Answered: Derive the following formulas relating…

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter7: Dry Friction

Section: Chapter Questions

Problem 7.75P: The single-plate clutch transmits the torque C from the input shaft on the left to the output shaft...

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Question

Derive the following formulas relating the load W and the force P exerted on the handle of the jack discussed in Sec. 8.2B. (a) P= (Wr/a) tan (0+φs) to raise the load; (b) P= (Wr/a) tan (φs-0) to lower the load if the screw is self-locking; (c) P= (Wr/a) tan (0-φs) to hold the load if the screw is not self-locking.

Expert Solution

Step 1

Let the load acting on the screw jack be 'W'

Let the normal reaction be 'N' & the frictional force be $μN$

Let the effort required is 'F'

For the equilibrium condition of the screw jack, we can apply the static equilibrium equation as

$Consider Case I : Lifting of the load \sum F_{x} = 0 F = μ N \cos α + N \sin α (1) Also \sum F_{y} = 0 W = N \cos α - μN \sin α (2) Divide equation (1) & (2) we get F = \frac{W (μ \cos α + \sin α)}{\cos α - μ \sin α} Again dividing above equation by \cos α we get & substituting μ = tanϕ F = \frac{W (tanϕ + \tan α)}{1 - μ \tan α} = W \tan (ϕ + α) Now let the force P is applied to the handle and' a' be the length of the handle Hence Torque due to force' F' = Torque due to force' P' applied at the handle F \times r = P \times a P = \frac{W \tan (ϕ + α) r}{a}$

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