A cable extends from point C to point E It exerts a 50lb for

A cable extends from point C to point E. It exerts a 50-lb force T on plate C that is directed along the line from C to E. Determine the y-component of T. Enter only the numerical value in units of lb.

Solution

displacement vector along C to E = CE = E - C

= ( 0, 2, 6) - (4, -4sin30, 4cos30 )

= -4i + 4j + 2.54k ft

direction vector along CE = CE / |CE|

= ( -4i + 4j + 2.54k) / sqrt( 4^2 + 4^2 + 2.54^2)

= - 0.645i + 0.645j + 0.41 k

Y-component of T = |T| (0.645) = 0.645 x 50 lb = 32.26 lb