Name: ____________________
Student ID# _______________
Physics 26 Lab Exam – SAMPLE (with answers) Date: ________ Time: _______
Lab Instructor: _____________
Instructions: Work individually to complete each exercise to the best of your ability, show all your work, and
clearly explain your answers in the spaces provided or on the back of these papers.
Be sure to record all measurements (in SI units) and show all calculations. For items that require a numerical
result, write your answer as you would for a formal lab report, including a meaningful label to identify a value.
Your answer will be graded based on the accuracy of your result and proper reporting of uncertainty,
significant figures, and units.
Once the lab exam begins, you are not permitted to receive any assistance from your TA or other students.
However, you may use your lab manual, graded lab reports, notes, and textbook as resources for this exam. The
questions may be answered in any order, so adjust your work according to the availability of the lab equipment.
Honor Pledge: All work presented here is my own. _______________________________
1. A simple pendulum is known to have a period of oscillation T = 1.55 s. Student A uses a digital stopwatch to
measure the total time for 5 oscillations and calculates an average period T = 1.25 s. Student B uses an analog
wristwatch and the same procedure to calculate an average period for the 5 oscillations and finds T = 1.6 s.
a) Which student made the more accurate measurement? Explain.
The measurement made by Student B is closer to the known value and is therefore more accurate.
b) Which measurement is more precise? Explain.
The measurement made by Student A is reported with more digits and is therefore more precise.
c) What is the most likely source of error that could account for the difference in the results?
Although the difference in period measurements is only 0.3 s, the original timing measurements must
have differed by 5 times this amount since we are told that the average period was calculated from the
total time for 5 oscillations. So even though reaction time (typically ~0.2 s) is a likely source of error,
this would not explain the discrepancy of approximately 1.5 s, or about one period. Therefore, the most
likely source of error is that Student A mistakenly measured only 4 oscillations instead of 5.
This example shows that a more precise measurement is not always more accurate.
2. The number of significant figures reported for a measured value suggests a certain degree of precision.
What is the relative uncertainty implied by the following numbers?
a) 0.30 implies an uncertainty of ± 3 % (possibly 2% from rounding error)
b) 9.8 implies an uncertainty of ± 1 % (possibly 0.5% from rounding error)
c) 52 implies an uncertainty of ± 2 % (possibly 1% from rounding error)
d) 0.503 implies an uncertainty of ± 0.2 % (possibly 0.1% from rounding error)
3. A student uses a protractor to measure an angle to be θ = 85° ± 1°. What should she report for sinθ ?
sin(θ) = 0.996 ± 0.002
(The uncertainty can be determined from either the max/min method or propagation of error.)
