The cable AB prevents bar OA from rotating clockwise about t

The cable AB prevents bar OA from rotating clockwise about the pivot O. If the cable tension is 780 N, determine the n- and t-components of this force acting on point A of the bar.

Solution

using cosine rule to find AB,

AB^2 = 1.6^2 + 1.3^2 - 2(1.6)(1.3)(cos(180-54))

AB = 2.59 m

using sine rule to find the angle,

AB / sin(180-54) = 1.3/ sin@

sin@ = 1.3 sin126 / 2.59 = 0.406

@ = 23.96 deg

Tn = 780sin23.86 = 316.76 N

Tt = Tcos23.96 = 780cos23.96 = 712.80 N