# Catenary - The Catenary and Parabolic Cables The Catenary y...

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1 The Catenary and Parabolic Cables The Catenary Assume that one has a cable which hangs under its own weight with only tangential forces acting along the length of the cable. The cable is assumed to have uniform density, w 0 , along its length. Arrange the coordinate system so that the y - axis passes through the lowest point of the cable. Consider a free-body diagram of that portion of the cable above the interval [0, x ] . Suppose that the length of this portion of the cable is s . Then its weight is w 0 s . In the free-body diagram this is a force acting downward on that portion of the cable. There is also a tangential force T 0 acting horizontally to the left in the free-body diagram. This force is due to the cable to the left of the figure. Similarly, there is a force T acting tangentially at the right in the free-body diagram. This force is due to the cable to the right of the figure. Since the cable is assumed static, the sum of the horizontal and vertical forces must be zero. This leads to two equations.

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Catenary - The Catenary and Parabolic Cables The Catenary y...

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