These are the equations needed In an experiment we are measuring the gravitation

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These are the equations needed

In an experiment we are measuring the gravitational acceleration in 2 different ways. The following table contains the data for two trials, A and B. Perform all bellow calculations for each trial by hand. Find the average and standard deviation for the gravitational acceleration in both trials. If the accepted value for gravitational acceleration is 9.82 m/s2, what is the percent difference between the accepted and averaged measured value? What is the percent error of the averaged measured value for each trial? How many standard deviations away is the averaged measurement value from the accepted value? Which trial is more random. A or B? Explain. Which trial has more systematic error, A or B? Explain. Which trial, A or B, is more accurate? Why? Which trial, A or B, is more precise? Why? Find the percentage uncertainty for the values with given uncertainties below. X=3.5 m 0.5 m Y=0.20 m/s .09 m/s Z=44. km 5. km Find the uncertainty for the values with given percentage uncertainties below. X=3.17m 6% Y=6.6m/s 12% Z=7.9 m/s/s 4.6% Assuming x, t, and a are related as in a=2x/t2, find the value for % sigma, if x = 9.0 0.3m and alpha =2.0 0.2 m/s/s. If alpha = 0.80 plusminus 0.04, and t=0.20 0.02 what is the value of sigma for z=exp(- alpha t)?(exp is the exponential function) Derive equation 1.3 using equation 1.2. Express % sigma z interms of % sigma w, % sigma x and % sigma y. if z=w/(x7y5)*%Percent Difference = |Observed Value- Accepted Value|/ Accepted Value.100% 1.13 If the quantity z is the product or quotient of x and y, i.e.z = x middot y or z = x/y then where % sigma z = sigma z/z.100%(% sigma z is read as % sigma z) and therefore, sigma z = z.% sigma z/100 1.7 For the same set of x's we can also define the RMS deviation from the mean, denoted by through the equation The quantity sigma is a measure of how dispersed the values of x away from their average, x are. If all x values are the same, then sigma is zero. The RMS deviation is frequently called the "standard deviation". (Strictly speaking,sigma is the standard deviation if the x values come from a particular kind of distribution of errors called the "normal" or "Gaussian" distribution). Note: Excel uses 1/(N-1) instead of 1/N in Eq. (2). This only makes a significant difference when the value of N is rather small, less than 10, say. Then it turns out that the estimate of sigma obtained with l/(N-1) corrects for the average over a small number of measurements having an error when compared with the average over many more measurements. Another equivalent expression for sigma in Eq. (2) is given by:

Explanation / Answer

Number of measurements in trial A, n= 9

Arthimetic mean(Xn) = sum of all value/n = 9.39

Deviation of (xi=9.23) = xi - Xn = -0.16

Deviation of (xi=9.59) = xi - Xn = 0.20

Variance = sigma^2 = 1/n*sum of square of Deviations

Variance = 1/9(5*0.16^2 + 4*0.20^2) = 0.032

Standard deviation = Sigma = sqrt(Variance) = 0.1789

Number of measurements in trial B, n= 9

Arthimetic mean(Xn) = 9.477

Deviation of (xi=9.13) = xi - Xn = -0.347

Simalarly others are -0.487 , 0.483 , -0.747 , -0.157 , -0.137 , 0.543 , 0.623 , 0.223

Standard Deviation = 0.4625

b) % Diff = (9.8-9.39)/9.8*100 = 4.18--------for trail A

% Diff = (9.8-9.477)/9.8 * 100 = 3.3 --------for trail B

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