Explaining Gun Recoil Using Newton's Second Law

In summary: F = (m_{bullet}v_{muzzle})^2 = m_{bullet}v_{muzzle}*(1-\frac{v_{muzzle}}{v_{0}})For a rifle, this expression becomes:AMaxF = (m_{bullet}v_{muzzle})^2 = (m_{bullet}*(1-\frac{v_{muzzle}}{v_{0}}))^2
  • #1
tim_mannire
14
0

Homework Statement



A gun that is fired "recoils". Explain using one of Newton's laws.

Homework Equations



??

The Attempt at a Solution



Newton's second law?? F=M/A
 
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  • #2
tim_mannire said:

Homework Statement



A gun that is fired "recoils". Explain using one of Newton's laws.

Homework Equations



??

The Attempt at a Solution



Newton's second law?? F=M/A
Nope, not the second law. Think about what happens, why does the gun recoil?
 
  • #3
Hootenanny said:
Nope, not the second law. Think about what happens, why does the gun recoil?

every action has an equal and opposite reaction. there for, it is related to Newton's third law. I'm not sure how to explain this scenario using Newton's third law.
 
  • #4
tim_mannire said:
every action has an equal and opposite reaction. there for, it is related to Newton's third law.
Correct.
tim_mannire said:
I'm not sure how to explain this scenario using Newton's third law.
What happens when you pull the trigger?
 
  • #5
Hootenanny said:
Correct.

What happens when you pull the trigger?

The gun has an equal and opposite reaction, when the bullet is fired it gains speed and momentum instantly, causing the gun to lunge backwards towards the shooter.

are there any more contributing factors?
 
  • #6
tim_mannire said:
The gun has an equal and opposite reaction, when the bullet is fired it gains speed and momentum instantly, causing the gun to lunge backwards towards the shooter.

are there any more contributing factors?
Nope sounds good to me. However, I would suggest that "in a very short period of time" would be better than "instantly". I would also mention that this change in momentum requires a force, the reaction of which is the recoil of the gun.
 
  • #7
Hootenanny said:
Nope sounds good to me. However, I would suggest that "in a very short period of time" would be better than "instantly". I would also mention that this change in momentum requires a force, the reaction of which is the recoil of the gun.

Ok, thanks very much for your help.
 
  • #8
tim_mannire said:
Ok, thanks very much for your help.
A pleasure :smile:
 
  • #9
tim_mannire said:
The gun has an equal and opposite reaction, when the bullet is fired it gains speed and momentum instantly, causing the gun to lunge backwards towards the shooter.

are there any more contributing factors?

You might want to show how the recoil force is calculated: The bullet accelerates down the barrel such that its maximum speed (at the muzzle) multiplied by its mass is equal to the average force x time it was accelerating. This is also the average force on the gun (and on the person holding the gun) during that time:

[tex]m_{bullet}v_{muzzle} = \bar F t[/tex]

Since the bullet accelerates from 0 to muzzle speed in time t, its average speed during acceleration is half of its muzzle speed:

[tex]\bar v = \frac{d_{barrel}}{t} = \frac{1}{2}v_{muzzle}[/tex]

From that you should be able to work out the time as a function of muzzle speed and barrel length and use that to find the expression for the average force [itex]\bar F[/itex]

AM
 

FAQ: Explaining Gun Recoil Using Newton's Second Law

What is Newton's First Law?

Newton's First Law, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an unbalanced force.

What is Newton's Second Law?

Newton's Second Law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be expressed as the famous equation F=ma, where F is force, m is mass, and a is acceleration.

What is Newton's Third Law?

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when a force is applied to an object, the object will push back with an equal force in the opposite direction.

How does Newton's Third Law relate to gun recoils?

When a gun is fired, the gunpowder inside the bullet explodes, creating a high-pressure gas that pushes the bullet out of the barrel. According to Newton's Third Law, the force of the gas pushing the bullet forward is met with an equal and opposite force pushing the gun backwards, resulting in the recoil.

Can Newton's Laws be applied to gun recoils?

Yes, all of Newton's Laws can be applied to gun recoils. The recoil of a gun can be explained by the application of Newton's Third Law, while the force and acceleration of the bullet can be calculated using Newton's Second Law. Additionally, the Law of Inertia can help explain why a gun will not fire if it is not held firmly in place.

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