Determine the magnitude and direction angles of F2 so that t

Determine the magnitude and direction angles of F2, so that the resultant of the two forces acts upward along the z axis of the pole and has a magnitude of 275 N.

Solution

Resultant points in z direction so x and y components of F2 must be equal in magnitude to x and y components of F1 respectively but in opposite direction

SO, x component of F2,X =-200 cos(45)

y component of F2,Y=-200 cos(60)

and resultant has magnitude 275 . Let z component be Z

So,

X^2+Y^2+Z^2=275^2

Z~+-213.6 N

Now magnitude of F1 is 200 cos(60)=100 N pointing upward along z axis. So Z ie z component of F2 must also point upward.

ie

Z=213.6 N

Let direction angles be:A,B,C . A is w.r.t. x axis , B w.r.t. y axis, C w.r.t. z axis

direction angles are given by

cos(A)=X/275

cos(B)=Y/275

cos(C)=Z/275