International Physics Olympiad · Year 1986

Problems

Problem 1A projectile is launched horizontally at speed $u$ from height $h$ . Find its flight time and horizontal range; use gravitational acceleration $g$ . 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 capacitor $C$ is charged to voltage $V$ and then isolated. Find its charge and stored energy. 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. While it remains isolated, a dielectric of relative permittivity kappa is inserted to fill the gap; the total charge therefore stays fixed.Solutions: 1
Problem 3Light of wavelength $λ$ in vacuum enters glass of refractive index $n$ . Find its speed and wavelength in glass. 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