Question

# Q. Calculate the resultant force, when four forces of 50 N due east, 40 N due north, 20 N due west and 60 N due south, are acted upon a body: l) 20$\sqrt{2}$ N, 60$°$, south-west 2) 20$\sqrt{2}$ N 45$°$, south-west 3) 20$\sqrt{2}$ N, 45$°$ north-east 4) 20$\sqrt{2}$ N, 45$°$ south-east

Open in App
Solution

## Dear student $Netforcealongeast={F}_{X}=\left(50-20\right)=30N\phantom{\rule{0ex}{0ex}}Netforcealongsouth{F}_{Y}=\left(60-40\right)=20N\phantom{\rule{0ex}{0ex}}Resul\mathrm{tan}tforce\phantom{\rule{0ex}{0ex}}F=\sqrt{{{F}^{2}}_{X}+{{F}^{2}}_{Y}}=\sqrt{{30}^{2}+{20}^{2}}=\sqrt{900+400}=10\sqrt{13}N\phantom{\rule{0ex}{0ex}}Anglemadebytheresul\mathrm{tan}twiththeeastbe\theta so\phantom{\rule{0ex}{0ex}}\mathrm{tan}\theta =\frac{{F}_{Y}}{{F}_{X}}=\frac{20}{30}=\frac{2}{3}\phantom{\rule{0ex}{0ex}}\theta ={\mathrm{tan}}^{-1}\left(\frac{2}{3}\right)=33.69°\phantom{\rule{0ex}{0ex}}Regards\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

Suggest Corrections
0
Related Videos
Basics
PHYSICS
Watch in App
Explore more