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Calculating Terminal Velocity

  1. Jul 23, 2013 #1
    1. The problem statement, all variables and given/known data
    An egg of mass 0.10 kg is dropped from rest at a height h. It is known that the egg dropped experiences a force due to air resistance of the form F = -kv, where v is the velocity of the egg and k is a constant of proportionality equal to 0.01781 N*s/m. What is the terminal velocity of the egg?

    2. Relevant equations

    V = sqrt(2mg/pAC)
    V_t is terminal velocity,
    m is the mass of the falling object,
    g is the acceleration due to gravity,
    C_d is the drag coefficient,
    \rho is the density of the fluid through which the object is falling, and
    A is the projected area of the object.

    3. The attempt at a solution
    The only thing I know about terminal velocity is the formula mentioned above, but it seems to me that I'm missing information (I don't have the projected area of the object, the density of the air, etc.)
    The only thing I can think of is that the air resistance covers all of these and can be substituted in, giving me V = sqrt(2mg/-kv). However, I checked this with dimensional analysis and it doesn't yield the correct units. This problem is really confusing me, so I'd appreciate any help on it!
  2. jcsd
  3. Jul 23, 2013 #2


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    Identify the forces acting on the egg as it falls. How do the forces relate to the acceleration of the egg? At terminal velocity, what is the acceleration?
  4. Jul 23, 2013 #3
    Thank you for the response!
    The forces acting on it are kv going upwards and mg going downwards. I'm taking the downwards direction as positive, meaning that the net force acting on it is mg-kv which is equal to ma. So the acceleration is equal to (mg-kv)/m, and I know that it is 0 when it reaches terminal velocity. So, I got (mg-kv)/m = 0, and solving for v, I got mg/k.
    Is this correct?
  5. Jul 23, 2013 #4


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    That's correct.
  6. Jul 23, 2013 #5
    Awesome, thank you for your help! Your questions really helped guide me :)
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