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Tension by an object suspended on two ropes.

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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, ¥è1 and ¥è2 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*cos¥è1 = t2*cos¥è2 ¡æ t1*cos¥è1 - t2*cos¥è2 = 0

The summation of forces for verticall direction :
t1*sin¥è1 + t2*sin¥è2 = P

The above two equations can be solved as follows:

t1*cos¥è1*sin¥è2 - t2*cos¥è2*sin¥è2 = 0
t1*sin¥è1*cos¥è2 + t2*sin¥è2*cos¥è2 = P*cos¥è2
t1*(cos¥è1*sin¥è2 + sin¥è1*cos¥è2) = P*cos¥è2
t1 = P*cos¥è2 / (cos¥è1*sin¥è2 + sin¥è1*cos¥è2)

t1*cos¥è1*sin¥è1 - t2*cos¥è2*sin¥è1 = 0
t1*sin¥è1*cos¥è1 + t2*sin¥è2*cos¥è1 = P*cos¥è1
t2*(cos¥è2*sin¥è1 + sin¥è2*cos¥è1) = P*cos¥è1
t2 = P*cos¥è1 / (cos¥è2*sin¥è1 + sin¥è2*cos¥è1)
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¢¹ Input data : P (N), ¥è1 (deg), ¥è2 (deg)


¢º t1


¢º 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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