Question

When a bullet is fired from a gun, which has more momentum? Bullet or gun?

Answer 1

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".
However, the physics behind all guns remain the same. Weapons such as cannons, shotguns and rifles, work on the basic idea of conservation of momentum and the change in energy from potential to kinetic.

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 the momentum doesn't change, i.e. 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 m_b and speed v_b out of the gun, it has momentum p_b given simply by
p_b = m_bv_b

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: p_g = -p_b, or
m_gv_g = -m_bv_b

Conservation of momentum is the law that is held true when the gun is fired and a "kick" is felt. When a bullet is fired from a gun, total momentum before is zero since nothing is moving. After firing the bullet there is a momentum in the forward direction. The gun must therefore have the same magnitude of momentum but in the opposite direction so that they cancel each other out leaving the total momentum still equal to zero. For this reason the gun must have a recoil velocity after the bullet is fired (i.e. the gun 'jumps' backwards and a 'kick' is felt).

As the bullet is propelled through the barrel, it gains momentum. In order for the entire system of the gun and the ammunition to have equal momentum, the gun must gain momentum in the opposite direction from the bullet. Momentum is a vector quantity, having both a direction and a direction. The faster an object is moving or the more mass it has, the more momentum it has in the direction of its motion (momentum = mass velocity). Because momentum is a conserved quantity, it cannot be created or destroyed (momentum before = momentum after). It can only be transferred between objects. Momentum is conserved because of Newton's third law of motion.

When one object exerts a force on a second object for a certain amount of time, the second object exerts an equal but oppositely directed force on the first object for exactly the same amount of time. The momentum lost by the first object is exactly equal to the momentum gained by the second object. Momentum is transferred from the first object to the second object. In this case, if a gun exerts a force on a bullet when firing it forward then the bullet will exert an equal force in the opposite direction on the gun causing it to move backwards or recoil. Although the action and reaction forces are equal in size the effect on the gun and the bullet are not the same since the mass of the gun is far greater than the mass of the bullet. The acceleration of the bullet while moving along the gun barrel would be much greater than the acceleration of the gun (acceleration= force mass).