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