- #1
albega
- 74
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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?
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?