Asian Physics Olympiad · Year 2009

Problems

Problem 1A particle of mass $m$ is attached to a light string of length $L$ and moves in a vertical circle. Its speed at the lowest point is $v_0$ . Find its speed at the highest point and the string tension at both points; assume the string remains taut. (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 2One mole of a monatomic ideal gas initially at $(P_0,V_0,T_0)$ is heated at constant pressure until its volume is $2V_0$ . Find the final temperature, work done by the gas, heat absorbed, and change in internal energy. Use the gas constant $R$ . (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 3Monochromatic light of wavelength $\lambda$ strikes normally a grating of spacing $d$ . Find the condition for order $k$ maxima and the first-order angle. (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