Physics (AS & A Level) Paper 41

(gravitational) potential at infinity defined as/is zero (gravitational) force attractive so work got out/done as object moves from infinity (so potential is negative) [2]

∆E = m∆φ = 180 × (14 – 10) × 108 = 7.2 × 1010 J increase [3]

energy required = 180 × (10 – 4.4) × 108 or energy per unit mass = (10 – 4.4) × 108 ½ × 180 × v2 = 180 × (10 – 4.4) × 108 or ½ × v2 = (10 – 4.4) × 108 v = 3.3 × 104 m s–1 [3]

e.g. time of collisions negligible compared to time between collisions no intermolecular forces (except during collisions) random motion (of molecules) large numbers of molecules (total) volume of molecules negligible compared to volume of containing vessel or average/mean separation large compared with size of molecules any two [2]

mass = 4.0 / (6.02 × 10 23) = 6.6 × 10–24 g or mass = 4.0 × 1.66 × 10–27 × 103 = 6.6 × 10–24 g [1]

3 kT = 2 1 m <c 2> 3 × 1.38 × 10–23 × 300 = 2 1 × 6.6 × 10–27 × <c 2> <c 2> = 1.88 × 106 (m2 s–2) r.m.s. speed = 1.4 × 103 m s–1 [3]

acceleration/force proportional to displacement (from fixed point) acceleration/force and displacement in opposite directions [2]

maximum displacements/accelerations are different graph is curved/not a straight line [2]

ω = 2π / T and T = 0.8 s ω = 7.9 rad s–1 [2]

a = (–)ω2 x = 7.852 × 1.5 × 10–2 = 0.93 m s–2 or 0.94 m s–2 [2]

∆E = ½ mω2 (x0 2 – x2) = ½ × 120 × 10–3 × 7.852 × {(1.5 × 10–2) 2 – (0.9 × 10–2) 2} = 5.3 × 10–4 J [3]

product of speed and density reference to speed in medium (and density of medium) [2]

α: ratio of reflected intensity and/to incident intensity Z1 and Z2: (specific) acoustic impedances of media (on each side of boundary) B1 [2]

in muscle: IM = I0 e–µx = I0 exp(–23 × 3.4 × 10–2) IM / I0 = 0.457 at boundary: α = (6.3 – 1.7) 2 / (6.3 + 1.7) 2 = 0.33 IT /IM = [(1 – α) =] 0.67 IT / I0 = 0.457 × 0.67 = 0.31 [5]

sketch: from x = 0 to x = R, potential is constant at VS smooth curve through (R, VS) and (2R, 0.5VS) smooth curve continues to (3R, 0.33VS) [3]

sketch: from x = 0 to x = R, field strength is zero smooth curve through (R, E) and (2R, 0.25E) smooth curve continues to (3R, 0.11E) [3]

line has non-zero intercept/line does not pass through origin charge is/should be proportional to potential (difference) or charge is/should be zero when p.d. is zero (therefore there is a systematic error) [2]

reasonable attempt at line of best fit use of gradient of line of best fit clear C = 2800 µF (allow ± 200 µF) [3]

energy = ½ CV 2 or energy = ½ QV and C = Q / V ∆ energy = ½ × 2800 × 10–6 × (9.02 – 6.02) = 6.3 × 10–2 J [3]

0.10 mm [1]

VH = (0.13 × 3.8) / (6.0 × 1028 × 0.10 × 10–3 × 1.60 × 10–19) = 5.1 × 10–7 V [2]

(non-uniform) magnetic flux in core is changing induces (different) e.m.f. in (different parts of) the core (eddy) currents form in the core which give rise to heating [4]

as magnet falls, tube cuts magnetic flux e.m.f./(eddy) currents induced in metal/aluminium (tube) (eddy) current heating of tube with energy taken from falling magnet or (eddy) currents produce magnetic field (M1) that opposes motion of magnet (A1) so magnet B has acceleration < g or magnet B has smaller acceleration/reaches terminal speed [5]

period = 15 ms frequency (= 1 / T) = 67 Hz [2]

zero [1]

Ir.m.s. = I0 / √2 = 0.53 A [2]

energy = Ir.m.s. 2 × R × t or ½ I0 2 × R × t or power = Ir.m.s. 2 × R and energy = power × t energy = 0.532 × 450 × 30 × 10–3 = 3.8 J [2]

e.g. background count (rate)/radiation multiple possible counts from each decay radiation emitted in all directions dead-time of counter (daughter) product unstable/also emits radiation self-absorption of radiation in sample or absorption in air/detector window three sensible suggestions, 1 each [3]

A = A0 exp(– ln 2 × t / T½) 1.21 × 102 = 3.62 × 104 exp(– ln2 × 42.0 / T½) or 1.21 × 102 = 3.62 × 104 exp(–λ × 42.0) T½ = 5.1 minutes (306 s) [2]

discrete energy levels (in nuclei) [1]