Asian Physics Olympiad · Year 2002

Problems

Problem 1A simple pendulum of length $L=1.0\,\mathrm m$ is displaced through a small angle and released. Take $g=9.8\,\mathrm{m/s^2}$ . Find its period and maximum speed for angular amplitude $0.10\,\mathrm{rad}$ . Treat the stated idealizations as exact: objects may be treated as point-like or uniform where appropriate, and any external effect not specified is neglected. (a) Establish the governing physical relation and state the sign convention and boundary conditions. (b) Evaluate the requested quantities from the supplied data with consistent units. (c) Check dimensions and explain the physical meaning of the resulting sign or limiting case.Solutions: 1
Problem 2One mole of monatomic ideal gas initially at $T_1=300\,\mathrm K$ is reversibly adiabatically compressed to half its volume. Let $\gamma=5/3$ . Find the final temperature, final-to-initial pressure ratio, and work done on the gas. Treat the stated idealizations as exact: objects may be treated as point-like or uniform where appropriate, and any external effect not specified is neglected. (a) Establish the governing physical relation and state the sign convention and boundary conditions. (b) Evaluate the requested quantities from the supplied data with consistent units. (c) Check dimensions and explain the physical meaning of the resulting sign or limiting case.Solutions: 1
Problem 3A sound source emits $f=500\,\mathrm{Hz}$ while moving directly toward a stationary listener at $v_s=20\,\mathrm{m/s}$ . Sound speed in air is $v=340\,\mathrm{m/s}$ . Find the heard frequency as it approaches and just after it passes. Treat the stated idealizations as exact: objects may be treated as point-like or uniform where appropriate, and any external effect not specified is neglected. (a) Establish the governing physical relation and state the sign convention and boundary conditions. (b) Evaluate the requested quantities from the supplied data with consistent units. (c) Check dimensions and explain the physical meaning of the resulting sign or limiting case.Solutions: 1