International Physics Olympiad · Year 2018

Problems

Problem 1A small mass $m$ slides without friction inside a circular loop of radius $R$ . It is released from rest at height $h$ above the loop's bottom. Find its speed at the top and the minimum $h$ for which it maintains contact throughout the loop. 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 2One mole of monatomic ideal gas at temperature T0 expands reversibly and isothermally from V0 to 2V0, then is cooled isochorically to T0/2. Find work and heat in each stage, and the gas's total entropy change. Use gas constant R. 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 3Light of wavelength $\lambda$ illuminates a metal with work function $W$ , where $hc/\lambda>W$ . Given Planck's constant $h$ and light speed $c$ , find the maximum photoelectron kinetic energy, stopping potential, and threshold wavelength. 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