Resolve the 250 N force into components


Resolve the 250 N force into components acting along the u and v axes and determine the magnitudes of these components.

Resolve the 250 N force into components

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

Solution:

Show me the final answer↓

We will first draw the components along the u and v axes like so:

Resolve the 250 N force into components

The angles were found using  alternate interior angles theorem, corresponding angles theorem and consecutive angles theorem.

 

We can now draw the components tail to tail as follows:

Resolve the 250 N force into components

We can now use sine law to figure out the forces.

\dfrac{250}{\sin120^0}\,=\,\dfrac{F_u}{\sin40^0}

(solve for F_u)

F_u\,=\,185.5 N

 

\dfrac{250}{\sin120^0}\,=\,\dfrac{F_v}{\sin20^0}

(solve for F_v)

F_v\,=\,98.7 N

 

Final Answers:

F_u\,=\,185.5 N

F_v\,=\,98.7 N

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-143.

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