International Physics Olympiad · Year 1994

Problems

Problem 1An object is thrown vertically upward from the ground with initial speed $u$ ; neglect air resistance. Find its maximum height and return time. 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 conducting rod of length $\ell$ moves at speed $v$ perpendicular to a uniform magnetic field $B$ . Its ends are connected by resistance $R$ to form a closed circuit. Neglect rod resistance; find the induced emf and current. 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 3A photon of wavelength $\lambda$ is backscattered through $180^\circ$ by an initially stationary electron. With electron Compton wavelength $\lambda_C=h/(m_ec)$ , find the scattered photon wavelength. 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