International Physics Olympiad · Year 2017

Problems

Problem 1A mass $m$ attached to a light spring of stiffness $k$ moves horizontally on a frictionless surface. It is displaced by $A$ from equilibrium and released from rest. Find the period, maximum speed, and first time it passes equilibrium. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.Solutions: 1
Problem 2A conducting bar of length L and mass m slides without friction on vertical rails separated by L in a uniform magnetic field B perpendicular to their plane. The rails are connected through resistance R; neglect other resistance. Released from rest, find terminal speed and Joule power at that speed. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.Solutions: 1
Problem 3A sound source of frequency $f_0$ is at rest in air where sound speed is $c$ . An observer moves directly toward it at speed $u<c$ . Find the observed frequency and its percentage increase over the source frequency. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.Solutions: 1