A couple acts on each of the handles

A couple acts on each of the handles of the minidual valve. Determine the magnitude and coordinate direction angles of the resultant couple moment.

A couple acts on each of the handles

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


Show me the final answer↓

Let us break the coupling moments being applied into components.







The resultant couple moment is then these two components added together.



We can now determine the magnitude of this coupling moment:

magnitude of M_{c}\,=\,\sqrt{(-16.625)^2+(-7.58)^2+(0)^2}

magnitude of M_{c}=18.27\,\text{N}\cdot\text{m}


The coordinate direction angles are:





Final Answer:

magnitude of M_{c}=18.27\,\text{N}\cdot\text{m}





This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 4, question 4-88.

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