International Physics Olympiad · Year 1967

Problems

Problem 1A sled of mass $m=2.0,\,\mathrm{kg}$ starts from rest on a smooth ramp of length $L=5.0,\,\mathrm{m}$ at $30^\circ$ to the horizontal. It enters a rough horizontal track with kinetic-friction coefficient $\mu=0.20$ . Neglect air resistance and use $g=9.8,\,\mathrm{m/s^2}$ . (a) Find acceleration and speed at the ramp bottom. (b) Find stopping distance on the horizontal track. (c) If that track is only $4.0,\,\mathrm{m}$ long, does the sled stop before its edge? 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 at $T_1=300,\,\mathrm{K}$ , $p_1=1.0\times10^5,\,\mathrm{Pa}$ is heated at constant pressure to $T_2=600,\,\mathrm{K}$ , then cooled at constant volume back to $T_1$ to complete a cycle. Use $R=8.31,\,\mathrm{J,mol^{-1}K^{-1}}$ and take $W>0$ as work done by the gas. (a) Find initial and maximum volume. (b) For the isobaric leg, find $W,\Delta U,Q$ . (c) Find final pressure and net cycle work. 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 3A source with constant emf $E$ and internal resistance $r>0$ is connected to a resistive load $R>0$ . Neglect lead resistance; let $I$ be current, $U$ the terminal and load voltage, and $P_R$ the load power. (a) Find current. (b) Find load voltage. (c) Find load power and power lost inside the source. 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