Force F with magnitude indicated acts at point O Determine t

Force

F

with magnitude indicated acts at point O.

Determine the magnitudes of the components F_aa and F_bb in pounds along directions a–a and b–b so that F = F_aa + F_bb.

F_aa = ?

F_bb = ?

lb

Solution

Here , for the force vector along these aa and bb

as F = Faa + Fbb

in such case ,

Faa = F * cos(62)

Faa = 490 * cos(62) = 230 lb

the force Faa is 230 lb

for the force Fbb

F^2 = Faa^2 + Fbb^2 + 2 * Faa * Fbb * cos(74 degree)

490^2 = 230^2 + Fbb^2 + 2 * Fbb * 230 * cos(74 degree)

solving for Fbb

Fbb = 373.9 lb

the force Faa is 230 lb and force Fbb is 373.9 lb