건축 Architecture

Tension by an object suspended on two ropes.

작성자 Uploader : prove 작성일 Upload Date: 2017-11-26변경일 Update Date: 2017-11-26조회수 View : 253

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As shown in the figure, the tension due to the object hanging on two ropes can be calculated as follows.

Let t1, t2 be the tension applied to the two ropes, θ1 and θ2 be the angles (degree) of the ropes to the horizontal plane, and P be the force by the object.

The summation of forces for horizontal direction :
t1*cosθ1 = t2*cosθ2 → t1*cosθ1 - t2*cosθ2 = 0

The summation of forces for verticall direction :
t1*sinθ1 + t2*sinθ2 = P

The above two equations can be solved as follows:

t1*cosθ1*sinθ2 - t2*cosθ2*sinθ2 = 0
t1*sinθ1*cosθ2 + t2*sinθ2*cosθ2 = P*cosθ2
t1*(cosθ1*sinθ2 + sinθ1*cosθ2) = P*cosθ2
t1 = P*cosθ2 / (cosθ1*sinθ2 + sinθ1*cosθ2)

t1*cosθ1*sinθ1 - t2*cosθ2*sinθ1 = 0
t1*sinθ1*cosθ1 + t2*sinθ2*cosθ1 = P*cosθ1
t2*(cosθ2*sinθ1 + sinθ2*cosθ1) = P*cosθ1
t2 = P*cosθ1 / (cosθ2*sinθ1 + sinθ2*cosθ1)
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▷ Input data : P (N), θ1 (deg), θ2 (deg)

▶ t1

▶ t2

If you use kN for the unit of force, then the unit of the results (t1 and t2) are kN.

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