In old science fiction movies, writers attempted to come

Chapter , Problem 92

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In old science fiction movies, writers attempted to come up with novel ways of launching spacecraft toward the moon. In one hypothetical case, a screenwriter envisioned launching a moon probe from a deep, smooth tunnel, inclined at 65.0 above the horizontal. At the bottom of the tunnel a very stiff spring designed to launch the craft was anchored. The top of the spring, when the spring is unstressed, is from the upper end of the tunnel. The screenwriter knew from his research that to reach the moon, the 318-kg probe should have a speed of at least when it exits the tunnel. If the spring is compressed by just before launch, what is the minimum value for its force constant to achieve a successful launch? Neglect friction with the tunnel walls and floor.

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