Phy 121L/131L

Pre-Lab: Uncertainties in Making Measurements Name:

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Choose the best answer. (7 pts total)

**You are using a ruler to measure lengths. Assume that you can reasonably measure to one-half of the smallest division. This means you can see if the length of the object is closer to one of the tick marks, half-way between two tick marks, or closer to the following tick mark. (If you can’t tell if a measurement is closer to a tick mark or half-way in between, then you can only reasonably measure to the nearest whole of the smallest division). This is your instrumental precision (instrumental uncertainty).**

1. If the smallest division on your ruler is 1 mm (= 0.1 cm), what is the numerical value of your instrumental precision (instrumental uncertainty)?

a. 1 mm b. 0.1 cm c. 0.05 cm d. 0.05 mm

2. If a rod is exactly three centimeters long, how would you record the length to reflect the precision of the instrument (and therefore, how well you can measure the length)?

a. 30 mm b. 3.0 cm c. 3.00 cm d. 30.00 cm

**A student made the following nine measurements of the time for a ball to roll down an inclined track: t = 2.47 s, 2.48 s, 2.37 s, 2.51 s, 2.42 s, 2.46 s, 2.39 s, 2.38 s, 2.49 s.**

3. If the stopwatch can measure to the nearest 0.01 s, what is the instrumental uncertainty, δinst?

a. 0.01 s b. 0.1 s c. 0.0 s d. 2.44 s

4. What is a reasonable estimate of the sample uncertainty, δsamp? (Choose the best answer)

a. 0.01 s b. 0.1 s c. 0.05 s

d. 0.06 s e. 0.07 s f. Answers c, d, and e are all reasonable estimates

5. What is a reasonable value for the overall uncertainty of the measurement, δt? To determine this, consider both the instrumental and sample uncertainties and choose the larger value. Remember there are often several different reasonable estimates of the sample uncertainty.

a. 0.1 s b. 0.01 s c. 2.44 s d. None of these.

6. What is the “best estimate” of the true value of the measurement, tbest? In most cases, this is the average of the measured values. Remember, this value should be rounded to the same decimal place as the uncertainty, δt.

a. 2.37 s b. 2.44 s c. 2.51 s d. 2.4 s

**The following question deals with the evaluation of the “significance” of “discrepancies.**

7. A student measures a density of (7.7 ± 0.2) g/cm3 for a steel cylinder and the range in accepted value for commercially available steel alloys is 7.8-8.0 g/cm3. Does the student’s experimental value agree with the accepted value?

a. The values do not agree. (There is a significant discrepancy.)

b. The values are close but do not quite agree. (There is a slightly significant discrepancy.)

c. The values agree within uncertainty. (There is no significant discrepancy.)

CSU Pomona Minor Update 3/28/2010 Dr. Julie J. Nazareth