Asian Physics Olympiad · Year 2008

Problems

Problem 1A particle of mass $m$ slides without friction from rest on a wedge of mass $M$ and incline angle $\alpha$ . The wedge rests on a smooth horizontal floor. Find the wedge's acceleration and the particle's acceleration relative to the wedge; gravity is $g$ downward. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.Solutions: 1
Problem 2A parallel-plate capacitor of plate area $A$ and separation $d$ is connected to a constant voltage $V$ . A dielectric of relative permittivity $\kappa$ fills a fraction $x$ of the plate length, parallel to the plates; the remainder is vacuum. Neglect edge effects. Find the capacitance, positive-plate charge, and stored field energy. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.Solutions: 1
Problem 3An object is placed a distance $u>f$ from a converging thin lens of focal length $f$ . Find the image distance $v$ and transverse magnification $m$ , and state whether the image is real or virtual. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.Solutions: 1