International Physics Olympiad · Year 2005
Problems
- Problem 1A small body of mass m is released from rest on a smooth straight ramp of length L inclined at angle α to the horizontal. The ramp ends at height h above a level floor, and the body leaves tangentially before landing. Neglect air resistance and take g=9.8 m/s². (a) Find the acceleration and travel time. (b) Find the speed and velocity components at the edge. (c) Determine flight time and horizontal range. 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 DC source of emf E and internal resistance r supplies a purely resistive load R in series; take E and r as constant and the leads ideal. The circuit reaches steady current, the terminal voltage is U, and useful power is delivered to the load. (a) Express current and load voltage in terms of R. (b) Find the load R for maximum power and that maximum. (c) Find efficiency there, defined as load power divided by the power supplied by the ideal emf. 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 3A thin converging lens in air has focal length f>0. An upright real object of height H lies on the principal axis at distance u>f from the optical center; use the convention that a real image on the opposite side has v>0. Neglect lens thickness and aberrations. (a) Establish the relation among u, v, and f. (b) Find v and identify the image as real or virtual. (c) Find signed magnification m and signed image height. 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