Flashcards · H556 · Topic 2

Foundations of physics flashcards

18 cards on Topic 2, subtopics 2.1 to 2.3. Pick a subtopic or study them all.

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The six SI base quantities used in H556, with units: Length (m), mass (kg), time (s), current (A), temperature (K), amount of substance (mol). The specification excludes luminous intensity.
The volt and the ohm in SI base units: V = kg m² s⁻³ A⁻¹ Ω = kg m² s⁻³ A⁻²
Homogeneity check: what it is, and what it cannot show: Reduce every term to base units: both sides, and any terms added or subtracted, must match. A match does not prove the equation is right, because missing numerical constants are invisible.
Prefixes p, n, μ, m, c, d: p 10⁻¹², n 10⁻⁹, μ 10⁻⁶, m 10⁻³, c 10⁻², d 10⁻¹.
Prefixes k, M, G, T, and converting km h⁻¹ to m s⁻¹: k 10³, M 10⁶, G 10⁹, T 10¹². Divide a speed in km h⁻¹ by 3.6 to get m s⁻¹.
How should table headings and graph axes be labelled?: Quantity / unit, for example current / A or speed / m s⁻¹. The entries are then pure numbers.

Systematic vs random error: effect, example and how to reduce: Systematic: same offset in every reading (zero error, uncalibrated scale); calibrate or correct; damages accuracy. Random: scatter about the true value (hand timing); repeat and average; damages precision.
Combining uncertainties: a + b or a − b: add absolute uncertainties. a × b or a ÷ b: add percentage uncertainties. aⁿ: n × the percentage uncertainty.
v = √(2gh) and h has a 3.0% uncertainty. What is the percentage uncertainty in v from h?: The power is ½, so 0.5 × 3.0% = 1.5%.
Two readings 120.0 cm and 45.0 cm, each ±0.5 cm. Uncertainty in the difference?: 75.0 cm ± 1.0 cm (absolute uncertainties add), which is about 1.3%.
Uncertainty in a gradient using worst lines: Draw the steepest and shallowest lines through all the error bars. Uncertainty = (steepest − shallowest) ÷ 2. Percentage uncertainty = that ÷ best gradient × 100.
Common estimates of uncertainty for a single reading and for repeats: Single reading: half the smallest scale division. Repeated readings: half the range. Quote it to 1 significant figure (occasionally 2) and match the decimal places of the value.

Scalar vs vector, with examples: Scalar: magnitude only, e.g. distance, speed, mass, energy, temperature. Vector: magnitude and direction, e.g. displacement, velocity, acceleration, force, momentum.
Forces of 24 N and 10 N act at right angles. Find the resultant.: √(24² + 10²) = 26 N, at tan⁻¹(10/24) = 22.6° to the 24 N force.
Resolving a force F at angle θ to an axis: Along the axis: F cos θ. Perpendicular to it: F sin θ. Cos goes with the axis the angle is measured from.
Weight components of a 5.0 kg block on a 20° slope (g = 9.81 N kg⁻¹): Weight = 49.05 N. Along the slope: 49.05 sin 20° = 16.8 N. Perpendicular to the slope: 49.05 cos 20° = 46.1 N.
How do you add two vectors that are not at right angles?: Draw them tip to tail; the resultant joins the start to the finish. Use a scale drawing (stating the scale), or the cosine and sine rules, or resolve both into perpendicular components first.
How do you subtract one vector from another, A − B?: Add the negative of B: reverse the direction of B and add it tip to tail to A, so A − B = A + (−B). Example: change in velocity Δv = v − u.