35 m 15 m 8.967 J 4.41 J 1.341 J 2462.625 J 4.307 J 2461.284 J 100% 0.040 0.45 m 16.5 m 15.876 J 6.468 J 2.216 J 2979.776 J 6.291 J 2977.560 J 100% Pull Down 0.010 0.05 m 17 m 0.049 J 1.666 J 0.027 J 3163. 105 J 1.661 J 3163.077 J 100% 0.020 0.15 m 26.5 m 0.029 J 5.194 J 0.025 J 7686.126 J 5. 164 J 7685.880 J 96% 0.030 0.25 m 36 m 0.074 J 10.584 J 0.684 J 14184.720 J 10.511 J 14184.036 J 100% 0.040 0.35 m 44 m 0.137 J 17.248 J 1.265 J 21189.52 J 17.115 J 1188.255 J 98%\fData Table 4: Springs in Parallel Applied Top Spring Force (N) Bottom Spring Force (N) Force (N) Top Spring Constant = 200 Mm, Bottom Spring Constant = 200 N/m Displacement (m) Spring Constant (N/m) 2 -10.0 N -10.0 N 400 N/ m -25.0 N 25.0 N -50.0 N 50.0 N 25.0 N 25.0 N Top Spring Constant = 200 Mm, Bottom Spring Constant = 500 N/ m 2 -5.7 N -14.3 N -14.3 N -35.7 N -28.6 N >71.4 N 14.3 N 35.7 N Top Spring Constant = 300 Mm, Bottom Spring Constant = 500 N/ m 20 -7.5 N 42.5 N -18.8 N -31.3 N -37.5 N -62.5 N 18.7 N 31.2 N Graph 2: Spring Constant for Springs in Parallel + A Displacemnt Applied Force 0.05 20 0.125 50 0.25 100 -0.125 -50 B Displacemnt Applied Force 0.029 20 0.071 50 0.143 100 -0.071 -50 C Displacement Applied Force 0.025 20 0.063 50 0.125 100 -0.063 -50 Spring Constant for Springs in Parallel 120 100 y = 701.53x - 0.166 y = 797.28x +0.1018 ... 80 Applide Force y = 400x +6E-15 60 D 40 C 20 bett.......... ........ Linear (A) -0.15 -0.1 0.05...... 0.05 0.1 0.15 0.2 0.25 0.3 ........ Linear (B) ........ Linear (C) 60 DisplacemnetData Table 5: Springs in Series Applied Left Spring Force (N) Force (N) Right Spring Force on Applied Force Right Spring Force on Left Spring(N) (N) Left Spring Constant = 200 N/m, Right Spring Constant = 200 N/m Displacement (m) Spring Constant (N/m) 2 -20 N 20N 100 N/m -50 N 50N -100 N 100N 50N -50 N Top Spring Constant = 200 N/m, Right Spring Constant = 500 Mm 2 -20 N 20N 142.857 N/m ~50 N 50N -100 N 100N SUN -50 N Top Spring Constant = 300 N/m, Right Spring Constant = 500 N/m 2 -20 N 20N 187.5 N/m ~50 N 50N -100 N 100N 50N -50 N Graph 3: Spring Constant for Springs in Series + A Displacement Applied Force 0.2 20 0.5 50 100 -0.5 -50 B Displacement Applied Force 0.14 20 0.35 50 0.7 100 -0.35 50 C Displacement Applied Force 0.107 20 0.267 50 0.533 100 -0.267 -50 Spring Constant for Springs in Series 1:20 y = 142.86x - 6E-15 100 y = 187.48x +0.0032 y = 100x +6E-15 80 Applied Force ............... B ....... ...... 20 ........ Linear (A) ........ Linear (B) -0.6 -0.4 -0 0.2 0.4 0.6 0.8 1 1.2 ........ Linear (C) Were.......... ............... -60 DisplacemntData Table 6: Energy Displacement Applied Force (N) Spring Potential Energy (J) (m) Spring Constant = 100 N/m 0.200 20 N 0.600 60 N 1.000 100 N -0.400 _40 N -0.600 _60 N Spring Constant = 200 Mm 0.200 40 N 0.600 120 N 1.000 200 N -0.400 -30 N '0500 420 N Spring Constant = 350 N/m 0.200 70 N 0.600 210 N 1.000 350 N .0400 _1 40 N -0.600 -210 N Graph 4: Energy versus Force + A Applied Force Potential Energy 20 2 60 18 100 50 -40 8 -60 18 B Applied Force Potential Energy 40 120 36 200 100 -80 16 -120 36 C Applied Force Potential Energy 70 210 63 350 175 -140 28 -210 63 Potential Energy Vs Applied Force 200 180 y = 0.1777x +57.25 Potential Energy 160 140 120 100 y=0.1777x +32,764"" -c 40 ........ Linear (A) 0.1777x+16.357 ........ Linear (B) ........ Linear (C) 300 -200 -100 100 200 300 400 Applied ForceExercise 2 - Questions 1. Compare the Weight and Displacement data collected in Exercise 1 in Data Table 1 to the Applied Force and Displacement data collected in Exercise 2 in Data Table 3. How are these data similar and how are they different? Discuss the reasons for these similarities and differences. 2. Is the effective spring constant for springs in parallel larger or smaller than the spring constant of each individual spring? Is the effective spring constant for springs in series larger or smaller than the spring constant of each individual spring? Explain your answers. 3. What is the relationship between the applied force of a hanging mass on a spring and the spring force of the spring? Use the data in Data Table 3 to support your answer. 4. Compare the effective spring constants calculated in Data Table 4 and Data Table 5 and the spring constants derived from the graphs in Graph 2 and Graph 3. Which method gives more reliable results and why? 5. What is the relationship between the spring potential energy of a spring and the spring constant of the spring? Use the data in Data Table 6 to support your answer. 6. Compare the graph in Graph 4 to the Energy Plot in the Energy page of the simulation. What do these two graphs tell you about the relationships between potential energy, displacement, and spring force