Why Does a Bullet Gain More Kinetic Energy Than the Gun When Fired?

[alan4cult]

Homework Statement

When a gun fires a bullet why is the kinetic energy gained by the bullet much greater than the kinetic energy gained by the gun?

Homework Equations

Kinetic Energy = 1/2 m v^2

The Attempt at a Solution

Ok I release that Kinetic Energy depends on the square of the velocity so does this mean that the velocity is more important that the mass of the bullet/gun?

 

[Dick]

Think about conservation of momentum. The gun and the bullet will have equal and opposite momenta after the bullet is fired. But the gun is much more massive.

 

[Moetasim]

Yes, the velocity of the bullet is more important in determining its kinetic energy compared to the mass of the bullet or gun. This is because kinetic energy is directly proportional to the square of the velocity, while it is only linearly proportional to the mass. This means that even a small increase in velocity can result in a significant increase in kinetic energy. In the case of a bullet being fired from a gun, the gun provides the initial velocity to the bullet, which is then accelerated further by the force of the gunpowder explosion. This results in a much higher final velocity for the bullet compared to the gun, leading to a greater kinetic energy for the bullet. Additionally, the design and construction of the gun allows it to absorb and dissipate some of the energy generated by the explosion, reducing the kinetic energy gained by the gun itself.