Find the momentum of the propellant gases in a coordinate system attached to the

Question

Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.

The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A .30 caliber bullet has mass 7.20 10^?3 m/s relative to the earth. Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle. kg. The loosely held rifle recoils at a speed of1.85m/s relative to the muzzle when fired from a rifle that has mass2.80kg and a speed of 601

Explanation / Answer

let Pb be momentum of bullet and Pr be momentum of gun and the momentum og gases be Pg
in the instant when the bullet is fired the bullet moves forward and the propellant gases are also ejected forward with high speed.
according to the law of conservation of momentum the momentum of system b4 and after firing should be same
assuming bullet forward direction as positive and recoil direction as negative we have
momentum of bullet = 7.2 x10-3 X( +601) =4.3272kgm/s

momentum of rifle = 2.8x(-1.85) = -5.18Kgm/s ( negative since velocity is opposite to bullet direction)

initial momentum = 0kgm/s

final momentum = P (bullet) +P(rifle)+ P(gases) = 0

so we have momentum of gases= 5.18-4.32= 0.86 kgm/s

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