International Physics Olympiad · Year 2006
Problems
- Problem 1Two masses m₁ and m₂ are connected by a massless inextensible string over a fixed, frictionless, massless pulley, with m₂>m₁. Both hang freely on opposite sides and are released from rest. Take g=9.8 m/s² and neglect air resistance. (a) Determine the motion directions and write Newton’s equations for both masses. (b) Find the acceleration and string tension. (c) After m₂ descends distance s, find both speeds and check by energy conservation. 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 2A monatomic ideal gas of n moles at fixed absolute temperature T is confined by a frictionless piston. It expands slowly and reversibly from V₁ to V₂>V₁, remaining in thermal equilibrium with a reservoir at T; R is the gas constant. (a) Write the equation of state and calculate work done by the gas. (b) Find ΔU and heat Q absorbed, taking work by the gas as positive. (c) Explain why ΔU is independent of atomic species in this isothermal process. 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 point sources S₁ and S₂ oscillate coherently in phase at frequency f in a uniform medium where waves travel at speed c, so λ=c/f. At point P their distances are r₁ and r₂. Assume equal amplitudes, no absorption, and phase difference due only to path difference. (a) Find the phase difference at P in terms of Δr=r₂−r₁. (b) State constructive and destructive conditions. (c) As P moves so Δr increases continuously from 0 to 3λ/2, count maxima and minima crossed, including endpoints when applicable. 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