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HW 7-2-solutions

# HW 7-2-solutions - madrid(tmm2353 HW 7-2 Antoniewicz(56445...

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madrid (tmm2353) – HW 7-2 – Antoniewicz – (56445) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 15.0points A package of mass 14 kg sits on an asteroid of mass 1 . 1 × 10 21 kg and radius 6 × 10 5 m. The asteroid has no atmosphere. Using a large and powerful spring, we want to launch the pack- age in such a way that it will never come back, and when it is very far away from the asteroid it will be traveling with speed 225 m / s. If the stiffness of the spring is 2 . 6 × 10 5 N / m, how much must we compress the spring? Assume that the mass loses contact with the spring when the latter reaches its equilibrium posi- tion, and use G = 6 . 7 × 10 - 11 N · m 2 / kg 2 . Correct answer: 3 . 99427 m. Explanation: For the spring-mass system, the total en- ergy is 1 2 kx 2 GMm R initially, where the first term corresponds to the potential energy of the spring and the second term corresponds to the gravitational potential energy of the package on the surface of the asteroid. This is also the total energy of the mass, when it is launched into space.

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