International Physics Olympiad · Year 1970

Problems

Problem 1A mass $m$ is attached to a light spring of stiffness $k$ on a smooth horizontal surface, with the other end fixed. Let equilibrium be $x=0$ , neglect spring mass and resistance, and release from rest at $x=A>0$ . (a) Write the equation of motion and find the period. (b) Find maximum speed and its location. (c) Find speed as it passes $x=A/2$ toward equilibrium. 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 2One mole of monatomic ideal gas in fixed volume $V$ is heated from absolute temperature $T_1$ to $T_2>T_1$ . Take $W>0$ as work done by the gas, neglect macroscopic kinetic and potential energy changes, and use gas constant $R$ . (a) Find initial and final pressure. (b) Find work, internal-energy change, and heat supplied. (c) Explain the heat sign and how pressure changes. 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 positive resistors $R_1,R_2$ are connected in parallel across an ideal constant voltage source $V>0$ ; neglect lead resistance. Let $I_1,I_2$ be branch currents, $I$ the total current, and $R_{eq}$ the equivalent resistance. (a) Find $R_{eq}$ and $I$ . (b) Find total power and power in each resistor. (c) For $R_1=R_2=R$ , compare equivalent resistance with $R$ and total current with one branch current. 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