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# UB PHY 158 - 158-M0 Hayden Title Page online rev 1

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VI-1Diameter of bob using ruler: d = 2.30 cm. 2.50 cm, 2.60 cm The range of values measured is maximum - minimum = 2.60 cm -2.30 cm = 0.3 cm or 3.0 mm. Diameter of bob using caliper: d = 2.54 cm, 2.55 cm, 2.53 cm. The range of values measured is maximum - minimum = 2.55 cm -2.53 cm = 0.02 cm or 0.2 mm. Measurements taken using the caliper has a range that is a factor of 15 smaller than the ruler. Hence the precision of the caliper is greater than that of the ruler.Thickness of 100 g mass using a ruler: t = 0.90 cm, 0.95 cm, 0.90 cm. The range is 0.05 cm/0.5mmThe thickness of the mass as measured by the caliper: t = 0.91 cm, 0.92 cm, 0.91 cm. The range is 0.01 cm or 0.1 mmEven in this instance the caliper is more precise as the range of measured values is still a fifth of that of the ruler. However in this instance the the difference is only 5x rather than the 15x of that for the pendulum bob.The range of values for the ruler measurement of the pendulum bob is 3 times larger than the range of values for the ruler measurement of the 100g mass. This is due to several things. The mass is narrower meaning that there is less chance for parallax error. The mass has two flat edges that you are measuring the distance between while the bob diameter changed depending on where you measure.Do At Home (1)Diameter of mug (sideway view): Left side (cm) Right side (cm) Total (cm)0.0 8.1 8.10.1 8.0 7.90.0 8.2 8.2Ranged of measured value is max – min : 8.2-7.9 = 0.3 cm or 3 mmDiameter of mug (vertical view): Left side (cm) Right side (cm) Total (cm)0.0 8.1 8.10.0 8.2 8.20.0 8.2 8.2Ranged of measured value is max – min : 8.2-8.1 = 0.1 cm or 1 mmThe uncertainty of the vertical view is lesser than that of the sideway view hence the vertical view is more accurate.Due to the distance between the ruler and the point of interest where we are measuring, the sideway view has a higher parallax error as the (relatively) large distance exaggerate the possible values that could be viewed by the person.VI-2l’=55cm l=55+2.54=57.54cmuncertainty of 0.3cmMeasured values of T in seconds1.37 1.58 1.421.46 1.63 1.471.54 1.57 1.571.51 1.44 1.411.57 1.32 1.60Excel returns the average value of T= 1.497 seconds. Excel returns the standard deviation of T as σt = 0.09239 seconds The standard deviation of the mean is given as σt/(n)^(1/2) = 0.09239/(15)^(1/2) = 0.02385 secondsHence T +/- σt = 1.50 +/- 0.02 secondsDo At Home (2)Data on single period of pendulum30 cm pendulum (second) 60 cm pendulum (second)1.01 1.401.13 1.441.05 1.381.08 1.431.08 1.38Ranged of measured value is max – min 30 cm pendulum (second) 60 cm pendulum (second)1.13 – 1.01 = 0.12 1.44 – 1.38 =0.06Fractional range δ is δ=range/average range30 cm pendulum (second) 60 cm pendulum (second)0.12/[(1.01+1.13+1.05+1.08+1.08)/5]=12/107 0.06/[(1.4+1.44+1.38+1.38+1.43)/5]=60/703The 30cm pendulum have greater spread of data in both the range and the fractional range.VI-3eye position 1 2 3x0 = 37.4 cmx0 = 37.6 cmx0 = 37.8 cmx=x0-xmFor example, when m=20, X0=37.6, Xm=35.3, 37.6-35.3=2.3 cmm (g) xm (cm) x (cm)20 35.32.320 35.42.220 35.12.540 32.6540 32.74.940 32.55.160 29.97.760 30.07.660 30.27.480 27.79.980 27.79.980 27.79.9100 25.312.3100 24.912.7100 25.112.5120 22.615120 22.914.7120 22.714.9 Slope7.991124360.52161324 intercept Slope unc0.066580020.64497715 unc int0 2 4 6 8 10 12 14 16020406080100120140f(x) = 7.99x + 2.12Hanging mass vs ElongationElongation (cm)mass (g)S + σs = 7.99 +/- 0.07 g/cmB + σb = 0.52 +/- 0.6 gK+σk= 7830 +/- 60 g/s^2VI-4X0=37.4m (g) xm (cm) x (cm)20 35.32.120 35.4220 35.12.340 32.64.840 32.74.740 32.54.960 29.97.560 30.07.460 30.27.280 27.79.780 27.79.780 27.79.7100 25.312.1100 24.912.5100 25.112.3120 22.614.8120 22.914.5120 22.714.7 Slope7.991124362.11983811 intercept Slope Unc0.066580020.63305309 unc intAs even with the parallax, the slope, slope unc., intercept and intercept unc. Are the same as VI-3 hence all calculation onwards will be the same therefore K+σk= 7830 +/- 60

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