Equations to do with the z distance of a screw helix.

[BlackWyvern]

Homework Statement

You have a screw with the distance between the threads being equal to 0.1mm. It takes a torque of 10Nm to turn the screw about 2pi radians. What would the torque be to turn a screw with the z distance equal to 0.2mm. Explain your reasoning.

Homework Equations

Not sure.

The Attempt at a Solution

I'm not sure how to do this at all. I guess we can assume that the resistive force we have to overcome is proportional to the length of metal we are driving into the material. So by that logic, and a simplification:

If we took the z index as the height of a rectangle, and the circumference of the screw as the width, the diagonal distance would be the distance of metal that goes through the wood. So we just find the ratio of the second diagonal, to the first, and multiply the Torque by this? Or is there something I'm missing, this seems too easy.

 

[Kurdt]

If the distance between the threads is measured as a z distance then one would expect that for each full turn the screw would move a distance of 0.1mm. However I am a bit perplexed by the question since that is not made clearand also does it mean the screw descends 0.2mm or the threads increase in separation to 0.2mm?

 

[BlackWyvern]

The screw would move down 0.1mm. But, the thread on the screw would move though more than that. This question is about ratios, and then applying them. But I just don't know much about screws and the forces on them. I know that they are a lever, but that's about it.