Physics 325 Spring 2011 Homework 3

Physics 325 Spring 2011 Homework 3 - are nearly in contact...

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Physics 325 Spring 2011 Homework 3A Name: ____________________________ Due: Feb 23, 2011 by 9am (lecture or 325 box) 1. (10 points) A satellite orbits the Earth in a circular orbit of radius r 0 . The satellite uses a powerful thruster to suddenly increase its velocity by a relatively modest factor , where 2 2 such that the satellite changes from a circular (old) to an elliptical (new) orbit. (Note that the Earth’s mass is much larger than that of the satellite). a) Derive an expression for the apogee distance R for the new orbit in terms of r 0 and . b) For 1.1 (i.e. 10% increase in the velocity immediately after thrust), evaluate R . Carefully draw a sketch of both orbits and show how the effective potential U eff changes due to the thrust by drawing U eff for both orbits with any appropriate labels (e.g. the apogee in the new orbit). 2. (10 points) Two uniform steel spheres with mass m and density
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Unformatted text preview: are nearly in contact with each other. (a) What is the gravitational force between the two? (b) Calculate the ratio of the gravitational force to the weight of the sphere if its density 8 g/cm 3 (about right for steel) and its mass m 1 kg . Physics 325 Spring 2011 Homework 3B Name: ____________________________ Due: Feb 23, 2011 by 9 am (lecture or 325 box) 3. (10 points) Calculate the gravitational potential due to a thin rod of length and mass M at a distance R from the center of the rod and in a direction perpendicular to the rod. 4. (10 points) Calculate the gravitational potential ( r ) in the plane of a thin circular ring of radius R and mass M , where r is the distance from the center of the ring. Its fine to write the answer as a Taylor series, but show at least the first and second term. Show the potential when r R and interpret....
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Physics 325 Spring 2011 Homework 3 - are nearly in contact...

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