Physics (AS & A Level) Paper 22

acceleration = change in velocity / time (taken) or rate of change of velocity [1]

v = 0 + at or v = at (a = 36 / 19 =) 1.9 (1.8947) m s–2 [2]

s = ½(u + v)t or s = v2 / 2a or s = ½at2 = ½ × 36 × 19 = 362 / (2 × 1.89) = ½ × 1.89 × 192 = 340 m (342 m / 343 m / 341 m) [1]

1. (∆KE =) ½ × 95 × (36) 2 = 62 000 (61 560) J [2]

2. (∆PE =) 95 × 9.81 × 340 sin 40° or 95 × 9.81 × 218.5 = 200 000 J [2]

work done (by frictional force) = ∆PE – ∆KE or work done = 200 000 – 62 000 (values from 1b(iii) 1. and 2.) (frictional force = 138 000 / 340 =) 410 (406) N [420 N if full figures used] [2]

–ma = mg sin 20° – f or ma = –mg sin 20° + f –95 × 3.0 = 95 × 3.36 – f f = 600 (604) N [2]

p = F / A use of m = ρV and use of V = Ah and use of F = mg correct substitution to obtain p = ρgh [3]

(when h is zero the pressure is not zero due to) pressure from the air/atmosphere [1]

gradient = ρg or P – 1.0 × 105 = ρgh e.g. ρg = 1.0 × 105 / 0.75 (= 133333) ρ = 133 333 / 9.81 = 14 000 (13 592) kg m–3 [2]

Young modulus = stress / strain [1]

E = (F × l) / (A × e) or e = (F × l) / (A × E) e ∝ 1 / E or ratio eC / eS = ES / EC or (1.9 × 1011) / (1.2 × 1011) or 19 / 12 (ratio =) 1.6 (1.58) [3]

two straight lines from (0,0) with S having the steepest gradient [1]

longitudinal: vibrations/oscillations (of the particles/wave) are parallel to the direction or in the same direction (of the propagation of energy) transverse: vibrations/oscillations (of the particles/wave) are perpendicular to the direction (of the propagation of energy) [2]

LHS: intensity = power / area units: kg m s–2 × m × s–1 × m–2 or kg m2 s–3 × m–2 RHS: units: m s–1 × kg m–3 × s–2 × m2 LHS and RHS both kg s–3 [3]

change/difference in the observed/apparent frequency when the source is moving (relative to the observer) [1]

wavelength increases/frequency decreases/red shift [1]

observed frequency = vfS / (v – vS) 550 = (340 × 510) / (340 – vS) vS = 25 (24.7) m s–1 [3]

diffraction: spreading/diverging of waves/light (takes place) at (each) slit/ element/gap/aperture interference: overlapping of waves (from coherent sources at each element) path difference λ/phase difference of 360(°)/2π (produces the first order) [3]

d sinθ = nλ or sinθ = Nnλ d = (2 × 486 × 10–9) / sin 29.7° (= 1.962 × 10–6) number of lines = 510 (509.7) mm–1 [3]

at least six horizontal lines equally spaced and arrow to the right [1]

charge used 2e gain in KE = 15 × 1.6 × 10–19 × 103 = 2 × 1.6 × 10–19 × V (p.d.across plates) or F (= W / d) = 15 × 1.6 × 10–19 × 103 / 16 × 10–3 (hence V = 7500 V or F = 1.5 × 10–13 N) E = V / d or E = F / Q E = (7500 / 16 × 10–3) or E = (1.5 × 10–13 / 3.2 × 10–19) E = 4.7 × 105 (468 750) V m–1 [4]

or KE (= ½mv2) = 15 × 103 × 1.6 × 10–19 v = [(2 × 15 × 103 × 1.6 × 10–19) / (6.68 × 10–27)]1/2 = 8.5 × 105 m s–1 (C1) a (= v2 / 2s) = (8.5 × 105) 2 / 2 × 16 × 10–3 = 2.25 × 1013 m s–2 F (= 6.68 × 10–27 × 2.25 × 10–13) = 1.5 × 10–13 N E = F / Q (C1) Q = 2e (C1) E = 4.7 × 105 V m–1 (A1)

charge exists only in discrete amounts [1]

E = I(R + r) or V = IR (total resistance =) 2.7 + 0.30 + 0.25 (= 3.25 Ω) I = 9.0 / (2.7 + 0.30 + 0.25) or 9.0 / 3.25 = 2.8 A [3]

V = IRext = 2.77 × 3.0 or 2.8 × 3.0 or V = E – Ir (C1) = 9.0 – 2.77 × 0.25 or 9.0 – 2.8 × 0.25 V = 8.3 (8.31) V or 8.4 V [2]

I = nevA v = 2.77 / (8.5 × 1029 × 1.6 × 10–19 × 2.5 × 10–6) = 8.1 (8.147) × 10–6 m s–1 or 8.2 × 10–6 m s–1 [2]

A reduces by a factor 4 (1/4 less) or resistance of Z goes up by 4× current goes down but by less than a factor of 4 (as total resistance does not go up by a factor of 4) so drift speed goes up [2]

both electron and neutrino: lepton(s) both neutron and proton: hadron(s)/baryon(s) [2]

ν β 0 0 0 1 1 0 1 1 n p + + → correct symbols for particles correct numerical values (allow no values on neutrino) [2]

up up down or uud → up down down or udd [1]

weak (nuclear) [1]