Asian Physics Olympiad · Year 2016

Problems

Problem 1A small object of mass $m$ is held at rest a height $h$ above the free top of a light vertical spring of stiffness $k$ standing on a horizontal floor. It is released, falls vertically, and contacts the spring; neglect air resistance and all losses, take compression as positive, and let gravity be $g$ . Let $x$ denote the greatest compression. (a) Find $x$ and check the limit $h=0$ . (b) Find the object's velocity when the compression is $y$ , where $0\le y\le x$ . (c) Find the compression at which its speed is greatest and that maximum speed.Solutions: 1
Problem 2A parallel-plate capacitor has plate area $A$ , vacuum gap $d$ , and is initially connected to an ideal source that holds voltage $V$ . A homogeneous linear dielectric of relative permittivity $\kappa>1$ is slowly inserted until it fills the gap; neglect fringing. Let $\varepsilon_0$ be the vacuum permittivity and $C_0=\varepsilon_0A/d$ . (a) Find the initial and final charge and field energy. (b) Find the work done by the source during insertion. (c) Find the mechanical work done by the field on the dielectric using energy conservation.Solutions: 1
Problem 3A transverse object of height $H$ is placed before a converging thin lens of focal length $f>0$ , perpendicular to its principal axis. Its distance from the lens is $u=3f$ ; use the convention that image distance $v>0$ lies opposite the object and signed transverse magnification is $M=-v/u$ . (a) Use the principal-ray construction to determine the image character and location. (b) Find the signed magnification and image height. (c) If a smaller object is placed at the same position, state what changes and what does not, explaining with the lens equation.Solutions: 1