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1. (60 points.) Consider a rope of uniform mass density ) = dm/ds hanging from two points, (x1, Y1) and (x2, y2), as shown in Figure 1. The gravitational potential energy of infinitely tiny element of this rope at point (x, y) is given byan d U=d m g y=\lambda g d s y where d s^{2}=d x^{2}+d y^{2} A catenary is the
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