International Physics Olympiad · Year 2003

Problems

Problem 1A string of length $L$ fixed at both ends carries waves at speed $v$ . Find the fundamental wavelength and frequency, and the frequency of the $n$ th harmonic. A uniform string of length $L$ has nodes at both fixed ends; consider mode number $n$ , a positive integer. (a) Find wavelength $\lambda_n$ and the number of interior nodes. (b) Find the fundamental frequency. (c) Find the frequency of mode $n$ and explain its harmonic relation. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.Solutions: 1
Problem 2A mass $m$ slides from rest down an incline at angle $\theta$ with kinetic friction coefficient $\mu$ . Find its acceleration and speed after distance $L$ . The block slides with constant kinetic-friction coefficient $\mu$ and constant acceleration; take downhill along the plane as positive. (a) Find the normal force $N$ . (b) Find acceleration along the incline. (c) Find the speed after distance $L$ and state the condition for downhill sliding. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.Solutions: 1
Problem 3An ideal monatomic gas with $n$ moles is heated at constant pressure from $T_1$ to $T_2$ . Find the work done, change in internal energy, and heat absorbed; use gas constant $R$ . The process is isobaric and only pressure-volume work occurs; take $W>0$ for work done by the gas and $Q>0$ for heat absorbed. (a) Find the work $W$ . (b) Find the internal-energy change $\Delta U$ . (c) Use the first law to determine the heat $Q$ absorbed. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.Solutions: 1