Suppose a measurement is repeated fifteen times and an average and a standard de

Question

Suppose a measurement is repeated fifteen times and an average and a standard deviation are calculated. Further suppose theory makes a prediction about the square of this average. Explain in words how to calculate the absolute error in the square of this average value. Explain in words how to calculate the percent error in the square of this average value. Review page four of Appendix C. In Experiment 2 you calculated an experimental value for the acceleration due to gravity. Suppose your result was 9.82 plusmn 0.02 m/s2. Long ago, a U.S. Coast and Geodetic survey made in Melbourne found the local value to be 9.792 m/s2. Given the number of significant figures in this value, let us assume a maximum error in this 'theoretical' value of plusmn 0.007 m/s2. (The reason being that if the error was as large as plusmn 0.008, then adding this to 9.792 would give 9.80 and the '2' in the thousandth's place would not be significant.) Complete the next three exercises using this information. Following page C-4, calculate d. Similarly, calculate sigma d. Given two measured lengths: L1 = 76.9 plusmn 0.5 and L2 = 62.4 plusmn 0.9 cm. What is the propagated error in the sum of these two lengths? Write the answer as 139.3 plusmn ____ cm. Electrical meters (ammeters and voltmeters) are often accurate to plusmn 3% of the value being measured. Ohm's Law states that R = V/I, where V is voltage (in Volts), I is current (in Amps) and R is Resistance (in Ohms). Calculate the propagated percent error in R if V = 15 Volts and I = 2.7 Amps.

Explanation / Answer

1. Square each of 15 readings, divide with the squared average. This gives you the error.

2. Multiply the above with 100

3,4. C-4 NOT AVAILABLE.

5. 0.9 cm

6. Percentage error gets added on multiplication or division. So, percent error is 3+3=6%. Error is then 0.333 Ohm

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