Determine the magnitude of the resultant force. Determine the coordinate direction angle α of the resultant force.

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.

Solutions

Expert Solution

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

genius_generous answered 1 year ago

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