International Physics Olympiad · Year 2019

Problems

Problem 1A bullet of mass $m$ travels horizontally at speed $v_0$ through a stationary wooden block of mass $M$ . After exiting, the bullet has speed $v_0/2$ . The block then slides on a rough horizontal surface with kinetic friction coefficient $\mu$ . Find the block's speed immediately after the interaction and its stopping distance. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.Solutions: 1
Problem 2An ideal transformer has $N_p$ primary turns and $N_s$ secondary turns; its primary is connected to an AC source of rms voltage $V_p$ . The secondary feeds a pure resistor $R_L$ with rms current $I_s$ . Find secondary voltage, primary rms current, load power, and voltage ratio. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.Solutions: 1
Problem 3A spacecraft moves at constant speed $v$ relative to Earth. Its onboard clock measures proper time $\Delta\tau=2.0$ years between two events occurring at the same spacecraft location. Given light speed $c$ and $v=0.8c$ , find the time between the events according to Earth clocks and the distance traveled by the spacecraft. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.Solutions: 1