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Tension force by an object hanging on two cords

ÀÛ¼ºÀÚ Uploader : metalheart ÀÛ¼ºÀÏ Upload Date: 2018-08-15º¯°æÀÏ Update Date: 2018-08-16Á¶È¸¼ö View : 511

Type1 Type2
Tension force by an object hanging on two cords, as shown in figure, can be calculated as below.

Letting the tension forces acting on the cords as t1 and t2, angle of each cord with respect to the horizon as ¥è1 and ¥è2,

Resultant force in the horizontal direction :
t1*cos¥è1 = t2*cos¥è2
            t1*cos¥è1 - t2*cos¥è2 = 0
Resultant force in the vertical direction : t1*sin¥è1 + t2*sin¥è2 = P

Combining these two equations, we get:
 
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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¡à t1


¡à t2


P, t1 and t2 are forces and have an identical unit.
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