A screw is nothing but an inclined plane. If you unwound it, it would be a ramp or wedge.
Inclined planes convert a long distance forward into a short distance up (or down). The shallow the ramp, the longer you have to push, but the easier it is to get to the height that is the top of the ramp.
This allows the screw to exert force up and down that is greater than it would if it were straight up and down. You spend more time turning the screw (because the ramp makes the distance longer), but that converts to greater pressure against the material up and down from the ramp.
This effectively makes the screw into a much longer nail. It goes in more slowly and with less effort, but you get the same result. With a screw, you take longer to drive it in, but it is easier. With nails, you need a hammer, and it is easy to find that there isn’t even enough material for the nail to have full effect.
So, the screw exerts more force against the material around it than a straight nail of similar length and diameter, and once there has the friction grip of a much longer nail.
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