# Pressure on nail and tip of nail hammered into a wooden board

While studying Pressure, I came across such a question:

A nail is driven into a wooden board by using a hammer. The impact of the hammer on the head of the nail produces a thrust of 25 N. If the area of the head is 0.5mm² and of the tip is 0.1mm², find the pressure on the head and on the tip of the nail.

I understand that a force of 25 N is acting perpendicularly on the head of the nail (provided by the hammer). So the pressure on the head would be 5 ⅹ 10⁷ Pa.

My question is: What about the pressure on the tip?

My understanding: The thrust acting on its tip must be provided by the wood.

What will the mag. of this force be? If it is equal to that provided by the hammer on the nail (assuming the force is completely transmitted through the nail to the wood), the nail won't move at all. But that's not the case.

I think the question is asking for you to consider an idealized situation where you can neglect the nail's movement. Otherwise more data should have been provided. Just assume the force is completely transmited through the nail and you're good.

• I guess that's the reason. I just found the solution -- the force on the nail by wood was taken of mag. 25 N Commented Feb 22, 2023 at 16:07
• If the whole force from the hammer transmitted right through the nail, or does the wood contribute friction which reduces the effect? Commented Feb 24, 2023 at 21:36

You've spotted that the assumption of equal force on head and tip can't be quite right. But it's probably not far out... Suppose that the nail's mass is 0.01 kg (10 gram) and its acceleration is 100 m s$$^{-2}$$ (that is 10 $$g$$). The nail would then need a net force of 1 N to act upon it, so if 25 N is applied by the hammer, the force on the nail-tip from the wood is 24 N.

• and the extra 1N would return a moment later as the nail slows down again, probably giving 26N, or maybe 25.5N for twice as long, etc... Commented Feb 22, 2023 at 22:42
$$F_{\rm head} - F_{\rm tip} = m_{\rm nail} a_{\rm nail}$$
$$F_{\rm head} - F_{\rm tip} \approx 0$$
$$F_{\rm head} \approx F_{\rm tip}$$