9. In the figure below, a thin horizontal bar AB of negligible weight and length

Question

9. In the figure below, a thin horizontal bar AB of negligible weight and length L is pinned to a vertical wall at A and supported at B by a thin wire BC that makes an angle with the horizontal. A weight W can be moved anywhere along the bar; its position is defined by the distance r from the wall of its center of mass. (a) Find the tension in the wire as a function of r (b) Find the horizontal component of the force exerted on the bar by the pin at A as a function of r. (c) Find the vertical component of the force exerted on the bar by the pin at A as a function of r. com

Explanation / Answer

(A) balancing moemnt about the point A,

M = ( x W ) - ( T L sin(theta)) = 0

T = W x / (L sin(theta))

(b) in horizontal, Fnet = Fx - t cos(theta) = 0

Fx = (W x) cot(theta) / L  

(C) in vertical,

Fnet = Fy - W + T sin(theta) = 0

Fy = W - (W x / L )

Fy = ( W / L) (L - x)

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