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Pressure is a scalar quantity, and I think I understand this in the context of pressures exerted by gases and liquids. However, I struggle to understand this in the context of solids. If I use a hammer to hit a nail into a wall, how is the pressure acting evenly in all directions? Intuitively, it seems like the pressure is directed in a specific direction, unlike what happens in a gas that explodes or an object submerged in water. Wouldn't there be a difference in the pressure experienced by the atoms in the wall if I hit them with the nail at a different angle, and surely there would be a difference in pressure for different atoms in the wall, as well as the air molecules beside the wall where the nail hits. Am I getting this confused with force or stress, and if so, what even is pressure (other than force divided by area)?

All explanations are welcome, but I would prefer intuitive explanations where possible that could be understood by a high school student, unless more complicated math is needed to help explain what is going on,

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  • $\begingroup$ You seem to be assuming that pressure does act in all directions in or on a solid. Do you have a reference that claims this is true? $\endgroup$
    – BowlOfRed
    Commented Dec 29, 2021 at 20:34
  • $\begingroup$ It is my understanding that pressure is a scalar because it acts uniformly in all directions. Is this not the case for solids? If so, would that suggest that there is a directional component to pressure? $\endgroup$
    – Juan
    Commented Dec 29, 2021 at 21:40
  • $\begingroup$ Pressure is a scalar because it is a factor between (directional) force and (directional) area. physics.stackexchange.com/questions/18255/…. $\endgroup$
    – BowlOfRed
    Commented Dec 29, 2021 at 22:53
  • $\begingroup$ Thanks for that. I can see in a purely mathematical sense how pressure can be a scalar (since force is a vector and area can be too), but this still does not make sense to me intuitively. I am struggling to visualize how pressure does not have a directional element in the hammer and nail situation I described (or even something like putting a glass on a table). I can understand the force as what directs the nail towards the wall, and even the stress as the resistance to deformation (stress is not a scalar), but what exactly is pressure in this context? I can't see how it's not directional. $\endgroup$
    – Juan
    Commented Dec 29, 2021 at 23:36
  • $\begingroup$ This link suggests that the types of situations I am thinking of (solid-solid interactions mainly) are more related to stress than to pressure. spark.iop.org/what-about-solids-pressure-and-stress This explanation makes more sense to me, but does that mean that pressure is not involved in solid-solid interactions at all? When high school science and physics books ask students to calculate the pressure from a book on a desk, are they wrong? Should they be asking to calculate stress? Is pressure not relevant here at all, or does it mean something else in these contexts? $\endgroup$
    – Juan
    Commented Dec 29, 2021 at 23:45

1 Answer 1

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In the case of solids, when you apply a force on the surface you have what is called a traction vector. This vector is defined locally as the force density over the surface.

Inside the solid you have stress. This is a quantity that is of a tensor nature. The traction on the surface is the projection of the tensor in the direction of the unit normal. That means that you can have both, shear and normal forces on surfaces of a solid.

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