MIT 8 01T  Exam 3 Sample Problems (5 pages)
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Exam 3 Sample Problems
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Exam
 Pages:
 5
 School:
 Massachusetts Institute of Technology
 Course:
 8 01t  Physics I
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8 01L Fall 2005 Exam 3 Sample Problems Note that some of these problems were from an exam allowing calculators Your exam will not allow calculators Problem 1 a Two large spherical stars with masses of M and 2M m M 2M are positioned a distance D apart measured from the center of one star to the center of the other star as shown A small spherical asteroid with D mass m is located with its center exactly halfway between the two large stars Find the magnitude and direction of the total gravitational force acting on the asteroid m b A small probe of mass m is released from rest at a distance of 2R above the surface of a spherical planet of mass M and radius R Find the speed that the probe will have when it hits the surface of the planet Assume that the planet does not have an atmosphere and no forces other than gravity act on the probe c Assume that the probe is released at the same distance from the planet but now with a velocity of vo GM 4R The probe has a rocket which fires to put it into a circular orbit at that height Find the speed the probe would have once it is in the circular orbit and using that find the work done by the rocket Assume that at all times the probe is at the same distance from the planet and that there are no forces acting on the probe other than the planet s gravity and the rocket 2R M R vo m 2R M R Extra Credit Question This question may require a lot of thought for the points available Try it only if you have finished with all other problems d Redo part b but assuming that the planet is a hollow shell and that the probe falls through a hole in the shell Find the speed of the probe when it gets to the center of the hollow shell Explain your answer Problem 2 a An object of mass M 2 kg is attached to a spring of spring k spring constant k 50 N m which is compressed a uncompressed distance d 20 cm and then released at rest Find the M speed of the object when it has gone past the point d where the spring is uncompressed and now the spring is
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