# How do I solve screw-jack problems?

For example, questions like the following one-

A square threaded screw of mean diameter 0.04 m and pitch 0.0025 m is used to lift a mass of 1 ton by a horizontal force applied at the circumference of the screw. What is the magnitude of the force if coefficient of friction is 0.06?

Do not solve the problem but instead explain it to me how I should approach such problems.

• What confusion/misunderstanding of physics concepts prevent you from doing the problem yourself? What do you not understand about friction, pitch, etc.? Or maybe you don't understand how the applied force effects the system? These would be better questions to ask here. Oct 12, 2020 at 11:11

A jack is a block sliding on a slope problem. You use a free body diagram to balance the forces and make sure to include friction in the direction of opposing motion.

If you unwrap a thread groove and the corresponding tooth on the nut you can find the balance of forces, which axially balances the applied force/weight $$F$$, and tangentially balances the torque input $$\tau$$. The angle of the wedge is called the lead angle $$\theta$$ with the relationship

$$\text{(pitch)} =R\, \tan \theta$$

The balance of forces is (for example)

\begin{aligned} F &= N \cos \theta - \mu N \sin \theta \\ \tfrac{\tau}{R} & = N \sin \theta + \mu N \cos \theta \end{aligned}

to be solved for the contact normal force $$N$$ and whatever is you are looking to solve for in each problem between $$F$$ or $$\tau$$.

• The answer is not easily readable due to the fact that it contains many technical terms such as "tooth" and "nut", if you had a short note on what the terms meant then I think that the readability would improve a lot. Edit: Here is a picture I Found on the internet for future readers: wonkeedonkeetools.co.uk/wp-content/uploads/2019/10/… Oct 12, 2020 at 13:16
• @Buraian - I added some annotations for clarity. But I think it does address the question of how to solve these problems. Oct 12, 2020 at 22:50

You can solve this type of problem by applying two principles:

1. Work energy principle : Work done by external force = gain in energy of object + energy “lost” due to friction. In this case the gain in energy of the object being lifted is all potential energy since we can assume that the initial and final kinetic energies are both zero.
2. A screw jack is simply an inclined plane wrapped around a cylinder.