International Physics Olympiad · Year 1988

Problems

Problem 1A uniform solid cylinder rolls without slipping down a height $h$ . Find its speed at the bottom; its moment of inertia about its axis is $mR^2/2$ . Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model.Solutions: 1
Problem 2A charge $q$ moves from rest through a potential difference $V$ in vacuum. Find its final speed for mass $m$ , assuming nonrelativistic motion. Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model.Solutions: 1
Problem 3A source emits sound of frequency $f$ and wavelength $λ$ in still air. An observer approaches it at speed $v_o$ ; sound speed is $c$ . Find observed frequency. Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model.Solutions: 1