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Flashcards · 7408 · Topic 1
Measurements and their errors flashcards
19 cards on Topic 1, subtopics 3.1.1 to 3.1.3. Pick a subtopic or study them all.
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3.1.1 Use of SI units and their prefixes
- The six SI base quantities used in the course, with their units
- Mass: kilogram (kg). Length: metre (m). Time: second (s). Amount of substance: mole (mol). Temperature: kelvin (K). Electric current: ampere (A). The candela is excluded from the specification.
- Write the newton, joule, watt and pascal in SI base units
- N = kg m s⁻² J = kg m² s⁻² W = kg m² s⁻³ Pa = kg m⁻¹ s⁻²
- Values of the prefixes T, G, M, k
- T (tera) 10¹², G (giga) 10⁹, M (mega) 10⁶, k (kilo) 10³.
- Values of the prefixes c, m, μ, n, p, f
- c (centi) 10⁻², m (milli) 10⁻³, μ (micro) 10⁻⁶, n (nano) 10⁻⁹, p (pico) 10⁻¹², f (femto) 10⁻¹⁵.
- How do you convert between eV and J, and between kW h and J?
- eV → J: multiply by 1.6 × 10⁻¹⁹ (J → eV: divide). kW h → J: multiply by 3.6 × 10⁶, since 1 kW h = 1000 W × 3600 s (J → kW h: divide).
- Convert 8.5 cm² into m²
- 1 cm² = (10⁻² m)² = 10⁻⁴ m², so 8.5 cm² = 8.5 × 10⁻⁴ m². The prefix is raised to the same power as the unit.
3.1.2 Limitation of physical measurements
- Accurate (measurement)
- Close to the true value.
- Precise (measurements)
- Repeat readings close to each other. A miscalibrated instrument can give precise but inaccurate readings.
- Resolution (of an instrument)
- The smallest change in a quantity an instrument can detect.
- Repeatable vs reproducible
- Repeatable: the same result on repeating with the same method and equipment. Reproducible: the same result with a different method or by a different person.
- Random vs systematic error: what each does and how to reduce it
- Random: unpredictable scatter about the true value; reduced by repeating and averaging. Systematic: every reading offset the same way; repeating does not help, so recalibrate or zero the instrument.
- Combining uncertainties: adding/subtracting, multiplying/dividing, raising to a power n
- Adding or subtracting: add the absolute uncertainties. Multiplying or dividing: add the percentage uncertainties. Raising to a power n: multiply the percentage uncertainty by n.
- A radius is measured to 2%. What is the percentage uncertainty in a volume proportional to r³?
- 3 × 2% = 6%.
- How do you find the uncertainty in a gradient from a graph with error bars?
- Draw the steepest and shallowest lines that pass through all the error bars. Uncertainty in gradient = (maximum gradient − minimum gradient) ÷ 2.
- How does a zero error show up on a straight-line graph?
- The gradient is correct but there is an unexpected intercept: a line that should pass through the origin does not.
3.1.3 Estimation of physical quantities
- Order of magnitude of a × 10ⁿ (1 ≤ a < 10): the rounding convention
- The nearest power of ten by ratio: 10ⁿ if a is below about 3.16 (√10), and 10ⁿ⁺¹ if a is above it.
- Order of magnitude of 2.9 × 10⁴, and of 8 × 10⁵
- 2.9 × 10⁴ → 10⁴. 8 × 10⁵ → 10⁶ (8 is above 3.16).
- Steps for a derived estimate
- Split the quantity into parts you can estimate, state each assumption, convert to SI units, combine using the physics, then round to the nearest order of magnitude and check it is sensible.
- Estimate the kinetic energy of a sprinter to the nearest order of magnitude
- m ≈ 80 kg, v ≈ 10 m s⁻¹. Ek = ½mv² = 0.5 × 80 × 10² = 4 × 10³ J, so the order of magnitude is 10⁴ J.