A package of mass m needs to be delivered to the Moon (mass M, radius R) from Earth (mass 81.3M, radius 3.7R). To do thi

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A Package Of Mass M Needs To Be Delivered To The Moon Mass M Radius R From Earth Mass 81 3m Radius 3 7r To Do Thi 1 (52.01 KiB) Viewed 30 times

A package of mass m needs to be delivered to the Moon (mass M, radius R) from Earth (mass 81.3M, radius 3.7R). To do this, you use a horizontal spring-loaded mechanism on the surface of the Earth that will launch the package at the necessary speed for it to reach the surface of the Moon. Over on the Moon, the package is received with another horizontal spring-loaded mechanism. The spring on the Moon has stiffness k, relaxed length Lo, and at its maximum compression it has length Lo/4. What should be the launch speed u, on Earth such that when the package is caught by the spring on the Moon, the package comes to rest when the spring is maximally compressed? Your answer should be expressed in terms of the variables known in the problem (m, M, R, k, Lo) and fundamental physical constants such as G. You do not need to simplify your final answer. The spring on Earth has stiffness 2k and relaxed length Lo. When the package is at rest and ready to launch, the spring is maximally compressed. What does this compression have to be in order for the package to reach the launching speed you found in the previous part? Use the variable v to represent the speed found in part 1.