Power Screw Lead

#547 / Mechanical Engineering Easy

Consider a square thread power screw uses 35 ft∙lb of torque to lift a 5,000 lb load. If the power screw’s overall efficiency is 85% and the thread coefficient of friction is 0.05, what is the lead in ft?

Expand Hint
The power screw’s efficiency is:
$$$\eta=\frac{Fl}{2\pi T}$$$
where $$F$$ is the load, $$l$$ is the lead, and $$T$$ is the torque.
Hint 2
The friction coefficient is not needed to solve the problem. It only exists to cause confusion.
The power screw’s efficiency is:
$$$\eta=\frac{Fl}{2\pi T}$$$
where $$F$$ is the load, $$l$$ is the lead, and $$T$$ is the torque.

Notice how the friction coefficient is not needed to solve the problem. It only exists to cause confusion. Solving for lead:
$$$0.85=\frac{(5,000lb)l}{2\pi (35ft\cdot lb)}$$$
$$$l=\frac{(0.85)2\pi (35ft)}{5,000}=\frac{186.925}{5,000}=0.037\:ft$$$
0.037 ft


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