Pitch calculation is always doubled

[wizdumb]

Homework Statement

A 945N resistance force is overcome with a 13.5N effort using a screwdriver whose handle is 24mm in diameter. What is the pitch of the screw?

Homework Equations

Given:
r = 24mm
FE = 13.5N
FR = 945N
Pitch = ?

r is radius
FE is force effort
FR is resistance force
Pitch is unknown spacing of screw

Basic equation:
FR * pitch = FE * 2pi * r

The Attempt at a Solution

Working equation
Pitch = (FE * 2pi * r) / FR

Substitution
Pitch = (13.5N * 2pi * 24mm) / 945N

Pitch = 2.154mm yet the answer is said to be 1.08mm which is exactly half of my initial answer. Is there something I am missing?

 

[anathema]

Hello, I see that you have correctly set up the equation and substituted the given values. However, the answer you have calculated is for the distance between threads, not the pitch. The pitch is the distance between the centers of two adjacent threads on the screw.

To find the pitch, you need to divide the distance between threads by the number of threads per unit length. In this case, the distance between threads is the circumference of the screwdriver handle, which is 2πr. The number of threads per unit length is given by the formula FR/FE.

Therefore, the pitch can be calculated as follows:

Pitch = (2πr) / (FR/FE)

Substituting the values, we get:

Pitch = (2π * 24mm) / (945N/13.5N)

Pitch = 1.08mm

I hope this helps clarify the concept of pitch for you. Let me know if you have any other questions.