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					    Physics 102                     Quiz #4                Spring 2005

              G = 6.67x10-11 S.I. units; 1 A.U. = 1.5x1011 m;

                                               y
1. (8 points) Given masses M1 =
                                               M2
48 kg at x = -2.5, y = 0 m; M2 =
37 kg at x = 0, y = +1.5 m; M3 =
29 kg at x = +3.0, y = 0 m; and                             M3    x
M4 = 14 kg at x = y = 0, find the         M1        M4
net force exerted on M4 by the
other three masses. Express your
answer in terms of the x and y
components of this net force.
2. (12 points) NASA recently reported the discovery of "hot spots" in the
gas disc orbiting a black hole at the center of the galaxy Markarian 766.
These spots had an orbital speed of 3.3x107 m/s and an orbital radius of 5
A.U. Assume that the orbits are circular.

a. What is the mass of the black hole?




b. What is the orbital period of the hot spots?




c. What is the escape velocity at that distance from the black hole?




d. Through interactions with the surrounding gas the hot spots will lose
energy. Will they then move to a circular orbit with a larger or a smaller
orbital radius as a result? Explain your answer carefully.
3. (10 points) Titan, the giant moon of Saturn, has a mass of 1.33x1023 kg
and a radius of 2.56x106 m. In January the Huygens space probe parachuted
through Titan's atmosphere and landed on the surface. The probe entered
the atmosphere at an altitude of 1000 km above the surface with a speed of
6200 m/s and impacted the surface with a speed of 5.0 m/s. The mass of the
Huygens probe is 319 kg.

a. What is the acceleration of gravity on the surface of Titan?




b. How much work was done by Titan's atmosphere in slowing the probe during
its descent?

				
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