1) For the figure shown: a) Determine angle between cables AB and AC. b) Determi

Question

1) For the figure shown:

a) Determine angle between cables AB and AC.

b) Determine the projection of force FAB on the strut OA.

Express result as a Cartesian vector.

c) Determine the magnitude of the vector perpendicular

to the projection of FAC on the strut OA.

Express this result as a Cartesian vector.

For the figure shown: Determine angle between cables AB and AC. Determine the projection of force FAB on the strut OA. Express result as a Cartesian vector. Determine the magnitude of the vector perpendicular to the projection of FAC on the strut OA. Express this result as a Cartesian vector.

Explanation / Answer

letO be origin,coordinates of A=(0,6,2) and coordinates of B and C are (0,-3,4) ,(5/2,0,5/2*(3)^0.5)

then slope of AB=(0-0,6+3,2+4)=(0,9,6);

then slope of AC=(-5/2,6,-2.33)

angle between AB andAC =>cos(theta) =(0*-5/2+9*6+6*-2.33)/(84.48) =0.473=>angle=61.7degrees

Fab on strut oA=70*(0+9*6+6*2)/68.41 =70*66/68.41 =67.533N

Fac on strut OA=60*(0+36-4.33)/49.39 = 38.46N

magnitude of vector perpendicular to OA is (Fac^2-38.46^2)^0.5 = 46.06N

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