FYKOS Year 30 Series 6 Problem 4 — shoot your rat · FYKOS 30 #30.6.4

Physics · mechanics · thermodynamics

Problem

Mirek wants to shoot a rat he sees at the dorm. To that end, he made a simple air gun which can be modeled as a tube with constant cross-section S=15  mmS=15\;\mathrm{mm} and length l=30  cml=30\;\mathrm{cm} closed on one side and open on the other. Mirek plans to place a bullet of mass m=2gm=2g into the tube so that the bullet seals to tube exactly and is fixed at a distance d=3  cmd=3\;\mathrm{cm} from the closed end. He that pumps up the closed section to a pressure p0p_{0} and then releases the bullet. He wants the speed of the bullet to be at least v=90  m⋅s−1v=90\;\mathrm{m}\cdot \mathrm{s}^{−1} as it exits the tube. What pressure will he need to achieve if the gas is ideal? Discuss the realism of the situation. Assume the bullet is released by a quasi-static adiabatic process where κ=7⁄5κ=7⁄5, as the gas is diatomic. Assume an external atmospheric pressure pa=105Pap_{a}=10^5Pa. Neglect losses due to friction, air resistance and gas compression ahead of the bullet.

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