# Unit for Impact Force

Forgive me if this is a newb question but I am not a trained scientist, much less a physicist. I'm just curious and would like to know if there's a unit to measure impact force.

I know the newton is the amount of force required to accelerate a mass of one kg at a rate of 1m/s^2 but what about the impact itself?.

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There is always some risk that you are mixing technical and non-technical uses of vocabulary. The SI unit of force is the Newton, the Newton, or the Newton. However, you may have a more general (i.e. non-technical) meaning of the word "force" in mind (my first guess, the impulse which has units of momentum, but there is also the possibility that you are interested in the peak acceleration or something else entirely). Would you care to clarify? – dmckee Aug 18 '11 at 18:23
As above really, I am tempted to believe you are interested in peak acceleration, ie the peak force during the time of impact, but remember in physical situations there is always some finite time over which processes occur. – Nic Aug 18 '11 at 18:26
I would echo what dmckee said. As far as physics is concerned, "impact force" is just a force that happens to occur during an impact - but presumably if that's what you meant by the term, you wouldn't be asking this question. So we can't be sure what you do mean without more information. – David Z Aug 18 '11 at 19:06
It sounds to me more like he's thinking "what unit do physicists use to quantify an impact". The answer to that is easy - they don't. There is no one quantity that is, or could be used, to quantify the nature of a collision. There a lots of specific questions that can be asked about a collision, and the answers to those can have units. – Alan Rominger Aug 18 '11 at 19:18
Thanks for the feedback, everyone. My question was not clear indeed and I realize there's a whole lot more factors to consider. I guess I'd be able to conceive the problem more accurately if I rephrased like this: what would the threshold maximum structural integrity of an object need to be in order to still be completely crushed between two surfaces, not counting their own material properties? (whew!) – Daze Aug 19 '11 at 0:55

I would refer you to a previous answer I gave, here:

Hammer vs large mass on nail

But I'll try to answer very simply for right here only. If you are referring to one free-moving objecting colliding and bouncing off another object then we can go about listing all the variables that would be sufficient to describe the approach/impact. Also, we are likely to consider one of the objects involved in the impact as the "lab" frame, just so we don't get into the complication of a 2-body problem.

Say a projectile is flying toward the ground, a wall, a nail, or whatever solid surface you want. The projectile has mass $m$ and velocity $v$. That can then give you impulse $I$ (but notation varies), and energy $E$. Either of these 2 sets of variables are sufficient to describe the nature of the projectile aside from material-specific concerns.

Into material specific, if one thing hits another, we can think of it like a spring, where $k$ is the functional constant for Hooke's Law, which is really the combined spring constant of the two objects. Again, if one item is at rest (or we use reduced mass), then we can find the time spent in contact before the projectile bounces back off, this is $t=\pi \sqrt{m/k}$. You should read up on Wikipedia and other resources for more specifics about the mechanics, but the force $F$ is not constant and follows a sinusoid profile over time (given the prior assumptions). For the force experienced in the impact:

$$F \propto \frac{I}{t} = \frac{m v}{\pi} \sqrt{\frac{k}{m}} = \frac{v}{\pi} \sqrt{m k}$$

In fact, this exact quantity would be the average force. For the maximum force, I believe it would be:

$$F_{max} = \frac{\pi}{2} F_{avg} = 2 v \sqrt{m k}$$

Although it's hard for me to think of something that would more appropriately be the "impact force", you still need to refine your question. It seems like some of the confusion is about units, and the is no single unit that will quantify the "force" or the "damage" from an impact, as it depends on a number of factors. Although the above expression only has 3 variables, a real life collision is much more complicated. The area and contour that the force is distributed over matters a great deal, and the assumption that the materials behave like a spring is wrong too, since plastic deformation and other things that can occur.

I hope this helps you to advance your thinking on the subject.

I guess I'd be able to conceive the problem more accurately if I rephrased like this: what would the threshold maximum structural integrity of an object need to be in order to still be completely crushed between two surfaces, not counting their own material properties?

That would be kinetic energy on the projectile side and the integral of the stress-strain curve on the side of the crushed object side. Imagine you have a rock flying toward a hard place, and in the middle is an object that may or may not get crushed. What matters is the stress strain curve.

The object will be conceptualized as a rod as above. The integral is illustrated here.

So the rod has some area that the projectile hits. The following determines if it is crushed.

$$\frac{1}{2} m v^2 < A \int_0^{\epsilon_y} \sigma(\epsilon) d\epsilon$$

If this is met it won't be crushed.

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Thanks, Z. Although I'm not able to wrap my head around everything you wrote, you still explained lots of things I hadn't even considered. I've added a comment below my question, I hope I'm not digging myself deeper. – Daze Aug 19 '11 at 1:29

$\sum Impact = \Delta Momentum$

Units for impact are the same as momentum ${\rm N\,s} = {\rm kg\,\frac{m}{s}}$.

Edit: I meant to say "Impulse" to describe impact forces.

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The word you are looking for here is "impulse". – dmckee Aug 18 '11 at 19:57