Asian Physics Olympiad · Year 2018

Problems

Problem 1Two small masses $m_1$ and $m_2$ are joined by a light inextensible string over a fixed pulley of radius $R$ and moment of inertia $I$ with a frictionless axle; $m_2>m_1$ . The string does not slip, both segments are vertical, and the string's mass is negligible. Release from rest and take $g=9.8\,\mathrm{m/s^2}$ . (a) Find the acceleration and pulley angular acceleration. (b) Find the tension in each segment. (c) Find the acceleration for a massless pulley and explain how it compares with the inertial pulley.Solutions: 1
Problem 2One mole of monatomic ideal gas initially at absolute temperature $T_i$ and pressure $p$ is heated slowly at constant pressure to $T_f>T_i$ . It obeys $pV=R_gT$ , where $R_g$ is the gas constant; neglect macroscopic kinetic and potential energy changes. Take work done by the gas and heat entering it as positive. (a) Find the volume change and work done by the gas. (b) Find the change in internal energy. (c) Find the heat added and the ratio of heat to work.Solutions: 1
Problem 3A metal of work function $W_0$ is illuminated by monochromatic light of frequency $f$ ; photoemission occurs only if a photon has enough energy. Let Planck's constant be $h$ , the electron charge magnitude be $e$ , and define positive stopping voltage $V_s$ as the voltage just sufficient to stop the fastest electron. (a) Find threshold frequency $f_0$ . (b) Express maximum kinetic energy $K_{\max}$ in terms of $f$ and give the emission condition. (c) Find $V_s$ and describe the slope and intercept of a plot of $V_s$ versus $f$ on the emission range.Solutions: 1