(c) Reflect:The tension is radial while the displacement is tangent to the circular path; thus there is no componentof the tension along the direction of the displacement and the tension in the ropes does no work on the child.7.49.Set Up:Apply to the motion of the stone on the moon with and at themaximum height. The conservation equation becomes with and Setting and gives Note that is the same on the earth and moon and let subscript 1refer to the moon and subscript 2 refer to the earth.Solve:Reflect:Gravity is stronger on earth so a larger initial speed is needed in order to achieve the same height as on themoon.7.50Set Up:Use with and Also apply and with to obtain Solve: (a) which is constant, so and,(b)(c)Now is constant, so Solving for 7.51.Set Up:Apply with and the result is Since is constant,Solve:7.51.Set Up:In part (a), substitute into to obtainAlso let subscript 1refer to the stronger spring and 2 to the weaker spring. Then and In part (b), applywhich results in Solve: (a)(b)7.53.
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