Understanding the Impact of Static and Sudden Forces on Pain Perception

[sophiecentaur]

There are two possible averages we could be discussing: the average over time and the average over distance. No one has specified which. It's a pity the word 'mean' hasn't been used here because 'average' is not very precise and this thread has got to a high level of pickiness (mea culpa as much as anyone).
The average in distance relates to the work done and the average in time relates to momentum change. The two 'averages' won't be the same in any real situation.
Imagine an experiment in which a car, traveling at a given speed, is required to stop, over a given distance.There are any number of possible force / time profiles to achieve that and a constant force with time would not be a constant rate of energy dissipation. It's just playing with numbers.

This just goes on and on and I'm sure we all know the Physics involved. I am just anxious that the frequently asked question: "What is the force of impact?" should be fielded and re-directed early, rather than being encouraged.

 

[AlephZero]

There are two possible averages we could be discussing: the average over time and the average over distance.

Three, not two. Everybody has ignored "average over the physical size of the objects", or alternatively, the fact that it isn't force that breaks things or hurts you, but stress - and sometimes, not even stress, but strain.

To extend Russ's example, dropping a brick so that one corner hits a concrete floor will have a different effect than dropping it from the same height, so that the whole of one face hits the floor.

If you assume the impact is between two rigid bodies, where the impact is "instantaneous", the only thing you can really calculate is the impulse (change in momentum), not the "maximum force."

If you assume the bodies are flexible and the impact takes a finite time, there are plenty of opportunities for different people to pick and choose inconsistent assumptions, and shift the debate from doing physics to scoring debating points.

 

[cjl]

But aren't we starting off with a 60N scenario? That certainly limits the 'Average' force - and it could even be the limit for the Maximum force.
And what is the time interval? Where do you actually say that the interaction of hand and book starts and finishes? What's the time profile of the force? My point is that the quantity Impulse is the relevant one, because it contains most of what's relevant and measurable in a situation like this.
[Edit: You beat me to the term Impulse, Z]

I would tend to think peak force would matter more than impulse as far as how much an impact hurts. Impulse is certainly important in determining the momentum change, but you can have the same impulse with dramatically different results as far as pain is concerned. If you punch a pillow and a concrete wall with the same velocity, the impulse is the same (since your arm went from some velocity to zero in both instances), but punching the concrete wall will hurt much more (and also involve a much higher peak force).

 

[MostlyHarmless]

I think the problem is, the OP doesn't understand what that would actually mean to hit our hand with a 100N book but only feel 60N. The only way this is possible is if at the moment it hit your hand, you were applying a upward force. You can't accelerate a 100N book into your stationary hand (slam it) and only feel a 60N force. The math does not add up.

 

[sophiecentaur]

Exactly. The though experiment and its 'results' are flawed.