# Homework Help: Variable mass problems

1. Apr 29, 2014

### albega

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. Apr 29, 2014

### dauto

First principles always work. Use that.

3. Apr 29, 2014

### albega

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