It is not often that artists need to deal with physics questions, but here's a good one (more than one actually). I hope someone out there will be in the mood for addressing this. It has to do with stone-carving techniques. If anyone wants to know more context, I'll be glad to fill it in, but here's the problem. A sculptor's punch is a square bar sharpened to a point in such a way that the tapering sides are four triangles. The degree of taper varies from tool to tool, and the angle matters for my purposes. The tool is driven into the stone at an oblique angle with one of the flat faces toward the block. It is hit one or more times to drive it far enough under the surface (a few cm) that a big chip bursts out in whatever direction the stone is thinner. You do this repeatedly to plow a wide furrow across the stone, ideally, one blow, one chip. (Actually, the sides often aren't quite flat, presumably in order get more expansive force deeper in the stone before the rupture starts.) The first thing I want to understand is the equation tells: * How much pressure is applied at the tip. * How much expansive pressure is applied to the sides (and how much of that is outward.) * How these vary with the depth of the penetration and the angle of the taper. Obviously, the pressure on the sides starts at zero when the chisel is on the surface, and increases as it gets deeper until the stone yields. Incidentally, measures of the compressive strength of stone come in two different flavors: units of force(e.g., daN) or units of pressure (kg/cm^2). I'm not clear on how one translates one to the other, because one is vector quantity and the other is sclar, no? (Hey, I already said I'm no physicist.) The reason the answer would be interesting, and the harder question below, have to do with the historical origin of the practice of using the tool in this way, which does not occur when you would expect it to, given the date of the advent of the rest of the standard tool set. (Formerly, punches used to be used at 90 degrees, not obliquely. This produced a cone shaped hole facing the direction the hammer is coming from, and is less efficient (and not good for other reasons), but stresses the tool differently (or so I think.)) My intuition is that the sideways stresses are much less at 90 degrees as follows below, but if anyone can explain this in mathematical terms, I'd be grateful: The chip is up to half-dollar size, and is a shallow truncated cone shape. The tool tip is below the center of the cone, but the truncated part of the cone usually jumps over the tool tip, which is of course the part that was most deeply embedded in the stone. In other words, the area covered by the chip surrounds the tool tip, and the missing chip exposes most of the tool, but the last little bit of the tip remains embedded---maybe a cm deep. (You can see this in the marks left behind.) That much can be observed, but is the following true: Just before the chip blows,there is tremendous pressure on the tool from all sides, but at the exact instant the chip blows out on one side, the pressure on that side drops to zero (correct?) so presumably the tool is bing banged sideways, even as the last cm of the tip is still stuck in solid rock. My ultimate goal is to understand the forces (that I think) are trying to break the tip at this point. It seems like both sheering and bending are occurring at the same time. bending: the embedded tip is preventing the tip of the chisel from moving sideway as pressure hits further up the shaft. Sheering: at least three things are resisting its ability to pivot despite the uneven pressure (the inertia of the chisel, the mass of users hand at gripping the other end, and the friction from hammer's momentum still pressing on the end of the tool) but I don't know how much they count against the abrupt pressure change. So would anyone care to illuminate what forces are in play in this situation, and how they could be calculated?