International Physics Olympiad · Year 2016

Problems

Problem 1Two masses $m_1>m_2$ are connected by a massless inextensible string over an ideal pulley. Released from rest, with friction neglected and constant $g$ , find the acceleration, string tension, and speed after the heavier mass descends distance $s$ . 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 capacitor $C$ initially carrying charge $Q_0$ is connected at $t=0$ to a resistor $R$ . Find charge $Q(t)$ , current $I(t)$ , and total heat dissipated by time $t$ , assuming no external source. 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 thin converging lens has focal length $f>0$ . A real object of height $h$ is placed a distance $u>f$ from the lens. Find the signed image distance $v$ , magnification $m$ , image height, and whether the image is real or virtual. 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