International Physics Olympiad · Year 2022

Problems

Problem 1A small body is projected from level ground with initial speed $u$ at angle $\theta$ above the horizontal in a uniform gravitational field of magnitude $g$ directed downward. Put the origin at launch, neglect air resistance and Earth curvature, and take $0<\theta<\pi/2$ so the body rises and returns to its launch height. (a) Resolve the initial velocity and write the time-dependent motion. (b) Find the flight time $T$ and maximum height $H$ . (c) Derive horizontal range $R$ and the angle that maximizes it for fixed $u$ .Solutions: 1
Problem 2One mole of a monatomic ideal gas, initially at absolute temperature $T_1$ , is heated to $T_2>T_1$ in a constant-pressure process. Let $R_g$ be the gas constant; assume thermodynamic equilibrium throughout and no phase change. Define $W$ as work done by the gas and $Q>0$ as heat absorbed, so the first law is $\Delta U=Q-W$ . (a) Use the equation of state to find the volume change and work. (b) Calculate the internal-energy change from the molecular degrees of freedom. (c) Determine the heat transfer, check its sign, and explain how it is divided between raising internal energy and doing work.Solutions: 1
Problem 3Monochromatic light of frequency $f$ shines on a metal with work function $\phi$ ; assume $hf>\phi$ so photoelectrons are emitted, and let $h$ be Planck’s constant. Each photon transfers its energy to one electron, and subsequent collisions are neglected; $e$ is the magnitude of the electron charge. The stopping potential $V_s$ means the magnitude of the reverse voltage just sufficient to prevent even the fastest electron from reaching the anode. (a) Write the energy balance for one photon and a maximum-energy electron. (b) Find $K_{\max}$ and $V_s$ . (c) Predict how they depend on light frequency and intensity.Solutions: 1