International Physics Olympiad · Year 2000

Problems

Problem 1Two masses $m_1>m_2$ are connected by a light inextensible string over a frictionless pulley. Find the acceleration and string tension; $g$ is gravitational acceleration. The ideal string and pulley constrain the two masses to accelerations of equal magnitude. (a) Write Newton’s equations for both masses. (b) Find their acceleration and the string tension. (c) If the heavier mass descends a distance $h$ from rest, find the speed of both masses. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.Solutions: 1
Problem 2Resistors $R_1,R_2$ are in series across an ideal source of emf $\mathcal E$ . Find the current and voltage across each resistor. The ideal source has emf $\mathcal{E}$ and the resistors are ohmic with positive values. (a) Find the equivalent resistance and circuit current. (b) Determine the voltage drop across each resistor. (c) Find the total power and check the voltage balance. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.Solutions: 1
Problem 3An object is placed at distance $d_o>f$ from a converging thin lens of focal length $f$ . Find image distance $d_i$ and signed magnification $m$ ; real images have $d_i>0$ . The thin lens is in air, and an object of height $h_o$ is perpendicular to the principal axis; a real image forms on the opposite side. (a) Find $d_i$ from the lens equation. (b) Find the signed magnification $m$ . (c) Find signed image height $h_i$ and state whether the image is upright or inverted. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.Solutions: 1