International Physics Olympiad · Year 2007
Problems
- Problem 1A body of mass m starts from rest on a frictionless track and descends a vertical height H, then moves onto a rough horizontal surface with kinetic-friction coefficient μ. The horizontal surface is long enough for the body to stop; take g=9.8 m/s² and neglect other resistance. (a) Find the speed on reaching the horizontal using mechanical-energy conservation. (b) Find friction and acceleration on the horizontal. (c) Determine stopping distance s using kinematics and confirm by work–energy. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.Solutions: 1
- Problem 2An ideal capacitor of capacitance C is charged to voltage V₀ and connected at t=0 to a resistor R initially carrying no current. Define discharge current as positive in the discharge direction and v(t) with the initial capacitor polarity; neglect inductance and wire resistance. (a) Establish the discharge differential equation and time constant τ. (b) Find v(t) and current i(t) for t≥0. (c) Calculate heat dissipated from 0 to t and check its limit as t approaches infinity. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.Solutions: 1
- Problem 3Two coherent point sources S₁,S₂ emit sinusoidal waves in phase, each of amplitude A and wavelength λ in a uniform medium. At point P let path difference be Δr=r₂−r₁; take source phase as zero and ignore amplitude decrease with distance. (a) Express the phase difference between waves arriving at P. (b) Find Δr values for intensity maxima and minima. (c) Write resultant intensity in terms of the one-source intensity I₁ and give its maximum and minimum. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.Solutions: 1