 # Physics Questions: Measurement Uncertainties

## Question

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.

g(m/s2) for Trial A 9.09 9.09 9.49 9.49 9.49 9.09 9.09 9.49 9.09
g(m/s2) for Trial B 9.93 10.19 9.16 8.93 9.62 9.24 10.42 10.00 9.80

Perform all calculations for this problem for each trial by hand (no Excel).
1. Find the average and standard deviation for the gravitational acceleration in both trials.

2. If the accepted value for gravitational acceleration is 9.82 m/s2, what is the percent difference between the accepted and average of experimental values?

3. How many standard deviations away is the average measurement from the accepted value in each trial?

4. What is the experimental error of the average measurement in each trial?

5. Which trial has more random error, A or B? Explain.

6. Which trial has more systematic error, A or B? Explain.

7. Which trial, A or B, is more accurate? Why?

8. Which trial, A or B, is more precise? Why?

9. Find the percentage uncertainty for the values with given uncertainties below.
X=4.3m ± 0.4 m
Y=1.76 m/s ± .09 m/s
Z=19. km ± 1. km

10. Find the uncertainty for the values with given percentage uncertainties below.
X= 1.34m ± 8%
Y= 22.6m/s ± 9.2%
Z= 14.92 m/s/s ± 2.5%

11. Assuming x, t, and a are related as in a=2x/t2, find the value for %σt if x = 5.0 ± 0.1m and a =10.0 ± 0.5 m/s/s.

12. If α = 0.60 ± 0.03 and t = 0.40 ± 0.01 what is the value of σ for z=exp(-αt)? (exp is the exponential function)

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