As seen in the figure, a thin horizontal bar AB of negligible weight and length

Question

As seen in the figure, a thin horizontal bar AB of negligible weight and length L = 13.0 m is hinged to a vertical wall at A and supported at B by a thin wire BC that makes an angle ? = 40° with the horizontal. A block of weight W = 290 N can be moved anywhere along the bar; its position is defined by the distance x from the wall to its center of mass. As a function of x, find the tension in the wire, and the horizontal and vertical components of the force exerted on the bar by the pin at A.

a ) What are the values for x = 6.50 m? Tension?

b) Horizontal component by pin?

c) Vertical component by pin?

Explanation / Answer

a)

Let the tension in the wire = T
Balance the clockwise and counterclockwise torques about the hinge:
290*x = T*sin40*13 => 290*6.50/(13*sin40) = T = 225.57N
(b)

The horizontal force on the hinge = T*cos40 = 172.8N
Because the bar is of negligible weight:
c)

290-T*sin40 = 41.4N

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