The AS core practicals flashcards

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Terminal velocity
The constant velocity reached when the resultant force on a falling body is zero (weight = upthrust + drag).
First harmonic of a stretched string
The lowest-frequency stationary wave: one loop, nodes at the two fixed ends, so λ = 2l.
Internal resistance
The resistance of the materials inside a source, which causes a p.d. (“lost volts”) of Ir when current flows.
Uncertainty of a single reading (AS)
Half the resolution of the instrument, e.g. ±0.005 mm for a micrometer that reads to 0.01 mm.
Uncertainty from repeated readings (AS)
Half the range of the repeats: (largest − smallest) ÷ 2.
Systematic error
An error that shifts every reading by the same amount or in the same direction; repeating does not reduce it.
CP2: viscosity from terminal velocity
η = 2r²g(ρs − ρf) / 9v, from W = U + 6πηrv. (No — derive it)
CP3: Young modulus
E = stress / strain = (F/A) / (Δx/l). (Yes)
CP5: frequency of the first harmonic
f = (1/2l)√(T/μ), from v = √(T/μ) and λ = 2l. (No — derive it)
CP6: diffraction grating
nλ = d sin θ, with d = 1/(lines per metre) and tan θ = x/D. (Yes)
CP7: resistivity
R = ρl/A, so ρ = (gradient of R against l) × A. (Yes)
CP8: terminal p.d. in straight-line form
V = ε − Ir (from ε = I(R + r)). (No — derive it)
CP1: what to plot and what the gradient gives
h against t²: straight line through the origin, gradient g/2.
CP2 with balls of different sizes: what to plot?
v against r²: straight line through the origin, gradient 2g(ρs − ρf)/9η.
CP3: what to plot and what the gradient gives
Stress against strain; the gradient of the straight section is the Young modulus.
CP4: how is λ found from a graph?
Distance moved by the microphone against number of in-phase positions passed: gradient = λ.
CP5: graph for varying length, and for varying tension
f against 1/l (gradient ½√(T/μ)); f² against T (gradient 1/4l²μ).
CP7: meaning of an intercept on the R–l graph
Contact or lead resistance. It adds a constant to every R, so the gradient (and ρ) is unaffected.
CP8: intercept and gradient of the V–I graph
Intercept on the V-axis = ε; gradient = −r.
CP2: why is the first timing band well below the surface?
The ball is still accelerating near the surface; timing must start once it moves at terminal velocity.
CP2: how do you check terminal velocity has been reached?
Time the ball over two equal distances in succession; equal times mean constant velocity.
CP3: why a long, thin wire?
Long → larger extension for the same strain; thin → larger stress for the same load. Both cut the percentage uncertainty in the extension.
CP4: what does it mean when the two traces are in phase?
The microphones are a whole number of wavelengths apart.
CP1: effect of the electromagnet releasing the ball late
Every time is too long by the same amount — a systematic error. Use the smallest current that holds the ball.
CP7 and CP8: why switch off between readings?
Current heats the wire or cell, changing its resistance (and the cell's e.m.f.), so readings drift.
A 2.00 mm steel ball (7800 kg m⁻³) falls through glycerol (1260 kg m⁻³) at 0.0102 m s⁻¹. Viscosity?
η = 2 × (1.00 × 10⁻³)² × 9.81 × 6540 / (9 × 0.0102) = 1.4 Pa s. (No — derive it)
A wire 2.50 m long, diameter 0.40 mm, extends 3.0 mm under 30 N. Young modulus?
A = 1.26 × 10⁻⁷ m²; stress = 2.39 × 10⁸ Pa; strain = 1.2 × 10⁻³; E = 2.0 × 10¹¹ Pa. (Yes)
At 2500 Hz the traces return to phase 5 times as a microphone moves 0.69 m. Speed of sound?
λ = 0.69 ÷ 5 = 0.138 m; v = 2500 × 0.138 = 345 m s⁻¹. (Yes)
A string (μ = 1.0 × 10⁻³ kg m⁻¹) of length 0.500 m is under 9.81 N. First-harmonic frequency?
v = √(9.81/1.0 × 10⁻³) = 99.0 m s⁻¹; f = 99.0 ÷ (2 × 0.500) = 99 Hz. (No — derive it)
300 lines mm⁻¹ grating, screen 1.50 m away, first-order spots 0.60 m apart. Wavelength?
θ = tan⁻¹(0.30/1.50) = 11.3°; λ = d sin θ = 3.33 × 10⁻⁶ × sin 11.3° = 650 nm. (Yes)
R–l graph gradient 8.0 Ω m⁻¹ for a wire of diameter 0.50 mm. Resistivity?
A = π(0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m²; ρ = 8.0 × 1.96 × 10⁻⁷ = 1.6 × 10⁻⁶ Ω m. (Yes)
V–I line: 1.48 V at I = 0 and 1.12 V at 0.60 A. ε and r?
ε = 1.48 V; r = (1.48 − 1.12) ÷ 0.60 = 0.60 Ω. (Yes)
“Be careful with the laser”
Too vague. State hazard + precaution: never look along the beam or at reflections; keep shiny objects out of its path.
Small-angle shortcut in CP6
Do not use sin θ ≈ x/D — grating angles are large. Find θ from tan θ = x/D, then take sin θ.
Area of a wire from its diameter
A = πd²/4 (or πr² with r = d/2). Convert mm to m before squaring.
Suggesting an improvement
Target the largest percentage uncertainty and give the reason, e.g. a longer wire gives a larger extension.
Combining percentage uncertainties at AS
Not required at AS: find the percentage uncertainty of a single quantity and compare. Combining belongs to Unit 6.
Highest observable grating order
n ≤ d/λ; round down to the whole number below, even if the decimal is large.

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