Asian Physics Olympiad · Year 2019

Problems

Problem 1A mass $m$ starts from rest and slides down a plane inclined by angle $\alpha$ to the horizontal. The kinetic-friction coefficient is constant, $\mu_k$ , and the plane is long enough; assume $\tan\alpha>\mu_k$ so the object accelerates downhill. Take $g=9.8\,\mathrm{m/s^2}$ . (a) Find the normal force and friction magnitude. (b) Find the acceleration along the plane. (c) Find speed after distance $s$ along the plane and the time taken to travel that distance.Solutions: 1
Problem 2A positively charged particle of charge $q$ and mass $m$ enters a uniform magnetic field of magnitude $B$ with velocity $v$ perpendicular to the field. The field region is wide enough for a circular orbit; neglect gravity and relativistic effects. (a) Find the orbit radius and direction of turning. (b) Find the period and cyclotron angular frequency. (c) If the particle travels a circular arc of angle $\phi$ (in radians) before leaving the field, find the time and arc length and explain how the time depends on $v$ .Solutions: 1
Problem 3A small source emits a pure tone of frequency $f_s$ in still air, where sound travels at speed $c$ . It moves uniformly straight toward a stationary listener at speed $v_s<c$ ; neglect reflections and wind. (a) During one emission period, determine the spacing between successive wavefronts in front of the source. (b) Find the frequency $f_o$ heard by the listener. (c) Find the limits of $f_o$ as $v_s\to0$ and $v_s\to c^-$ , explaining why an approaching source raises the frequency.Solutions: 1