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Problem of photon torpedo

  1. Jan 29, 2007 #1
    1. The problem statement, all variables and given/known data
    A star-wars laser satellite, whose mass is 5000 kg, is orbiting Earth at a speed of 10.0 km/s. It launches a photon torpedo at an enemy missile which is directly in front of it. The photon torpedo contains [tex]10^3^3[/tex] photons, each having a wavelength of 200nm. What is the speed of the weapons satellite just after the launch?

    2. Relevant equations
    Conservation Of Momentum(?)(COM)
    [tex]K_m_a_x = hf - \varphi[/tex]
    [tex]KE = \gamma mc^2 - mc^2[/tex]
    [tex]p = E/c[/tex]
    [tex]v = f\lambda[/tex]
    3. The attempt at a solution

    Since we have [tex]\lambda = 200nm[/tex] we can then obtain f = 1.5*10^15 Hz.

    However, from here on, i am lost. How do we use the number of photons and equate it in to [tex]p = E/c[/tex] and finally COM. And then there is also a problem of E which i am unable to find since i don't have h, [tex]K_m_a_x = hf - \varphi[/tex].

    Any help will be appreciated. Thanks
  2. jcsd
  3. Jan 29, 2007 #2
    This feels like the typical momentum problem involving light, but using sci-fi scale numbers. In these cases, there are a few things to take into consideration:
    -conservation of momentum
    -conservation of energy

    As for the relevant equations, there may have been some confusion on what [tex]K_m_a_x = hf - \varphi[/tex], the photoelectric work function, is used for.
    There is also another equation that can be used to find the energy of the photon, not involving [tex]p[/tex]. And h is Plank's constant. Take another look at the possibilities. =)
  4. Feb 2, 2007 #3
    Well i have calculated i out heres what i have obtain :

    [tex]p = \frac{h}{\lambda} * 10^3^3[/tex] Since no. of photon is [tex]10^3^3[/tex]

    Then using Conservation of momentum, i get :

    [tex]mv = p_p_h_o_t_o_n[/tex]
    Which works v out to about 662.6 m/s
    The speed of satellite is therefore 10,000 - 662.6 = 9337.4 m/s

    Can anyone confirm my result?
  5. Feb 2, 2007 #4

    Meir Achuz

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    What you do seems correct, but the answer should be to 2 sf, so
    \delta v=660 and v_sat=9,300.
  6. Feb 2, 2007 #5
    Thanks for the help
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