# A large rock falls on your toe. Which concept is most important in determining how much it hurts?

A) The mass of the rock B) The weight of the rock C) Both the mass and the weight are important. D) Either the mass or the weight, as they are related by a single multiplicative constant, g.

Similarly, if the large rock merely sits on your toe, which concept is most important in determining how much it hurts?

For a falling rock, to me it seems that mass would be most important as the pain level would be proportional to the change in momentum, or the impulse, on your foot.

For a stagnant rock, it seems either weight or mass would be the same.

Am I correct?

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Is this a test question? This looks like a "read my mind" pedagogy question. –  Ron Maimon Sep 5 '12 at 1:23
Hi Bob, and welcome to Physics Stack Exchange! Generally we discourage questions that just ask for someone to confirm something you've already figured out. When you have a specific concept that you're not sure about, that's the point at which it's appropriate to ask a question here. –  David Z Sep 5 '12 at 4:26
Pain is a biological attribute and inappropriate for a physics question, since it depends on biophysical constants. –  anna v Sep 5 '12 at 4:41
@DavidZaslavsky, I would disagree here, because there is a physical aspect of pain. Neurons have to stimulated and I think the question of what stimulates the neurons is within this community. –  ja72 Sep 5 '12 at 15:53
Maybe $Pain \propto F_{impact}$ as noted in the answers –  raindrop Nov 21 '12 at 16:02

The two situations are actually the same courtesy of Einstein's principle of equivalence.

Take the static rock on your toe first: what you feel is the force exerted on your toe by the rock, and of course in a gravitational field this is equal to the mass multiplied by the gravitational acceleration. The force is what we call weight.

Now consider the rock hitting your foot: just as above what you feel is the force exerted on your toe by the rock, and this is also a product of the mass of the rock and it's acceleration. The only difference is that for the static rock the acceleration is provided by gravity and in this case the acceleration (i.e. decelleration) is provided by the squishing of your toe. We wouldn't generally call this force weight, but actually it is physically the same as the weight in a gravitational field, as Einstein pointed out.

So I suppose you'd say the it's the weight that's important in both cases, provided you're willing to be a bit flexible about the meaning of weight.

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Neither. The most important factor is the acceleration of gravity.

Pain as perceived by sensory neurons is triggered by pressure or force near the free ends of the nerves. For the pain of a falling rock the important quantity is impact force. To calculate this you need the kinetic energy of the object before the impact and a measure of the total deflection before it bounces of (or mangles your foot).

Work done by the foot resisting the falling rock $W \approx \frac{1}{2} F_{peak} \cdot d = F_{average} \cdot d$ where $d$ is the deflection amount.

This work comes from the kinetic energy of the rock $K=m \cdot v = m \sqrt{2 g h}$ where $h$ is the drop height, $m$ the mass of the object and $g$ gravity.

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