A system consists of forces F1 acting at 2 3 1 and F2 acting

A system consists of forces F_1 acting at (2, 3, 1) and F_2 acting at (5, 4, 2) and couples M_1 acting at (3, 3, 4) and M_2 acting at (4, 3, 2), where F_1 = 5i+3j+2k (N) F_2= 4i-2j+3k (N) M_1 = 12i + 15j - 18k (N-m) M_2= 24i - 12j + 20k (N-m) Represent the system by a wrench and find where its line of action intersects with the x-z plane.

Solution

solution:

1)here forces F1 is acting at pointA(2,3,1) and hence it moment about origin is vector product

M1\'=rao\'*F1\'=3i+j-9k

F1=5i+3j+2k

2)here second force F2 acting at point B(5,4,2)also produce moment about origin as

M2\'=rbo\'*F2\'=16i-7j-18 k

F2\'=4i-2j+3k

3) moment of couple is same about any point due M1 and m2 are and about origin is given by

M1=12i+15j-18k

M2=24i-12j+20k

4) it is concurrent system withresultant force

Fr=F1+F2=9i+j+5k

5)resultant couple around origin

Mr=M1\'+M2\'+M1+M2=55i-3j-25k

6) wrench is moment along rsultant force

unit vrctor along Fr\' is

Fr^=.87i+.096j+.4835k

hence moment along Fr\' is

Mr\'=Mr\'.Fr^=47.85-.2901-12.087=35.4724 Nm

6) intercept is given as

Mr\'=Fr\'.d\'

d\'=6.72i+60.48j+12.09k

hence xz intercept are

dx=d\'*i

dz=d\'*k

c(6.72,0,0),D(0,0,12.09)