International Physics Olympiad · Year 1989

Problems

Problem 1A block slides from rest down a frictionless track through vertical height $h$ , then enters a vertical loop of radius $R$ . Find the speed at the loop bottom. 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 vertical loop has radius R; angle theta is measured from the upward vertical at its center, and the block slides on the inner surface.Solutions: 1
Problem 2A series circuit has resistance $R$ and ideal capacitance $C$ , initially uncharged, connected at $t=0$ to a constant battery $V$ . Find the charge as a function of time. 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 3In vacuum, photons of energy $E$ scatter from electrons initially at rest through angle $\theta$ . State the Compton wavelength-shift relation using electron mass $m_e$ and light speed $c$ . 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