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#