Phy lab 4.docx - .

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VI-1 m (g) x (cm) x = x – x 20.0 26.1 2.7 40.0 23.6 5.2 60.0 21.1 7.7 80.0 18.4 10.4 100.0 16.0 12.8 120.0 13.4 15.4 Calculated these values using the Linest Function Slope 7.864043 -1.03852 y-intercept Uncertainty in slope 0.047033 0.471421 Uncertainty in y- intercept 2 4 6 8 10 12 14 16 18 0 20 40 60 80 100 120 140 f(x) = 7.86x - 1.04 m versus x = x0 - xm x = x0 - xm (cm) m (g) slope : s = k g k = s g = 7.864043 980 cm / s 2 = 7706.76214 = 7706.762 N / m σ k = k ( σ s s ) 2 = 7706.762 N m ( .047033 7.86043 ) 2 = 46.11352523 = 46.1135 k ±σ k = 7707 ± 46.11
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VI-2 m m C N T T 40 48.9 238 118.75 0.505263 0.255291 40 48.9 238 118.75 0.505263 0.255291 40 48.9 237 118.25 0.5074 0.257454 60 68.9 201 100.25 0.598504 0.358207 60 68.9 201 100.25 0.598504 0.358207 60 68.9 201 100.25 0.598504 0.358207 80 88.9 177 88.25 0.679887 0.462246 80 88.9 177 88.25 0.679887 0.462246 80 88.9 177 88.25 0.679887 0.462246 100 108.9 161 80.25 0.747664 0.559001 100 108.9 160 79.75 0.752351 0.566032 100 108.9 160 79.75 0.752351 0.566032 120 128.9 148 73.75 0.813559 0.661879 120 128.9 148 73.75 0.813559 0.661879 120 128.9 147 73.25 0.819113 0.670945 Values calculated by linest function Slope 0.005116298 0.051707 Y-intercept Uncertainty in slope 2.51431E-05 0.002133 Uncertainty in y- intercept 25 30 35 40 45 50 55 60 65 70 0 0.5 1 1.5 2 2.5 3 f(x) = 0.04x + 0.08 T2 vs. m m (g) T2 (s2) T 2 = 4 π 2 m k + 4 π 2 α m s k
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y = sx + b s = 4 π 2 k k = 4 π 2 s = 39.4784176 .005116298 = 7716.207618 = 7716.20762 N m σ k = k ( σ s s ) 2 = 7716.20762 ( 2.51431 10 5 .005116298 ) 2 = 37.91987485 = 37.9199 k ±σ k = 7716 ± 37.92 The spring constants are in range of each other. VI-3 Mass of spring = 2.8g b = 4 π 2 α m s k .051707 = 4 π 2 α 2.8 7716.208 α = 3.609404032 = 3.61 VI-4 28.8 30.05 108 53.75 1.116279 1.246079 28.8 30.05 109 54.25 1.105991 1.223216 28.8 30.05 109 54.25 1.105991 1.223216 37.3 38.55 96 47.75 1.256545 1.578904 37.3 38.55 97 48.25 1.243523 1.54635 37.3 38.55 96 47.75 1.256545 1.578904 45.9 47.15 87 43.25 1.387283 1.924555 45.9 47.15 88 43.75 1.371429 1.880816 45.9 47.15 88 43.75 1.371429 1.880816 54.4 55.65 80 39.75 1.509434 2.278391
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