An air rifle shoots a lead pellet by allowing high-pressure air to expand, prope

Question

An air rifle shoots a lead pellet by allowing high-pressure air to expand, propelling the pellet down the rifle barrel. Because this process happens very quickly, no appreciable thermal conduction occurs and the expansion is essentially adiabatic. Suppose the rifle starts with 11.0 cm^3 of compressed air, which behaves as an ideal gas with Gamma = 1.40. The expanding air pushes a 1.00-g pellet as a piston with cross-sectional area 0.0375 cm^2 along the 50.5-cm-long gun barrel. What initial pressure is required to eject the pellet with a muzzle speed of 115 m/s? Ignore the effects of the air in front of the bullet and friction with the inside walls of the barrel. atm

Explanation / Answer

work W = dK

F * s = KE = 0.5*M*V^2

F = 0.5*M*V^2/s =

F = (0.5*0.001*115*115)/0.505

F = 13.094 N

presurre = F/A = 13.094/0.0375e-4

P = 34.91*10^5 Pascals

1.013*10^5 pascals = 1atm

P = 34.91/1.013 = 34.46 atm

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