International Physics Olympiad · Year 2015

Problems

Problem 1A particle of mass $m$ slides from rest without friction down a plane of length $L$ inclined at angle $\alpha$ , then leaves its edge and lands on a floor $H$ below the edge. With gravitational acceleration $g$ , find the sliding time, launch speed, and horizontal range from the edge. 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 initially at temperature $T_0$ expands isobarically until its volume doubles, then cools isochorically to $T_0/2$ . Find the maximum temperature, work and heat in each stage, and total work. Use $C_V=3R/2$ . 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 photon of wavelength $\lambda$ is backscattered through 180° by a free electron initially at rest. Given electron mass $m_e$ , Planck's constant $h$ , and light speed $c$ , find the scattered wavelength, the energy transferred to the electron, and the condition for the electron kinetic energy to equal the incident photon energy. 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