Women's Biathlon
Although guns may not be everyday things for many of us, gun recoil is
certainly something we're aware of (at least those of us that don't
make Hollywood action films with guns whose recoil would instantly
kill the person firing them!). Gun recoil is a result of momentum
conservation, which is an extremely important fundamental
principle. Newton was talking about momentum conservation when he
wrote "every action has an equal and opposite reaction".
Momentum Conservation
Momentum characterizes an object's resistance to change in
motion. If this is motion along a straight line, we call it linear
momentum; if it is rotational motion we call it angular
momentum. The basic idea is the same: moving things like to keep
moving, and to change their motion we have to apply a force. If no
force is present, then momentum doesn't change, ie. it is conserved.
Now, you might point out that a bullet coming out of a gun has a huge
force on it from the exploding gunpowder. True enough, and that force
is what propels the bullet forward. However, if you look at a
bullet and gun together (say while the bullet is still in the
barrel but already heading out at full speed), you can say there is no
net force on the bullet-gun system. So the momentum of
the bullet plus gun should be conserved.
If the bullet has mass mb and speed
vb out of the gun, it has momentum
pb given simply by
pb = mbvb
in the forward direction. To balance this momentum (and keep the net
momentum of the bullet-gun system zero), the gun recoils with momentum
in the opposite direction: pg = -pb, or
mgvg = -mbvb
Although the bullet's mass is small, its speed is quite large, so it
released with large momentum. The gun has much larger mass, so the
recoil speed is much smaller, but still large enough to give a serious kick
against the shooter's shoulder.
Example: Winchester .308
Let's look at an example. A Winchester .308 cartridge launches a
bullet of mass 150 grains (1 grain = 64.8 mg) with a speed of 2820
ft/s (1 ft = 30.5 cm). In MKS units, then, pb =
8.4 kg m/s. This rifle has a weight of about 8 lbs, or a mass
of mg = 3.8 kg. That means the recoil speed of
the rifle will be
vg = - pb/mg = -2.2 m/s
This primary recoil is noticeable, but not the main recoil that
one feels.
Secondary Recoil
There are actually two distinct recoils from a gun: the first, primary
recoil, which I've described above, conserves momentum of the
gun-bullet system. However, a larger secondary recoil comes slightly later,
when the bullet leaves the muzzle: then the hot expanding gas behind
the bullet shoots out of the muzzle, and the muzzle recoils further
like a rocket. This is, again, conservation of momentum,
but in this case is is the gas momentum out of the barrel
that makes the secondary recoil. Gun manufacturers make baffles that
reduce the flow of gas out of the muzzle to reduce secondary recoil.
Primary recoil cannot be reduced, since it is simply associated with
the forward momentum of the bullet.
Equations
Summary
- The total momentum of a system is conserved if there are no
outside forces acting on it.
- Gun recoil results from conservation of total momentum of the
bullet-gun system: the backward recoil gun momentum balances the
forward bullet momentum to maintain zero total momentum.
- Gun recoil actually has two parts: primary recoil from the
escaping bullet and secondary recoil from the escaping gas
behind the bullet.
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