What is the ideal mechanical advantage (IMA) of a screw with a pitch of 4 mm and a circumference of 50 mm?

To determine the ideal mechanical advantage (IMA) of a screw, you can use the formula:

[ IMA = \frac{\text{Circumference}}{\text{Pitch}} ]

In this scenario, the screw has a pitch of 4 mm and a circumference of 50 mm. Plugging these values into the formula gives:

[ IMA = \frac{50 \text{ mm}}{4 \text{ mm}} = 12.5 ]

This result indicates that for every rotation of the screw, the load moves vertically by the pitch distance while the force applied is distributed over the entire circumference, leading to an IMA of 12.5. The higher the IMA indicates an efficient mechanical advantage, which suggests that less input force is needed for the same output effort compared to a simple machine with a lower IMA.

This is why the answer of 12.5 reflects the ideal mechanical advantage for the screw with the values provided. The calculations clearly show the relationships between the circumference and pitch, confirming the choice as the most appropriate interpretation of the problem based on the mechanical principles at play.