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Variable mass problems

  1. Apr 29, 2014 #1
    I'm a little confused about these.

    Sometimes I have seen solutions where F=d(mv)/dt=mdv/dt+vdm/dt is used and solved as a differential equation. An example is this:
    A water drap falls through a cloud. It has initial mass m which increases at a constant rate km as it falls. Show that it's equation of motion is given by
    kv+(1+kt)dv/dt=g(1+kt)
    with v it's velocity and g the gravitational acceleration.

    Sometimes however this does not seem to be applicable and we must work from first principles, equation a differential change in momentum dp to a differential impulse Fdt. An example is deriving the rocket equation, or a hot air balloon dropping sand.

    My questions are:
    How do I know which method to use?
    Is the second method one that works for all cases whilst the first is just a special case?
    If so when can I use the first method?
     
  2. jcsd
  3. Apr 29, 2014 #2
    First principles always work. Use that.
     
  4. Apr 29, 2014 #3
    Ok but it would be nice to understand why the first method works in some cases if anybody could explain that...
     
    Last edited: Apr 29, 2014
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