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Homework Help: Potential Energy Functions

  1. Sep 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Imagine that a treasure chest of mass m=100kg falls to the ground from a jet flying at an altitude of 35 km.
    (a) calculate the chest's initial potential energy according to formula V(z)=mgz
    (b) caculate the chest's initial potential energy according to formula V(r)=-G(m1m2/r)
    (c) Are answers different? Explain why this is.
    (d) Caculate change in chest's ptoential energy during its fall according to formula V(z)=mgz
    (e) Calculate change in chest's potential energy during its fall according to formula
    V(r)=-G(m1m2/r)
    (f) Are answers different? Explain why this is.

    2. Relevant equations

    V(z)=mgz

    V(r)=-G(m1m2/r)

    r=35000m + re = 6,415,000m

    re=center of earth to surface=6,380,000m

    3. The attempt at a solution

    (a) I know this answer is 3.4x10^7 J
    (b)V(chest)=[-3.99x10^14 Jm/kg(100Kg)]/6,415,000m = 3.41x10^7J (WRONG)
    (c) The answers should not be the same because the formula used in A and B are for different things. The formula used in A is only for kinetic energy near the earths surface while the formula used in B should be used for items in space (Not very clear on this)
    (d) V(chest)=mg(change in z)=-3.4x10^7J (is a negative number reasonable??)
    (e) V(chest)=-GMm[(1/re)-(1/re+r)]=-3.4x10^5 J
    (f) The answers should not be the same because the formula used in A and B are for different things. The formula used in A is only for kinetic energy near the earths surface while the formula used in B should be used for items in space (Not very clear on this).
     
  2. jcsd
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