International Physics Olympiad · Year 1999
Problems
- Problem 1An object falls from rest through height H with constant gravity g. Find speed after falling distance x and time to fall H. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.Solutions: 1
- Problem 2A rod of length ℓ moves at speed v perpendicular to itself and uniform field B, closing a circuit through R. Neglect rod resistance. Find emf, current, and magnetic drag. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.Solutions: 1
- Problem 3A photon of wavelength λ Compton-scatters from a free electron at rest; the scattered direction is at angle θ. Find final wavelength and maximum shift; electron mass mₑ. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.Let E_i,E_f be the photon energies before and after scattering and p_i,p_f their momentum magnitudes; E_e,p_e are the scattered electron’s total energy and momentum magnitude.Solutions: 1