IBDP Physics 5.1 – Electric fields: IB Style Question Bank SL Paper 2

a.

ma \(= – \)kx;
\(a = – \frac{k}{m}x\); (condone lack of negative sign)
\(\left( {{\omega ^2} = \frac{k}{m}} \right)\)

or

implied use of defining equation for simple harmonic motion \(a = – {\omega ^2}x\);
\(\left( {{\rm{so }}{\omega ^2} = \frac{k}{m}} \right)\)
\(ma = – kx\) so \(a = – \left( {\frac{k}{m}} \right)x\);

(i) 0.833 (Hz);

(ii) frequency/period is the same so ω is the same;
k is the same (as springs are identical);
(so m is the same)

(ii) end displacements correct \( \pm \) 0.01m;
maximum lower than 0.16J;
maximum equal to 0.04J \( \pm \) half square;

(i) \(l = \frac{{\pi {d^2}R}}{{4\rho }}\) seen / correct substitution
into equation: \(24 = \frac{{l \times 1.7 \times {{10}^{ – 8}}}}{{\pi \times {{\left( {0.15 \times {{10}^{ – 3}}} \right)}^2}}}\); } (condone use of r for \(\frac{d}{2}\) in first alternative)

99.7 (m);
Award [2] for bald correct answer.
Award [1 max] if area is incorrectly calculated, answer is 399 m if conversion to radius ignored, ie: allow ECF for second marking point if area is incorrect provided working clear.

(ii) any line showing resistance decreasing with increasing diameter and touching
point;
correct curved shape showing asymptotic behavior on at least one axis;

current/conduction is (related to) flow of charge;
conductors have many electrons free/unbound / electrons are the charge carriers / insulators have few free electrons;
pd/electric field accelerates/exerts force on electrons;
smaller current in insulators as fewer electrons available / larger current in conductors as more electrons available;

(i) use of total resistance = 11Ω; (can be seen in second marking point)
\(\frac{1}{{11}} = \frac{1}{R} + \frac{1}{{24}}\);
20.3(Ω) ;

(ii) as current is same in resistor network and cell and resistance is same, half of emf must appear across resistor network;
6.0 (V);

or

\(I = \frac{{12}}{{\left( {11 + 11} \right)}} = 0.545\left( {\rm{A}} \right)\);
V=(0.545×11=) 6.0 (V);

Other calculations are acceptable.
Award [2] for a bald correct answer.

(iii) use of 22 (ohm) or 11+11 (ohm) seen;
use of \(\frac{{{V^2}}}{R}\) or equivalent;
6.54 (W);
Award [3] for bald correct answer.
Award [2 max] if cell internal resistance ignored, yields 3.27 V.