1) Rank the following measurements in order from the most precise to
the least precise based on the relative uncertainty implied by each value:
9.7 m, 13 m, 1.45 m, 2.1 m,
0.005 m

(Use > or = , so that A > B means A is more precise than B, and A =
B indicates equal precision)

a) 0.005 > 1.45 > 9.7 = 2.1 > 132) A group of students are told to use a meter stick to find the length of a hallway. They make 6 independent measurements: 4.402 m, 4.217 m, 4.345 m, 4.925 m, 4.372 m, 4.289 m. How should they report their best estimate of the length of the hallway?

b) 0.005 > 1.45 > 2.1 > 9.7 > 13

c) 1.45 > 9.7 = 13 = 2.1 > 0.005

d) 1.45 > 9.7 > 2.1 > 13 > 0.005

a) L = 4.33 ± 0.03 m3) A student uses a protractor to measure an angle to be A = 82

b) L = 4.43 ± 0.25 m

c) L = 4.325 ± 0.073 m

d) L = 4.425 ± 0.104 m

a) sin(A) = 1.0 ± 0.2

b) sin(A) = 0.99 ± 0.02

c) sin(A) = 0.990 ± 0.002

d) sin(A) = 0.9903 ± 0.0024

4) Which period is more *accurate*, and why?

a) Student A's period of 1.25 s because a digital stopwatch is more reliable.5) Which measurement is more

b) Student A's period of 1.25 s because the stopwatch can measure to 0.01 s.

c) Student B's period of 1.6 s because it is closer to the known period than A's value.

d) There is not enough information to answer this question.

a) Student A's period of 1.25 s because a digital stopwatch is more reliable.6) What is the most probable source of error that could explain the difference in the results?

b) Student A's period of 1.25 s because the stopwatch can measure to 0.01 s.

c) Student B's period of 1.6 s because it is closer to the known period than A's value.

d) There is not enough information to answer this question.

a) Human reaction time in starting and stopping the timing devices.

b) The stopwatch may run too fast; not calibrated properly.

c) The amplitude of oscillation may have been too large for one pendulum.

d) Student A mistakenly measured 4 oscillations instead of the intended 5.

h = 5.25 ± 0.15 m, t = 1.14 ± 0.06 s.

7) Use the equation a = 2h/t^{2} to determine the average acceleration
and its uncertainty.

a) 8.08 ± 0.1 m/s8) Comment on the accuracy of the acceleration result. Do you think the student made any mistakes?^{2}

b) 8.08 ± 0.88 m/s^{2}

c) 8.08 ± 0.06 m/s^{2}

d) 8.1 ± 0.9 m/s^{2}

a) The uncertainty is high; probably a mistake in height measurement or reaction time with stopwatch.9) What one suggestion would you tell this student to improve the accuracy of the experimental result?

b) Although a < g, the result seems reasonably accurate since air resistance would reduce the ball's acceleration.

c) The result does not agree with 9.8 m/s^{2}, so the student must have made a mistake.

d) The result can only be as accurate as the measurements; cannot tell if a mistake was made.

a) Measure height better, maybe use a long tape measure that does not stretch.10) A student measures the ratio of the circumference of a circle divided by its diameter to be 3.3 ± 0.1, where the reported uncertainty is the standard error found from repeated measurements. Does this result agree with the known value of PI = 3.14159...?

b) Improve the precision of the time with more trials or automatic device.

c) Get an assistant to time when the ball hits the ground.

d) Reduce or eliminate air resistance.

a) No, the uncertainty range of the measured result does not include the value of PI.

b) The probability of agreement is about 5%.

c) The relative error is 5%, which is small enough to be considered acceptable.

d) We need to know how the measurements were made to answer this question.