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Phys105_ps5_2009

Phys105_ps5_2009 - Physics 105 Problem Set 5 Due Thursday 3...

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Physics 105 Problem Set 5 Due: Thursday, October 22, 2009, 3 PM to 208 Jadwin. Reading: For the 3 weeks before midterm break; roughly 1 chapter per week: K&K, chapters 6, 7, 9. Our first midterm exam is Mon., Oct. 19, in class. The problems on this exam will be from the material in the first 4 problem sets, and Chapters 1-4 of K&K. Problem 1. The “slingshot” maneuver: In the inertial reference frame of the Sun, a planet is moving in a circular orbit about the Sun with speed v . A spacecraft of mass m approaches the planet, moving antiparallel to the planet’s motion with speed u i before it is accelerated by the planet’s gravity. The spacecraft then passes pretty close to the planet, remaining outside of its atmosphere so the encounter is elastic. After the spacecraft leaves the gravitational influence of the planet, it is moving directly away from the Sun with a new speed u f . What is u f ? What is the energy gained by the spacecraft from the planet? (In the reference frame of the Sun.) Make the approximations of ignoring the Sun’s gravitational
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