Determine the magnitude of the vertical force


Determine the magnitude of the vertical force F acting on the handle of the wrench so that this force produces a component of moment along the AB axis (x axis) of the pipe assembly of (M_A)_x=\left\{-5i\right\} N•m. Both the pipe assembly ABC and the wrench lie in the x-y plane. Suggestion: Use a scalar analysis.

Determine the magnitude of the vertical force

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

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As with the previous question, we will use scalar analysis. Let us calculate the perpendicular distance from the x-axis to force F as follows:

Determine the magnitude of the vertical force

Diagram not to scale

The distance d can be calculated using geometry.

d=0.15\sin45^0+0.2\sin45^0

d=0.2475 m

 

Let us now write an equation for the moment along the x-axis.

M_x=\sum M_x

M_x=(F)(d)

Substitute the values we know:

-5=(-F)(0.2475)

(Force F is negative because it is applied downwards (negative z-axis))

F=20.2 N

 

Final Answer:

F=20.2 N

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 4, question 4-61.

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