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
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
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