Question

A force of 100 N hangs in the center of a cable between two anchor points that are the same height off the ground and 30 m apart horizontally. The object creates a sag of 2 m in the cable. Find the force exerted by each end of the cable on its anchor point.

Answer 1

378.3N

Step-by-step explanation:

According to Newton's 3rd law, the force exerting on each anchor points would equal to the tension force T on each cable, which is created to support the 100N in the center

As the system remain balanced, then vertically the tension force would support the 100N

`2T_v = 100`

`2Tcos\theta = 100`

where Θ is the angle between the cable and the vertical line intersecting the force F. As it's 15m halfway between the 2 anchor

`tan\theta = 15/2 = 7.5`

`\theta = tan^(-1)7.5 = 1.44 rad`

`cos\theta = cos(1.44) = 0.132`

therefore 2T0.132 = 100

T = 100/(2*0.132) = 378.3 N