In the figure a thin horizontal bar AB of negligible weight

In the figure, a thin horizontal bar AB of negligible weight and length L = 4.0 m is hinged to a vertical wall at A and supported at B by a thin wire BC that makes an angle ? = 41° with the horizontal. A block of weight W = 230 N can be moved anywhere along the bar; its position is defined by the distance x = 2.61 m from the wall to its center of mass. Find (a) the tension in the wire, and the (b) horizontal and (c) vertical components of the force on the bar from the hinge at A.

Solution

a)

Let the tension in the wire = T

Balance the clockwise and counterclockwise torques about the hinge:

230*x = T*sin41*4 => 230*2.61/(4*sin41) = T = 228.772 N

(b)

The horizontal force on the hinge = T*cos41 = 172.49 N

Because the bar is of negligible weight:

c)

230-T*sin41 = 79.9255  N