These seven original questions cover the four lessons in uncertainty and practical-data reasoning. Write your reasons in full sentences before opening each answer.
Questions
Question 1. Four timings of 10 oscillations are 15.2 s, 15.6 s, 15.0 s and 15.4 s. The stopwatch resolution is 0.01 s. Find the mean, the spread and the uncertainty to quote.
Answer
Mean = (15.2 + 15.6 + 15.0 + 15.4) ÷ 4 = 61.2 ÷ 4 = 15.3 s.
Spread = (15.6 − 15.0) ÷ 2 = 0.3 s.
The spread is larger than the resolution, so quote 15.3 ± 0.3 s.
Question 2. A student quotes the time in Question 1 as 15.30 ± 0.01 s. State what is wrong.
Answer
The uncertainty of 0.01 s is the stopwatch resolution, but the readings differ by 0.6 s, so the real uncertainty is larger.
The result claims more certainty than the data show. Use the larger uncertainty, which is 0.3 s.
Question 3. Explain why a best-fit line is preferred to joining every point on a graph.
Answer
The points scatter because of random errors in measurement. A best-fit line gives one estimate of the underlying relationship, with roughly equal numbers of points on each side.
Joining every point records the errors as if they were real and gives different gradients for different sections.
Question 4. A best-fit line on a V-I graph passes through (0.20, 1.00) and (0.60, 3.00). Find the resistance.
Answer
Gradient = (3.00 − 1.00) ÷ (0.60 − 0.20) = 2.00 ÷ 0.40 = 5.0 Ω.
The gradient of a V-I graph is the resistance.
Question 5. A balance reads 0.6 g with nothing on the pan. An object reads 25.4 g. Find the true mass and say whether repeating the reading would help.
Answer
True mass = 25.4 − 0.6 = 24.8 g.
Repeating would not help, because the offset shifts every reading by the same amount. The zero reading must be subtracted from each reading.
Question 6. A graph of extension against force should pass through the origin, but the best-fit line crosses the vertical axis at 0.8 cm. Suggest a cause.
Answer
A systematic offset is likely, for example the spring was already extended by the weight of the holder or the ruler zero was set incorrectly.
The intercept of 0.8 cm shows the size of the offset. Each extension reading should be reduced by 0.8 cm, or the zero reading should be recorded and subtracted.
Question 7. A block has a mass of 38.6 g (3 s.f.) and a volume of 15 cm³ (2 s.f.). Calculate the density and give it to a suitable precision.
Answer
Density = 38.6 ÷ 15 ≈ 2.573 g/cm³.
The volume has two significant figures, so the answer is 2.6 g/cm³.
See stating a conclusion at a precision justified by the data.
If you got these wrong
Questions 1 and 2 link to resolution versus spread. Questions 3 and 4 link to best-fit lines. Questions 5 and 6 link to systematic offsets.
The timed original practice session builder can turn this set into a timed session. For a teacher to work through the questions you missed, see online one-to-one Physics tuition.