# Newton's law, gun recoils

## Homework Statement

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

??

## The Attempt at a Solution

Newton's second law?? F=M/A

Hootenanny
Staff Emeritus
Gold Member

## Homework Statement

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

??

## 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?

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.

Hootenanny
Staff Emeritus
Gold Member
every action has an equal and opposite reaction. there for, it is related to Newton's third law.
Correct.
I'm not sure how to explain this scenario using newton's third law.
What happens when you pull the trigger?

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?

Hootenanny
Staff Emeritus
Gold Member
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.

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.

Hootenanny
Staff Emeritus
Gold Member
Ok, thanks very much for your help.
A pleasure Andrew Mason
Homework Helper
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:

$$m_{bullet}v_{muzzle} = \bar F t$$

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

$$\bar v = \frac{d_{barrel}}{t} = \frac{1}{2}v_{muzzle}$$

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 $\bar F$

AM