Re: weight of a bird in a cage

["Inge H. A. Pettersen" <ingep@ONLINE.NO>]

"Carl E. Mungan" wrote:

> A bird is sitting on a perch in a cage. The cage is on a scale. The bird
> begins to fly around in the cage. What will the scale register?
> (i) What difference will it make if the cage is sealed (preventing air
> circulation to and from the outside) versus ventilated?

If no ventilation the "natural" system to consider consists of the bird, the
air
and the cage as described by an observer (assumed Newtonian inertial) at rest
with respect to the scale.
When the bird flies, the mass center of the system will have a time dependence
according to this observer. Using first Newtons second law for the mass center
to find the direction of the acceleration and then applying Newtons third law
to
find the "reaction force" from the scale on the system one obtains:
If the the acceleration of the mass center is purely horizontal, the scale will
read the
same as if the bird was at rest. If the acceleration of the mass center has a
vertical component
upwards the scale will read more than the case when the bird is at rest wrt the
cage. The case
with vertical acceleration component downwards gives the opposite result.

If ventilated, one has to do *in principle* the same reasoning, but in this
case mass is
in general changing too. Therefore Newtons second law has to be used in the
form
net force = time derivative of linear momentum. The boundary conditions are
thus not
completely given: The time derivative of the linear momentum *vector* for the
air comming in
and out must be specified.