In: Physics
Determine the magnitude of the resultant force. Determine the coordinate direction angle α of the resultant force. Determine the coordinate direction angle β of the resultant force.Determine the coordinate direction angle γ of the resultant force.
F1 can be written as:
F1 = 90*(4/5) x + 90*(3/5) y
= 72 x + 54 y
F2 can be written as
F2 = 150 cos 60 sin 45 x + 150 cos 60 cos 45 y + 150 sin60 z
= 53 x+ 53 y + 130 z
F3 = 200 z
F= F1 + F2 + F3
= 125 x + 107 y + 330 z
Magnitude of force = cube root (125^3 + 107^3 + 330 ^3)
= 339.5 N
Cos Alpha = x / sqrt (x^2+y^2+z^2)
= 125 / sqrt (125^2 + 107^2 + 330^2)
= 125 / 368.75
Alpha = 70 degree
Cos Beta = y / sqrt (x^2+y^2+z^2)
= 107 / sqrt (125^2 + 107^2 + 330^2)
= 107 / 368.75
Beta = 73 degree
Cos gama = z / sqrt (x^2+y^2+z^2)
= 330 / sqrt (125^2 + 107^2 + 330^2)
= 125 / 368.75
gama = 26.5 degree