LAB_M9_Report

VI-1 Mass of holder = 5.1 g Mass of spring = 2.8 g Mass of flag = 3.5 g x_0 = 24.5 cm x = x_0 – x_m cm m(g) x_m(cm) x(cm) = x_0 - x_m 20 21.8 40 19.1 60 16.4 80 13.7 100 10.7 120 8 16.5 2.7 5.4 8.1 10.8 13.8 0 20 40 60 80 100 120 140 0 5 10 15 20 m vs x x(cm) m(g) y = 7.22x +1.03 slope 7.22191168 1.03074343 intercept slope unc 0.06054808 0.64524198 intercept unc S = k/g S = 7.22 g/cm = 0.722 kg/m K = S * g = 0.722 * 9.8 K = 7.08 σ k = σ s *g = 0.0061 * 9.8 σ k =0.0598 k ±σ k = 7.1 ± 0.1 N/m

VI -2 N = (2(C -1) +1)/4 T =60/N Example: when C is 106, N is 52.75 and T is 1.14 m(g) m_T(g) C N T T^2 40 48.6 106 52.75 1.13744076 1.29377148 40 48.6 102 50.75 1.18226601 1.39775292 40 48.6 106 52.75 1.13744076 1.29377148 60 68.6 197 98.25 0.61068702 0.37293864 60 68.6 197 98.25 0.61068702 0.37293864 60 68.6 197 98.25 0.61068702 0.37293864 80 88.6 166 82.75 0.72507553 0.52573452 80 88.6 174 86.75 0.69164265 0.47836956 80 88.6 149 74.25 0.80808081 0.65299459 100 108.6 156 77.75 0.77170418 0.59552734 100 108.6 139 69.25 0.86642599 0.750694 100 108.6 156 77.75 0.77170418 0.59552734 120 128.6 142 70.75 0.84805654 0.71919989 120 128.6 142 70.75 0.84805654 0.71919989 120 128.6 139 69.25 0.86642599 0.750694 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 20 40 60 80 100 120 140 m(g) T^2 vs m T^2(s^2) y = -0.0046x +1.095 slope -0.0046158 1.09539972 intercept slope unc 0.00294869 0.25020487 intercept unc S = -0.0046 g/s^2 = -4.6e-6 kg/s^2 S = 4 π 2 k K = 4 π 2 S = 4 π 2 − 4.6e-6 K = -8.6e6 σ k = 4 π 2 σ s = 4 π 2 2.9 e − 6

l'(cm) l = l' + d/2 C N T T^2 28 29.25 111 55.25 1.08597285 1.17933703 28 29.25 112 55.75 1.07623318 1.15827787 28 29.25 112 55.75 1.07623318 1.15827787 34 35.25 105 52.25 1.14832536 1.31865113 34 35.25 104 51.75 1.15942029 1.34425541 34 35.25 104 51.75 1.15942029 1.34425541 41.5 42.75 98 48.75 1.23076923 1.5147929 41.5 42.75 98 48.75 1.23076923 1.5147929 41.5 42.75 99 49.25 1.21827411 1.48419181 45.5 46.75 93 46.25 1.2972973 1.68298028 45.5 46.75 92 45.75 1.31147541 1.71996775 45.5 46.75 92 45.75 1.31147541 1.71996775 52.5 53.75 86 42.75 1.40350877 1.96983687 52.5 53.75 86 42.75 1.40350877 1.96983687 52.5 53.75 86 42.75 1.40350877 1.96983687 58 59.25 83 41.25 1.45454545 2.11570248 58 59.25 83 41.25 1.45454545 2.11570248 58 59.25 84 41.75 1.43712575 2.06533042 0 0.5 1 1.5 2 2.5 0 10 20 30 40 50 60 70 T^2(s^2) l(cm)) T^2 vs l y = 0.03x + 0.19

slope 0.03219525 0.19764437 intercept slope unc 0.0009253 0.04225221 intercept unc S = 0.03 s^2/cm = 3 s^2/m S = 4 π 2 g g = 4 π 2 S = 4 π 2 3 g = 13.15 m/s^2 σ g = 4 π 2 S + σ s - 4 π 2 S − σ s σ g = 0.82 m/s^2 g±σ g = 13.15 ± 0.82 m / s 2 The calculated value of g is not within the range of the accepted value of 9.8 m/s^2 VI -5 W = 1.35 cm M = 100 g t(s) watch t(s) timer v_m = W/t timer ln v_m 30 0.0363 37.1900826 3.61604213 60 0.0522 25.862069 3.25277738 90 0.0744 18.1451613 2.89840393 120 0.0985 13.7055838 2.61780332 150 0.1085 12.4423963 2.5211097 180 0.1367 9.87564009 2.29007113 210 0.1496 9.02406417 2.19989481 240 0.178 7.58426966 2.02607632 270 0.1982 6.81130172 1.91858325 300 0.5149 2.62186832 0.96388716