A student measures the period of a pendulum (T) for five different lengths L. As
ID: 3327350 • Letter: A
Question
A student measures the period of a pendulum (T) for five different lengths L. As in problem 1, the formula forg is g=4 (pi) L/T^2. He now calculates the five values of g, and uses the AVERAGE and STDEV functions of Excel, finding 965.6, and 3.26, respectively.
a) Assuming all the errors are random and independent, calculate the SDOM and the difference D compared to the expected value of 979.6, and the t value. Do you think his measurements were done correctly?
b) The student is suspicious that a systematic error in the length measurement might be causing problems. Calculate D in % and use it to estimate how large a systematic error in length would be required to explain the result.
3. A student measures the period of a pendulum (T) for five different lengths L. As in problem 1, the formula forg is g=4 Tº L/T2. He now calculates the five values of g, and uses the AVERAGE and STDEV functions of Excel, finding 965.6, and 3.26, respectively. a) Assuming all the errors are random and independent, calculate the SDOM and the difference D compared to the expected value of 979.6, and the t value. Do you think his measurements were done correctly? b) The student is suspicious that a systematic error in the length measurement might be causing problems. Calculate D in % and use it to estimate how large a systematic error in length would be required to explain the result.Explanation / Answer
A) Mean of the sample = 965.6
standard deviation of sample = 3.26
Standard Deviation of Mean = s/ sqrt(n) = 3.26/ sqrt(5) = 1.46
Difference D = (979.6 - 965.6) = 14
t - value = 14/ 1.46 = 9.59
As t- value is too high that p- value = 0.000000001 level so we can say that either sample is correct or measurements are taken incorrectly.
2. Percentage Difference = Abs(D)/ g0 * 100 = 14 * 100/ 979.6 = 1.43%
As length is proportional to g here so a systematic error in length of 1.43% will produce such an error.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.