International Physics Olympiad · Year 2001

Problems

Problem 1A projectile is launched from level ground at speed $u$ and angle $\alpha$ above horizontal; neglect air resistance. Find its range and the angle giving maximum range; gravity is $g$ . Treat the projectile as a point mass returning to its launch height; take vertical upward as positive and neglect drag. (a) Find the flight time and range $R$ . (b) For fixed $u$ , find the launch angle and maximum range. (c) Find the maximum height for a general launch angle. 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 2An 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
Problem 3A 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