International Physics Olympiad · Year 1971

Problems

Problem 1A small slider of mass $m$ starts from rest at the top of a straight track of length $L$ , inclined at $30^\circ$ to the horizontal. The track is smooth, the slider may be treated as a point particle, and the gravitational acceleration has constant magnitude $g$ ; take down the track as positive. (a) Find the acceleration and the normal reaction. (b) Determine the time to traverse $L$ and the speed at the bottom. (c) Check the final speed using the change in gravitational potential energy, and state which results are independent of the mass.Solutions: 1
Problem 2A battery is modeled by a constant emf $E$ in series with internal resistance $r>0$ and supplies a purely resistive load $R>0$ ; neglect lead resistance and temperature changes. Let $I$ be the circuit current, $U$ the terminal voltage (also the load voltage), and $P_R$ the load power. (a) Find $I$ and $U$ in terms of $E,r,R$ . (b) Calculate $P_R$ and the power dissipated inside the source. (c) Determine the value of $R$ that maximizes $P_R$ , the maximum power, and the efficiency at that operating point.Solutions: 1
Problem 3A small upright object of height $h$ is placed perpendicular to the principal axis of a thin converging lens, at distance $u=2f$ from its optical centre; the focal length is $f>0$ and $u>f$ . The media on both sides are the same. Use $u>0$ , take a real image on the opposite side to have $v>0$ , and define signed magnification by $m=-v/u$ . (a) Find the image distance $v$ in terms of $f$ . (b) Find the magnification and image height, and state whether the image is real or virtual and upright or inverted. (c) If the object is moved a small distance farther from the lens, determine the image’s direction of motion from the dependence of $v$ on $u$ .Solutions: 1