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Some expensive electronics or mechanical devices are designed to be shock-resistant. However, the manufacturers often market the level of shock-resistance in units of g-force (I know g-force is really a measure of acceleration). I'm not really convinced that that's the proper unit.

In fact, the Wikipedia article for mechanical shock describes shock as a sudden acceleration or deceleration. Here, the term "sudden" seems to imply that the acceleration or deceleration is not constant during a shock, which would mean that there should be a jerk component to the equation that describes the movement or position of the object as a function of time.

So here are my three related questions:

  1. Is shock better expressed as g-force per second? If not, why (i.e. why is g-force a better unit)?
  2. When you bang a smaller object that is reasonably rigid (e.g. a wristwatch with stainless steel case and bracelet) against another object that is reasonably massive, immovable, and rigid (e.g. a brick wall), how does the plot of position as a function of time actually look like, supposing we can record time and distances with extreme precision?
  3. Do common mechanical devices suffer mostly from high acceleration or from high jerk?

Update The ISO 1413 shock resistance standard seems to give some clues. The testing procedure consists of letting a 3 kg hard plastic hammer traveling at 4.43 m/s hit a watch. Which suggests that we really care about the instantaneous transfer of energy or of momentum. But how fast does the transfer happen? Is it in the millisecond or nanosecond granularity?

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why jerk, why not snap, crackle or pop? – alancalvitti Feb 18 at 5:14
The time scale of the transfer is set by the mechanical properties of the watch. If the watch is made out of hard, stiff materials, it will decelerate the hammer more quickly. – Ben Crowell Apr 10 at 5:09

2 Answers

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Shock is better expressed as g (or other unit of acceleration) because f = ma. Acceleration is proportional to the mechanical force applied to the object, which in turn quantifies its internal mechanical stresses.

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Shocks by definitions are discontinuous therefore non-differentiable jumps in the relevant quantities (e.g., pressure jump across a shock mechanical shock in gas). So strictly speaking I think one cannot assign an appropriate derivative description - acceleration, a jerk, and so on. However, from a practical point of it would really depend on what quantity one might want to emphasize on, if the change in force what matters one might call it a jerk.

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How can shocks be discontinuous? Doesn't an object in fact accelerate or decelerate really really fast at the instant of impact only because of the eletroweak force getting into effective range at the particle or atomic level? Doesn't it only appear to be discontinuous because the human eyes and brains cannot capture the motion fast enough? – Kal Feb 15 at 23:49
OK that's fair. What I meant to say was that shock represent changes at the molecular/atomic time and spatial scales. So, in a continuum mechanics approach it is better treated as a jump process. If you are willing to model the molecular dynamics to calculate the changes in force you will have to allow a rather fluctuating description to capture the actual dynamics. Besides, even in the any case not only do you have a force, the force-field is changing at a rate, that also changes, so you will need a much higher derivative than acceleration. – Sankaran Feb 16 at 0:51
So, it really comes down to what derivative you really care about for what the purposes of whatever you are trying to do. I would prefer a jerk over an acceleration and maybe a higher derivative to describe the process. – Sankaran Feb 16 at 0:52
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Well I do think shock is a terminology usually reserved for more steady pressure wave propagation kind of situation. For instance in supersonic flow, a blast wave from an explosion. Essentially a process in which a flow propagates faster than the speed of sound such that molecules ahead of it will not see that slap coming. The hammer on a watch situation is much less steep I think (even before the hammer hits the air ahead of it will hit the watch). Anyways regardless, I think it is about what quantity one is interested. Here I think... – Sankaran Feb 16 at 6:46
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"impulse" is a much better word. Terminology aside though an impulse is like a delta function or a very sharp gaussian. It is sort of pointless to ask what the maximum force is just like it is meaningless to ask what a delta function is at x=0. I think only a integrated quantity across a small time window has meaning (again like a delta function convoluted with some function). So you are right! It probably is calibrated to some energy delivered in a small unit of time. The unit of time must be chosen or agreed by the regulating agency on some practically-motivated reason. – Sankaran Feb 16 at 6:51
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