Understanding the Impact of Static and Sudden Forces on Pain Perception

[sophiecentaur]

The average force is just a number. It has absolutely no relevance to anything. The above Maths looks right (apart from the Delta sign which doest come out on my screen) but what has that got to do with the OP, or anything? I'm not sure what you are trying to justify or prove, any more. I am merely anxious that the OP would not get the impression that his original ideas were a suitable way into 'collisions'. Could you even suggest an occasion when the average force could be of use?

 

[arildno]

Being the most eaily calculable force within an extremely complicated collision scenario makes it conceptually useful for establishing a lower bound for the magnitudes of forces involved.
Why should it be less useful than the value of the non-obtainable value of the peak force, for example?

 

[sophiecentaur]

I have similar reservations about the peak force, too. But at least the peak force gives an idea of the strength of structure needed. I'm not sure that "it will need to be at least as strong as xyz" would be a sound way to start an engineering design. I guess it would be useful in deciding whether to reject a design out of hand, though.

Have you not read the plethora of posts which ask "What was the force of collision when my car was hit by my neighbour's Ferrari?" This was a similar question and it doesn't come from any relatively well informed direction. It comes from the direction of intuition, which is why I have been banging on in this way.

 

[Dale]

I keep a book that his weight is 10kg(100 Newton,lets say). My hand will feel a force of 100 Newtons.
Now let's say that the book is up of a desk,and with some force(lets say 60 Newtons) I hit that.

Why I will feel more pain the second time,while I feel less Newtons?
It is about the time?

If you do not feel pain at 100 N then you won't feel pain at 60 N (assuming same contact area).

 

[russ_watters]

But does 'average force' matter? Is it of interest to anyone? It doesn't indicate the 'pain' or damage involved. It doesn't even represent anything about the Work done or energy input.

Yes, average force times distance traveled in decelerating during the collision equals work or energy absorbed.

But the OP just says 60N. Given the level of understanding that the OP has, I'd expect that to be maximum force. And it is what it is; it is less than 100N, so the feeling of the impact is less than the feeling of lifting the book (neither would involve pain, as Dale said). That said, I'm sure the OP is thinking of hitting the book hard enough to feel pain, which would be much more than a 60N force. There is probably a conceptual error there.

My problem with even considering any 'average' force is that the same effect can be achieved with a single, short burst of high force (with a hammer), which could be many times the weight of the object or a long acting small force (using a bungee) which would involve a very small force - much less than the weight. Exactly the same 'average' force in each case, but very different maximum forces / damage / pain.

That doesn't compute. Obviously, large force is larger than a small force; the averages are not the same. The energies or impulses might be, but impulse and energy aren't force (I know you know that).

For example, if you drop a brick from a meter onto a sidewalk, the average force it applies during the collision is vastly larger than the average force applied if you drop it on a thick carpet even though the energy absorbed is the same.

 

[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.