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:
- Is shock better expressed as g-force per second? If not, why (i.e. why is g-force a better unit)?
- 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?
- 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?
Best Answer
There are definitely situations in materials science and mechanical engineering when jerk is more important than acceleration as a factor in causing damage. A term I've seen used is "load rate." This can refer to either $dF/dt$ or $da/dt$, which differ by a factor of $m$. You'll see the acronyms ALR and ILR for average and instantaneous load rate.
A steady force can't cause wave excitations, but a varying force can. For example, when you're machining something on a mill or lathe, jerk produces "chitter," which can spoil your work. Engineers designing cams work very hard to minimize the jerk of the cam follower: "Remember also that jerk translates to an impulse and excessive impact ultimately leads to scuffed and pitted cam follower." (Blair 2005)
I know of a couple of good examples involving the human body. In crewed spaceflight, astronauts are exposed during a launch not just to high accelerations but also sometimes to what's known as a "pogo," which means an oscillating acceleration in the longitudinal direction. A pogo with an amplitude as small as $0.5g$ can apparently cause extremely unpleasant sensations in the eyeballs and testicles, as well as heating of the brain and viscera (Seedhouse 2013). Heating is a phenomenon you can't get from a static force.
Another human-body example involves running injuries. Measurements using accelerometers attached to runners' feet, legs, or hips show that during a stride cycle, there are typically two different peaks, an impact peak and another "active" peak that occurs during propulsion. The impact peak has a smaller acceleration but a larger jerk, and seems to be the factor that causes injuries: "increased impact loading was associated with an elevated risk of sustaining a running injury while peak vertical force was not." (Davis 2010)
G. P. Blair, C. D. McCartan, H. Hermann, "The Right Lift", Race Engine Technology, Vol. 3 lssue 1, August 2005
Irene Davis, quoted in http://lowerextremityreview.com/news/in-the-moment-sports-medicine/impacts-spell-injury , 2010
Erik Seedhouse, 2013, Pulling G: Human Responses to High and Low Gravity