International Physics Olympiad · Year 1987

Problems

Problem 1A mass $m$ attached to a spring of constant $k$ oscillates without damping with amplitude $A$ . Find its maximum speed and period. 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 2An ideal gas with $n$ moles is heated at constant pressure from absolute temperature $T_1$ to $T_2$ . Find heat supplied; molar heat capacity at constant pressure is $C_p$ . 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. The gas receives heat Q and does work W; take work done by the gas as positive and use the gas constant Rg.Solutions: 1
Problem 3Two in-phase coherent sources emit waves of equal amplitude and wavelength $\lambda$ with path difference $\Delta$ . State the condition for constructive interference. 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