Please answer the following question
A traffic light of weight W hangs from two light cables; one on each side of the light.
Each cable hangs at a 45 degree angle from the horizontal. What is the tension in each cable?
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The traffic light of mass X hangs down supported by two light cables which are at an angle of 45 degree with the horizontal. Now the force due to the mass X is given as the weight W.
Also the angles that the cables make with the horizontal are 45 degrees. Let the tension in the cables be T. Now T can be divided into the horizontal and vertical components which would be T cos 45 and T sin 45 resp.
For equilibrium, the weight of the light has to be balanced by the sum of the vertical components of the cables. Therefore W = 2*T sin 45.
=> W = 2*T*(1/sqrt 2)
=> W = T* sqrt 2
=> T = W / sqrt 2
Therefore the tension in each of the cables in W/ sqrt 2
Assuming that there is no frictional force between the cables supporting the traffic light and the other component of the total system supporting the the traffic light, the sum of total tension in the cables will be exactly equal to the force exerted by the weight of the traffic light. Further, the division of this total tension between the two cables will depend on the the extent to which the two cables are stretched when fitted. It is possible to fit the cables in such a way that the tension in one cable is more than the other. In this situation, one of the two cables will elongate or stretch more than the other under the effect of the higher tension. However in properly fitted system care would be taken to keep the tension in both the cables equal.
Please not that the angels of the cable, which is flexible, has no effect on either the total tension in the two cables, or the distribution of the tension between the two cables.
The method of calculating tension in the answer posted above will be applicable for calculating tension created in members of a rigid system supporting the weight.
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