Asian Physics Olympiad · Year 2021

Problems

Problem 1A small ball is launched from the edge of a cliff of height $h=20$ m with initial speed $v_0=20$ m/s at $30^\circ$ above the horizontal. Neglect air resistance and take $g=10$ m/s $^2$ . Set the origin at the foot of the cliff, with $x$ horizontal in the launch direction and $y$ upward; the ground is $y=0$ . (a) Find the time from launch until impact. (b) Find the horizontal coordinate and both velocity components at impact. (c) Determine the maximum height above the ground and when it is reached.Solutions: 1
Problem 2One mole of monatomic ideal gas starts at state $A$ with $T_A=300$ K and $V_A=0.010$ m $^3$ . It follows a three-step cycle: (1) heat at constant volume from $A$ to $B$ , where $T_B=600$ K; (2) expand isothermally from $B$ to $C$ until the volume doubles; (3) compress at constant pressure from $C$ back to $A$ . Use $R=8.31$ J mol $^{-1}$ K $^{-1}$ , molar $C_V=3R/2$ , and define work $W$ as positive when done by the gas. (a) Find the pressures at $A,B,C$ . (b) Calculate work and heat for each leg. (c) Check the first law over the complete cycle.Solutions: 1
Problem 3A thin converging lens of focal length $f=20$ cm stands in air. A small luminous object of height $H=2.0$ cm is perpendicular to the principal axis, $u=30$ cm in front of the lens. Use the convention that a real image has $v>0$ , the lens equation $1/f=1/u+1/v$ , and lateral magnification $m=-v/u$ . (a) Find the image distance and height. (b) State whether the image is real or virtual and upright or inverted. (c) The object is moved farther away to $u=60$ cm; find the new image and describe the size change.Solutions: 1