Three forces act on the pole, as shown in the figure below. Find: (1) FRijk, the
ID: 1844269 • Letter: T
Question
Three forces act on the pole, as shown in the figure below. Find: (1) FRijk, the resultant force vector passing through the origin of the axes (point O) in {i,j,k} format (2) FRmag, the magnitude of resultant force FR (3) MRijk, the resultant moment vector passing through the origin of the axes (point O) in {ij,k} format (4) MRmag, the absolute magnitude of resultant moment MR Example of {i,j,k} form: 22.4i-1 1 .3j-70.3k A (3,-4,0) B (4,3,0) C (-4,3,0) Answer all numeric solutions with five significant figures. Fi =72kN D (0,0,H) F2=67kN F3=75kN H = 10mExplanation / Answer
F1 in vector form is
unit vector along F1
=(3i-4j-Hk)/sqrt(9+16+H2)
F1=F1(3i-4j-Hk)/sqrt(25+H2)
F2 in vector form is
unit vector along F2
=(4i+3j-Hk)/sqrt(16+9+H2)
F2=F2(4i+3j-Hk)/sqrt(25+H2)
F3 in vector form is
unit vector along F3
=(-4i+3j-Hk)/sqrt(16+9+H2)
F3=F3(-4i+3j-Hk)/sqrt(25+H2)
1) Resultant force vector
FRijk = F1+F2+F3
=72(3i-4j-10k)/sqrt(25+100)+67(4i+3j-10k)/sqrt(25+100)+75(-4i+3j-10k)/sqrt(25+100)
FRijk =(184i+138j-2140k)/sqrt125
2) FRmag=sqrt(1842+1382+21402)/sqrt125=192.5kN
3) MRijk=FRijk *-10k
=(184i+138j-2140k)/sqrt125*-10k
MRijk=(1840j-1380k)/sqrt125
4) MRmag=sqrt(18402+13802)/sqrt125
=205.7kNm