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Dropping objects air resistance

  1. Aug 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A creature of mass [itex]m[/itex] and bottom surface area of [itex]A[/itex] is dropped from a height [itex]h[/itex] towards the ground. The creature dies if a force of [itex]F_K[/itex] or greater acts on it. What is the value range of acceleration due to gravity, [itex]g[/itex], for such creature to survive the fall?

    2. Relevant equations

    Surely the problem requires air resistance since mass and surface area are mentioned. I think this can be modelled as [itex]F_D=-k \cdot v[/itex] unless anyone has any better ideas?

    3. The attempt at a solution

    The question is what else to do - we'll need a differential equation, then to solve it for [itex]g[/itex] in terms of [itex]F_K[/itex], [itex]h[/itex], [itex]m[/itex] and [itex]A[/itex] (probably work out the terminal velocity first and then relate it to [itex]F_K[/itex] and [itex]g[/itex])? I hope we can assume that height [itex]h[/itex] is sufficient that terminal velocity will be reached. If not, we might have to use something more fundamental.
     
  2. jcsd
  3. Aug 17, 2013 #2

    rude man

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    Depends on the softness of the ground. Use the impulse formula. F*Δt = Δp and Δt =√(2s/g). But you need to know s, the distance over which the fall was cushioned, i.e. the softness of the ground.

    The presence of A in the problem statement does suggest that air resistance was to be considered. Could be a red herring. I would ignore it or get an explanation from the instructor.
     
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