# Newton's law, gun recoils

1. Jun 25, 2008

### tim_mannire

1. The problem statement, all variables and given/known data

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

2. Relevant equations

??

3. The attempt at a solution

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

2. Jun 25, 2008

### Hootenanny

Staff Emeritus
Nope, not the second law. Think about what happens, why does the gun recoil?

3. Jun 25, 2008

### tim_mannire

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. Jun 25, 2008

### Hootenanny

Staff Emeritus
Correct.
What happens when you pull the trigger?

5. Jun 25, 2008

### tim_mannire

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. Jun 25, 2008

### Hootenanny

Staff Emeritus
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. Jun 25, 2008

### tim_mannire

Ok, thanks very much for your help.

8. Jun 25, 2008

### Hootenanny

Staff Emeritus
A pleasure

9. Jun 25, 2008

### Andrew Mason

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