Question #626cb

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Answer 1 · 2018-01-23T11:50:25

$"the resultant force is 19.08 Newtons and its direction makes 33"$ $"degree angle with positive x-axis."$

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$"resultant force="vec (OC)$
$vec(OC)=vec(OD)+vec(DC)$

$"resultant force="vec F$
$vec F=vec u+ vec l+vec k$
$u=10N$
$l=12*cos(60)=12*1/2=6 N$

$vec(OD)=u+l=10+6=16N$

$k=12*sin 60=12*sqrt 3/2=6 sqrt 3N$
$vec(DC)=k=6 sqrt 3 N$
$F=sqrt((OD)^2+(DC)^2)$

$F=sqrt(16^2+(6sqrt 3)^2)$

$F=sqrt(256+108)$

$F=sqrt(364)$

$F=19.08 N$

$tan beta=(DC)/(OD)$

$tan beta=(6sqrt 3)/16=0.64951905$

$beta=33 deg$