How can we calculate the damage done by a bullet?

Question

I think damage done is momentum (mass X velocity). Is it true? If else, what is it?

Answer 1

I don't agree.

When two bodies collide the total momentum does not change.
E.g. if a bullet doesn't strike through, body and bullet move together in the direction of the shot after the collision. That's why, a person shot in the breast falls at his back.
The damage is done by "the energy". By the collision the bullet transfers a part of its kinetic energy due to deformation work. Hence the change of kinetic energy gives the magnitude of damage done.

For the case, that the bullet hits a body at rest doesn't strike through, it can be calculated as follows:
Let m1 the mass of the bullet and m2 the mass of the body, v1 the velocity before and v2 the velocity after collision. Latter one can be derived from momentum balance:
m1*v1=(m1+m2)*v2
=>
v2=m1/(m1+m2) *V1

The kinetic energy difference is:
E= 1/2*m1*v1²-1/2*(m1+m2)*v2²
= 1/2*v1²(m1-m1²/(m1+m2))
=1/2*m1v1² *{m2/(m1+m2)}

The term before the accolade represents the kinetic energy of the bullet and the term in accolades its fraction, which is transferred due to collision. Since the mass of the body is usually much greater than bullet mass, the bigger part of the bullet energy is transferred in demolition work.

Answer 2

The damage is the energy dissipated during the collision. Before the collision, the bullet has kinetic energy E1 = m1 * v1^2 / 2 (m is the mass and v the velocity). After collision, supposing it hits a heavy enough (thus stable) object (such as a human body >:)), with initial energy ), the bullet will stop (inelastic collision). Thus the final energy will be 0. The energy variation will be E1, and it's also the damage done by the bullet.
If the object hit is lighter, of mass m2 : m1 * v1 = (m1+m2) * v2 from where you get v2 - the speed of the object - bullet system after the collision. The energy after the collision is E2 = (m1 + m2) * v2^2 / 2 and the variation in energy is E = E1 - E2, that dissipates in the collision.

Answer 3

You are talking Damage here not energy.
I agree with others on what they say but they forget, you want damage.
To add to what they said I would have to say that the damage is done by how fast the bullet slows down after it make contact.
Let me explain. If you fire a steel round into a body it will make more or less of just a round hole about its size.
But if you use lead, or other types of soft material with same weight as the steel, Then when it makes contact it will shatter or spread out making a very much bigger hole in what it hits.
I would have to say that the material of the bullet would be what determines damage.
Remember penetration and damage are two different things.

Answer 4

kinetic energy possessed by bullet initially was the total energy it was having if it get in the body and stop their the total energy transfferred can be taken as damage done
u can also find out time to stop the bullet by and hence the distance travelled by it in the body which can also be taken as damage done

Answer 5

Kinetic energy = 1/2mv^2

Answer 6

you need to know about 'momentum transfer'. this is very important physical amount for the damage..