Asian Physics Olympiad · Year 2025

Problems

Problem 1A cart of mass $m$ moves at speed $u>0$ along a frictionless straight track and undergoes a one-dimensional elastic collision with a stationary cart of mass $2m$ . Find the signed velocity of each cart after the collision, taking the first cart's initial direction as positive. Treat the carts as point masses and neglect external horizontal impulse during contact. (a) Write momentum conservation. (b) Use the elastic-collision condition to obtain a second relation and calculate both signed velocities. (c) Check the kinetic-energy balance and interpret the signs without confusing velocity with speed.Solutions: 1
Problem 2At $t=0$ , an initially uncharged capacitor of capacitance $C$ is connected in series with a resistor $R$ and an ideal battery of emf $E$ . Take current in the charging direction as positive and neglect internal resistance. Find the charge $q(t)$ on the positive plate, current $i(t)$ , and energy stored in the capacitor for $t\geq0$ . Assume ideal components with constant values $R>0$ , $C>0$ , and $E>0$ , a switch closed at $t=0$ , and no initial capacitor charge. (a) Derive the differential equation from Kirchhoff’s loop rule. (b) Find $q(t)$ and then the current, identifying the circuit time constant. (c) Find the capacitor energy and check the limits at $t=0$ and as $t$ becomes very large.Solutions: 1
Problem 3Monochromatic light of frequency $\nu$ illuminates a metal with work function $\Phi$ , where $h\nu$ > $\Phi$ . Use Einstein's photoelectric equation, neglect all losses, and assume the emitted electrons are nonrelativistic. Let h be Planck's constant, e > 0 the magnitude of the electron charge, and m_e its mass. Find the maximum kinetic energy K_max, the stopping potential magnitude V_s, and the maximum electron speed. Assume monochromatic illumination, with each emitted electron absorbing one photon; neglect electron interactions and losses in the metal. (a) Write energy conservation for the most energetic electron. (b) Deduce the magnitude of the retarding voltage that stops it. (c) Calculate its maximum speed in the nonrelativistic approximation and state the emission threshold.Solutions: 1