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Physics problems Classical Mechanics and Gravitation

  1. Oct 4, 2005 #1
    Hi i was wondering if anyone could help me with the following problems please,I'm a bit confused!

    Q1. A 9.4 kg projectile is fired vertically upwards. Air drag dissipates
    68 kJ during its ascent. How much higher would it have gone were air drag
    negligible?

    Here I used the formula mgh and worked out the height to be 738.17m.Is this right If not what formula and method should I use?

    q2 Suppose the Sun were to run out of nuclear fuel and collapse to form a
    white dwarf star, with a radius equal to that of the Earth (6.4 x 10 6 m).
    Assuming no mass loss, what would then be the Sun’s new rotational
    period. Assume that both the Sun and the white dwarf are uniform solid
    spheres. (The period of the sun is currently about 25 days. The moment of
    inertia of a sphere is 5
    r M 2 2
    and the solar radius is 6.7 x 10 8 m.)

    Completely lost on this q don't know where to start?

    Q3 The Martian satellite Phobos travels in an approximately circular orbit of
    radius r = 9.4 x 10 6 m with a period T of 459 minutes. Calculate the mass of
    Mars from this information.

    I used keplers 3rd law here Gm=4piR^2/T^2 and found the mass to be 6.43 x10^-13 is this the correct way for doing this?
     
  2. jcsd
  3. Oct 4, 2005 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Your answer is correct.
    Angular momentum must be conserved in this scenario:
    [tex]L = I\omega = L' = I'\omega'[/tex]
    where:
    [tex]I = \frac{2mr^2}{5}[/itex]

    Since m remains constant, [itex]\omega[/itex] must change as r changes. Work it out.

    I don't think you have Kepler's third law stated correctly.

    The centripetal acceleration has to be supplied by gravity. The centripetal acceleration for Phobos is: [itex]a_c = \omega^2 r[/itex]. The gravitational acceleration is:

    [tex]a_g = \frac{GM_{mars}}{r^2}[/tex]

    Equate the two and work out [itex]M_{mars}[/itex] from that.

    AM
     
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