## Penetration of certain objects

Hi, I'm new to physics forums and I was wondering how to calculate the force required to penetrate objects of varying densities, for example an arrow shot at a plank of wood with a density of approximately 1.2 x 10^3 kg/m^3. Lets assume the arrowhead and the plank are perpendicular at the site of impact. You can make reasonable assumptions. Also, if possible how would the calculation change if I wanted to penetrate, say, 10 cm of this wood?

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 Unfortunately, it's more complicated than that. It has to do with more than just density. You have to take into consideration the actual intermolecular forces of the substance you're shooting through. For example, if it were just based on density, then it would be easier to shoot an arrow through a plank of oak (.85 x 10^3 kg/m^3) than it would be to shoot through an equal volume of water (1.0 x 10^3 kg/m^3), which I'm sure you know from experience not to be the case. In fact, if density alone determined resistance to penetration, then anything that floats in water would be easier to shoot through than the water itself! All things considered, there isn't a simple formula for this. So, sorry to shoot an arrow through your bubble, but welcome to PF!
 What you need is to look at something about the lines of the strength of the material, in your case wood. What you want to look for would be the amount of pressure that a certain type of wood could withstand to a certain depth. I think that is shear stress.....maybe.....