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A 77 kg man holds a 3 kg rifle and shoots a 4 g bullet with a speed of 450 m/s. The gun then recoils backward.

a. With what speed does the rifle recoil if held loosely by the man?

b. If the rifle is held firmly by the man, how fast do the man and the rifle recoil together?

Answer :

Final answer:

The rifle recoils at a speed of 0.6 m/s when held loosely by the man. If held firmly, the combined man and rifle recoil back at approximately 0.0225 m/s. Both scenarios demonstrate conservation of momentum in an isolated system.


Explanation:

Understanding Recoil in Firearms


The problem involves a man firing a rifle, which results in recoil due to the conservation of momentum. In both parts of the question, we will apply the principle of conservation of momentum to find the speed of the rifle's recoil.



a. Speed of the Rifle Recoil


When the rifle is fired, the total momentum before the shot must equal the total momentum after shooting. Initially, both the man and the rifle (and the bullet) are at rest, so the initial momentum is 0.


Momentum Before: 0


After shooting, the bullet and rifle will both have momentum. The momentum of the bullet can be calculated using the formula:



  • Momentum of Bullet = mass of bullet velocity of bullet

  • Mass of the bullet = 4g = 0.004kg

  • Velocity of the bullet = 450m/s

  • Momentum of Bullet = 0.004kg 450m/s = 1.8 kg·m/s


Since momentum must be conserved, the momentum of the rifle (which recoils back) will be equal in magnitude but opposite in direction. If we denote the recoil speed of the rifle as vr, we can say:



  • 0 = (momentum of bullet) + (momentum of rifle)

  • 0 = 1.8 kg·m/s + (mass of rifle velocity of rifle)

  • Let the mass of the rifle = 3kg

  • Thus, we have: 1.8 = 3 vr

  • Solving for vr: vr = 1.8 / 3 = 0.6 m/s


The rifle recoils backward at a speed of 0.6 m/s.



b. Speed if the Rifle is Held Firmly


If the man holds the rifle firmly and we consider the combined mass of the man and rifle, we will still use conservation of momentum, but now we include the mass of the man.


Combined Mass = Mass of Man + Mass of Rifle = 77kg + 3kg = 80kg


Using the momentum conservation principle, we again set the total momentum before and after the shot equal:



  • 0 = (momentum of bullet) + (momentum of man + rifle)

  • 0 = 1.8 kg·m/s + [80 vmr]

  • Solving for vmr:

  • 1.8 = -80 vmr

  • vmr = -1.8 / 80 = -0.0225 m/s


The negative sign indicates the direction of motion, so the man and the rifle recoil together at a speed of approximately 0.0225 m/s backwards.


Learn more about recoil here:

https://brainly.com/question/47476422


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Rewritten by : Jeany

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