Asian Physics Olympiad · Year 2022

Problems

Problem 1Masses $m_1=2$ kg and $m_2=3$ kg hang from the ends of a light inextensible string passing over a fixed frictionless pulley of negligible radius. The system is released from rest and the string remains taut. Take $g=10$ m/s $^2$ and choose each mass's direction of motion as positive. (a) Determine the direction and acceleration of each mass. (b) Find the string tension. (c) Find their speed after moving $s=0.80$ m from rest, and check it by energy conservation.Solutions: 1
Problem 2An initially uncharged capacitor $C=100\ \mu\mathrm F$ is connected at $t=0$ in series with a resistor $R=10\ \mathrm{k\Omega}$ and an ideal source of emf $E=12$ V. Let $q(t)$ be the capacitor charge and $i(t)=\dot q(t)$ the current. (a) Find the time constant $\tau$ and the long-time charge $q_\infty$ . (b) Write expressions for $q(t)$ and $i(t)$ . (c) Find when the charge reaches $90\%$ of its final value and the current at that instant.Solutions: 1
Problem 3A fixed loudspeaker emits sound of frequency $f=680$ Hz in still air, where the sound speed is $v=340$ m/s. A runner moves directly toward the speaker at $v_o=20$ m/s; after passing it, the runner recedes at the same speed. For nonrelativistic Doppler shifts in still air, use $f'=(v\pm v_o)f/v$ for a stationary source and $f'=fv/(v\mp v_s)$ for a stationary observer. (a) Find the frequencies heard while approaching and receding. (b) Find the wavelength the runner encounters in each case. (c) Now the source moves at $v_s=17$ m/s toward a stationary observer; find the observed frequency.Solutions: 1