International Physics Olympiad · Year 1968

Problems

Problem 1Two small masses $m_1>m_2$ hang from a light inextensible string over a light frictionless pulley. The string remains taut, motion is vertical, and $g$ is constant. Take downward for $m_1$ and upward for $m_2$ as positive. (a) Find their common acceleration. (b) Find the tension. (c) Evaluate the acceleration for $m_1=3m_2$ and check equal masses. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.Solutions: 1
Problem 2A reversible Carnot engine operates between large reservoirs at constant absolute temperatures $T_h>T_c>0$ . Each cycle absorbs heat $Q_h>0$ from the hot reservoir and rejects heat of magnitude $Q_c>0$ to the cold reservoir; there are no other energy transfers. (a) Relate the heats to reservoir temperatures. (b) Find useful work per cycle. (c) Find efficiency and consider the limit $T_c o T_h$ . Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.Solutions: 1
Problem 3Two very wide parallel plates separated by $d$ are held at potential difference $V>0$ , producing a uniform field; neglect edge effects. Axis $x$ points from the positive to the negative plate. A test particle of signed charge $q$ and mass $m$ lies between them. (a) Find field magnitude and direction. (b) Find the electric force, including for $q<0$ . (c) Find field work and potential-energy change for displacement $s$ along $x$ . Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.Solutions: 1