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Chapter 1: Q17E (page 264)

The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A 30 caliber bullet has mass 0.00720 kg and a speed of 601 m/s relative to the muzzle when fired from a rifle that has mass 2.80 kg. The loosely held rifle recoils at a speed of 1.85 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.

Short Answer

Expert verified

Thus, the momentum of the propellant gases is 0.85 kgm/s.

Step by step solution

01

Given in the question.

Mass of bullet is m =0.00720 kg

Mass of rifle is M =2.80 kg.

Speed of bullet when fired is V =601 m/s.

Speed of rifle recoils when fired is v =1.85 m/s.

02

Law of conservation of momentum.

Use the law of conservation of momentum which states that the momentum of the bodies before collision is equal to the sum of the momentum of the bodies after collision. After collision, the bodies will move with a common velocity

03

Obtain the momentum of the system.

Use the conservation of momentum to obtain the momentum of the propellant gases:

P=-mV+MvP=-(0.0072)(601)+(2.8)(1.85)P=0.85kgm/s

Hence, the momentum of the propellant gases is 0.85 kgm/s.

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