# Recoil from a shotgun

First of all I'd like to point out that I'm a complete layman when it comes to physics and I apologise if this isn't the correct forum for this.

If I were to sit on an office chair on a laminated floor and fired a shotgun out in front of me roughly how far backwards would I recoil, imagine I weight 170lbs, I'll let you choose both the office chair and shotgun being used (I haven't got a shotgun to use as an example, this is purely hypothetical).

Also if I was to fire the shotgun in the same situation as above but facing a wall would I be projected further?

According to this article (the choice of article has no significance other than it came up first in my Google search):

Remington's 12-gauge 2 3/4-inch Premier Magnum turkey load has 1 1/2 ounces of shot and a 1260 fps muzzle velocity

Converting these figures to metric, $m_{\text{shot}} = 0.0425$ kg and $v_{\text{shot}} = 384$ m/sec, so the momentum of the shot is:

$$p = m_{\text{shot}}v_{\text{shot}} = 16.3 \space \text{kg.m/s}$$

To conserve momentum your momentum would also change by the same amount, so:

$$m_{\text{Luke}}v_{\text{Luke}} = m_{\text{shot}}v_{\text{shot}} = 16.3$$

and if we divide $16.3$ by your mass of about $77$ kg we find your velocity to be:

$$v_{\text{Luke}} = \frac{16.3}{77} = 0.21 \space \text{m/s}$$

Your question asked how far the chair would move, but there is no way to calculate this because it depends on the frictional losses as the chair rolls and I have no way to know this. The best I can do is give you the initial velocity of the chair ($0.21$ m/s). You'd have to try experimentally measuring the chair+you roll distance as a function of initial velocity to determine the distance.

• yeah, but how far would he move? you need some office chair parameters too – Aksakal almost surely binary Apr 3 '14 at 17:09
• @Aksakal: it's impossible to predict how far the chair would move. That will depend on the friction in the wheels and the surface that it's rolling on. Since I rather doubt the manufacturers provide this information you would have to determine the frictional loses in the chair by experiment. – John Rennie Apr 3 '14 at 17:15
• Don't forget the momentum of the gases that leave the barrel along with the shot (but at higher speeds)... – DJohnM Apr 3 '14 at 17:59
• Shouldn't this question be closed now? – user42733 Apr 3 '14 at 18:14
• @User58220: true, though I have no way of knowing what fraction of the momentum is carried by the gases. In any case, I think this is one of those approximate calculations in which understanding the method is more important than the final result. – John Rennie Apr 4 '14 at 6:04