Final-solutions

# Assume that it is steered into a circular orbit with

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Unformatted text preview: ssume that it is steered into a circular orbit with no change in energy. (a) [6pt] What is the total mechanical energy of the satellite? Assume it would have zero total energy if it were at rest infinitely far from the earth, and see the front page for useful constants. Its initial kinetic energy just after launch is (with 1 GJ = 109 J) Its initial potential energy is The total mechanical energy is Alternative solution: , so and 3 (b) [6pt] What is the radius of the satellite’s circular orbit? The potential energy in orbit is The kinetic energy in orbit must be expressed in terms of the radius. Equating the gravitational acceleration to the centripetal acceleration gives. Therefore, the total energy in orbit is The alternative solution to (a) gives (The two solutions agree to within 1%, and are consistent within the approximations in the numerical inputs.) Problem 4: [12pt] Tarzan plans to cross a gorge by swinging in an arc across a hanging vine, which is 8.40 m long. (a) [6pt] If the vine initially makes an angle of 35.0o with respect to vertical and Tarzan starts out at rest, what is his maximum speed while swinging across the gorge? If Tarzan starts at rest, his speed after dropping a distance is given by so that The distance he drops can be obtained from geometry. If the vin...
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