Find resultant of two forces and find moment of resultant force about point D(0,3,-2)m

Mumbai University > FE > Sem 1 > Engineering Mechanics

Marks : 06

Years : DEC 2015

$F_1=5000 × \hat{AB} = \dfrac {5000 ×((5-0)i+(-2-0)j+(-4+1)k)} {\sqrt{(5-0)^2+ (-2-0)^2+(-4+1)^2}} \\ F_1 = 4055 \bar i- 1622\bar j - 2433.32 \bar k \\ F_2= 8000 × \hat{BC} = \dfrac {8000 ×((3-5)i+(3+2)j+(4+4)k)}{\sqrt{(3-5)^2+ (3+2)^2+(4+4)^2}} \\ F_2= -1659.12 \bar i + 4141.8 \bar j + 6636.5 \bar k $

Resultant,

$R=F_1+F_2=2395.88 i ̅+ 2525.8 j ̅+ 4193.18 k ̅ (N) $

Moment of R about D,

As $F_1$ and $F_2$ are concurrent at B, R is also passing through B

$M_D^R =\begin {vmatrix} i&j&k\\ 5&-5&-2\\ 2395.88&2525.8&4193.18\\ \end{vmatrix} \\ M_D^R=15964.7 i ̅- 25808.7 j ̅+ 24610 k ̅ (Nm) $