Flashcards · 9630 · AS Topic 1

Measurements and their errors (AS Level) flashcards

15 cards on AS Topic 1, subtopics 3.1.1 to 3.1.3. Pick a subtopic or study them all.

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The six SI base units needed for 9630: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K) and mole (mol).
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
Powers of ten for the prefixes T, G, M, k, c, m, μ, n, p, f: T 10¹², G 10⁹, M 10⁶, k 10³, c 10⁻², m 10⁻³, μ 10⁻⁶, n 10⁻⁹, p 10⁻¹², f 10⁻¹⁵.
Converting squared and cubed units: 1 cm² and 1 mm³ in SI units: Apply the power to the whole prefix factor: 1 cm² = (10⁻²)² m² = 10⁻⁴ m²; 1 mm³ = (10⁻³)³ m³ = 10⁻⁹ m³.
Converting electronvolts and kilowatt-hours to joules: eV → J: multiply by 1.60 × 10⁻¹⁹. kW h → J: multiply by 3.6 × 10⁶ (1000 W × 3600 s). Divide to convert back.

Random error vs systematic error: Random error scatters readings either side of the true value and is reduced by repeating and averaging. Systematic error shifts every reading the same way and is not reduced by averaging.
How do you remove a systematic error?: Zero or recalibrate the instrument, correct readings for the zero error, or change the technique (for example read at eye level to avoid parallax). Repeating readings does not remove it.
Accuracy, precision and resolution: Accurate: close to the true value. Precise: repeat readings agree closely. Resolution: the smallest change the instrument can detect or display.
Repeatable vs reproducible: Repeatable: the same result when the same operator repeats it with the same method and equipment. Reproducible: the same result with a different operator, method or equipment.
Combining uncertainties: sums, products and powers: Sum or difference: add absolute uncertainties. Product or quotient: add percentage uncertainties. Power n (including roots): multiply the percentage uncertainty by n.
How do you find the uncertainty in the gradient of a graph?: Draw the steepest and shallowest lines that still pass through all the error bars. Gradient uncertainty = (steepest gradient − shallowest gradient) ÷ 2.

What does "to the nearest order of magnitude" mean?: To the nearest power of ten. A common convention: a leading figure below about 3.2 rounds down, above it rounds up (so 2.9 × 10⁸ is 10⁸ and 3.4 × 10⁸ is 10⁹).
Rough reference sizes: a person's mass, an atom's diameter, the Earth's radius: Person: about 10² kg. Atom: about 10⁻¹⁰ m. Earth's radius: about 10⁷ m (6.4 × 10⁶ m).
Method for an estimation question: State each estimated value, combine them in the relevant equation, round the final answer to an order of magnitude, then check it is plausible.
Estimate the kinetic energy of a 70 kg sprinter at 8 m s⁻¹: ½ × 70 × 8² = 2240 J, so about 10³ J.