- #1

albega

- 75

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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?