Asian Physics Olympiad · Year 2000

Problems

Problem 1Two small masses $m_1=2.0\,\mathrm{kg}$ and $m_2=1.0\,\mathrm{kg}$ are joined by a light inextensible string over an ideal pulley. $m_1$ rests on a smooth plane inclined at $30^\circ$ to horizontal and $m_2$ hangs vertically. The system is released from rest; take $g=9.8\,\mathrm{m/s^2}$ . (a) Find the acceleration and direction. (b) Find the tension and normal force on $m_1$ . (c) Find the distance each mass travels in the first $2.0\,\mathrm{s}$ , assuming the string stays taut.Solutions: 1
Problem 2One mole of monatomic ideal gas initially at $T_0=300\,\mathrm K$ and volume $V_0=2.0\,\mathrm L$ is heated in a cylinder with a freely moving piston, so the gas pressure remains constant throughout. The gas expands to $2V_0$ . Assume quasistatic equilibrium, neglect piston friction, and use $R=8.31\,\mathrm{J/(mol\,K)}$ . (a) Find the final temperature and gas pressure. (b) Calculate the work done by the gas and its change in internal energy. (c) Find the heat transferred to the gas and state its sign.Solutions: 1
Problem 3A thin converging lens has focal length $f=20\,\mathrm{cm}$ . An object of height $h_o=2.0\,\mathrm{cm}$ is perpendicular to the axis, $u=30\,\mathrm{cm}$ from the lens on the object side. Neglect thickness; use positive object distance and focal length, $v>0$ for a real image beyond the lens, and $m=-v/u$ . (a) Find image distance and nature. (b) Find magnification, image height, and orientation. (c) Locate a screen for a sharp image.Solutions: 1