International Physics Olympiad · Year 1992

Problems

Problem 1A mass $m$ moving at speed $v$ undergoes a one-dimensional elastic collision with a stationary mass $M$ . Find both final velocities. Use an idealized laboratory-frame model: stated parameters remain constant during the process unless the motion itself makes a quantity vary. State a clear sign convention and use the defined symbols consistently. (a) Write the governing laws or constraints. (b) Derive the requested quantities symbolically and state their physical direction or meaning. (c) Check dimensions and examine a simple physical limit to validate the result. Finally, verify that every equation is dimensionally consistent and that the results satisfy the initial conditions. Since no numerical data are specified, the exact answers are expressions in the defined symbols.Solutions: 1
Problem 2A capacitor of capacitance $C$ , initially at voltage $V_0$ , discharges through a resistor $R$ . Find its charge $q(t)$ and the current magnitude. Use an idealized laboratory-frame model: stated parameters remain constant during the process unless the motion itself makes a quantity vary. State a clear sign convention and use the defined symbols consistently. (a) Write the governing laws or constraints. (b) Derive the requested quantities symbolically and state their physical direction or meaning. (c) Check dimensions and examine a simple physical limit to validate the result. Finally, verify that every equation is dimensionally consistent and that the results satisfy the initial conditions. Since no numerical data are specified, the exact answers are expressions in the defined symbols.Solutions: 1
Problem 3Monochromatic light of vacuum wavelength $\lambda_0$ illuminates two slits separated by $d$ normally; a screen is at distance $Lgg d$ . Find the fringe spacing. Use an idealized laboratory-frame model: stated parameters remain constant during the process unless the motion itself makes a quantity vary. State a clear sign convention and use the defined symbols consistently. (a) Write the governing laws or constraints. (b) Derive the requested quantities symbolically and state their physical direction or meaning. (c) Check dimensions and examine a simple physical limit to validate the result. Finally, verify that every equation is dimensionally consistent and that the results satisfy the initial conditions. Since no numerical data are specified, the exact answers are expressions in the defined symbols.Solutions: 1