If the tension in the gantrycrane hoisting cable is T 5 14 k

If the tension in the gantry-crane hoisting cable
is T 5 14 kN, determine the unit vector n in the
direction of T and use n to determine the scalar
components of T. Point B is located at the center of
the container top.

Solution

Co-ordinates of B = (15.5, 20, 3) {as seen from the diagram}

Co-ordinates of A = (5, 12, 20) {as seen from the diagram}

Vector along BA (i.e. along T) = {(15.5 - 5), (20 - 12), (3 - 20)} = (10.5, 8, -17)

Unit vector along BA = (1/21.523)*(10.5, 8, -17) {Magnitude of BA = 21.523}

n = (0.4878, 0.37, - 0.7898)

Finding scalar components of T

= 514* n = (514)* (0.4878, 0.37, - 0.7898) = (Fx, Fy, Fz) = (250.73, 190.18, -405.957) ...........ANS