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A 72.0 kg piece of a satellite left over from an explosion with zero orbital velocity in space falls from a distance of 190 above the surface of the earth down toward earth. It arrives with 29.5 Km (M="mega") kinetic energy on earth. How many MJ energy have been lost due to friction in the earth's atmosphere ? Use the exact expression for the gravitational potential energy.

  • physics - ,

    What are the units of the "190" elevation from which it fell?

    29.5 Km is not a measure of energy. Please copy the question more carefully

  • physics - ,

    190Km *
    29.5 MJ *

  • physics - ,

    The gravitational potential energy change is
    deltaPE = -G*M*m/R + G*M*m/(R+h)
    where G is the universal gravity constant, M is the mass of the earth, m is 170 kg and R is the radius of the earth (6,378,000 m). h is the initial altitude above the Earth's surface.

    This can also be written
    deltaPE = -mgR + mgR[R/(R+h)]
    = -mgR{1 - [1/(1 + h/R)]}
    = -170kg*9.8 m/s^2*6378*10^3 m
    *{1 - [1 - 1/(1 + (190/6378))]
    = -1.063*10^10*0.0289 = -3.071*10^8 J

    So 307 MegaJoules of gravitational PE is lost. If the kinetic energy on arrival is 29.5 mJ, the remainder has been lost due to frictkion, and converted to heat.

  • physics - ,

    thank you, but for some reason its wrong

  • physics - ,

    it says "Make sure you calculate with at least 3 significant digits. Express your answer using two significant figures."

  • physics - ,

    The above equation is all right -- just make sure you use the right value for mass (72 kg; not 170). Also, make sure you convert the 190km into meters--therefore your calculations would be (190,000m/6.4e6m). If you do all the conversions right, you should get the right answer! Good luck.

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