# The force of a bullet

pixel01
How can I calculate the force of a bullet shot against a wall if the velocity v and mass m are given?

## Answers and Replies

Mentor
How can I calculate the force of a bullet shot against a wall if the velocity v and mass m are given?

Force = mass x acceleration, right? If the bullet doesn't deform as it stops, then you just need to graph the deceleration versus time, and that will net you the force versus time with a little math.

Is this homework? If so I should move it to Homework Help, Intro Physics.

pixel01
Force = mass x acceleration, right? If the bullet doesn't deform as it stops, then you just need to graph the deceleration versus time, and that will net you the force versus time with a little math.

Is this homework? If so I should move it to Homework Help, Intro Physics.

This is not homework A similar scenario is how can I estimate the force of a hammer when you hit a nail into the wall.

everypot
No. You need to know many details about the wall, like the material, the structure, the density, and so on to make a calculation.

But why do you want to know the force? Force is not a very useful concept.
Actually, in advanced/modern physics, force is of little importance.

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tonyh
How can I calculate the force of a bullet shot against a wall if the velocity v and mass m are given?
I think you'll need more information that just the initial momentum (P). If you had the time (t) taken for the bullet to come to rest you could treat it as a simple 1-D collision:

change in P = average force (F) * t

Lojzek
How can I calculate the force of a bullet shot against a wall if the velocity v and mass m are given?
The mass and velocity only give you kinetic energy: E=m*v^2/2
The force is not yet determined, since it depends on the length of the path of deceleration. Let's say that a bullet does not deform itself and penetrates a distance of s into the wall. Then the force (averaged over the deceleration path) is F=E/s=m*v^2/(2s). A hard wall will stop the bullet faster (smaller s) and produce greater force. (however the force comes before acceleration, so it would be more consistent to say that a hard wall will act with a greater force and so stop the bullet faster).
If the wall is very hard (bullet deformation is comparable or larger than wall deformation), then one should take the wall penetration depth+bullet deformation for s (although the exact calculation would be more difficult, since this is no longer a rigid body movement).

TPDC130
For a nice simple answer, use the fact that force is the rate of change of momentum.

F=(mv-mu)/t

if you assume that the bullet stops immediately when it hits the wall, then its final velocity is 0. Therefore the force F=mv/t.

Although there might be a bit of difficulty in measuring t since the bullet stops almost instantaneously.