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Newton's 2nd Law problem (resent)

Sorry for sending again, 'cause I make some typing mistakes.


To me, if an object has a mass which is increasing with time, the force to
maintain its constant vel can be found from F=vdm/dt.
So for the rotor blade, I don't quite see why dm/dt is the rate of mass
flow
through the rotor blades. However, in mathematical derivation, F=mdv/dt +
v dm/dt,
v of the object is constant in the second term (vdm/dt).
Leigh, I can see your point in starting from first principle (i'm actually
teaching my students to solve from first principle, i.e considering the
rate
of change of momentum (impulse-momentum form)), but I still can't reconcil
with using vdm/dt. All the texts are using this method (find F from
mdv/dt)
without starting from first principle. Another classic example is to find
the extra force to maintain constant vel of the conveyer belt if luggage
is
dropping on it at a constant rate (but the luggage itself increases vel
from
0 to that of the belt).
Leigh, could you help me to resolve this confusion, 'cause some students
are
asking me, and I think I can't say the approach of using the formulae of
F=vdm/dt is WRONG, particularly if it still gives the correct answer?

rom

----- Original Message -----
From: Leigh Palmer <palmer@SFU.CA>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, February 11, 2000 3:03 AM
Subject: Re: Newton's 2nd Law problem


Newton's 2nd law:
F = d(mv)/dt
and can be expressed as:
F = m dv/dt + v dm/dt
In a question like what is the force/lift on a holicopter when the mass
is
"pushed" down at speed of v m s-1 and at a rate of m kg s-1, most texts
have
used:
F = v dm/dt
Isn't the above equation for constant vel but changing mass?

You must be careful about the meaning of your symbols.
What mass is changing? There is no nuclear process going
on here.

dm/dt refers to the rate of air mass flow through the
rotor. v refers to the (change in) the downward velocity
of the air produced by the rotor

My understanding is that the vel is accelerated by the rotor from a
speed
of
0 to v and is hence not constant.
If I use impulse = change in momentum
to find the answer, it is definitely more convincing,
since
F dt = final mom - initial mom
= mv -0
So F = mv/dt
where the mass per unit time is known.
I am confused, as both cases will still give the same answer. Can
someone
help?

You clearly understand the physical situation. Your only
confusion lies in the interpretation of that silly
formula (F = m dv/dt + v dm/dt) which is impossible
without a careful definition of the terms in it.

This is an example of how a student who might understand
is thrown by a "formula" which looks like an easy way to
get at the answer. The formula itself is dangerous.
Standing alone it can be a barrier to understanding. My
advice is that you never use it, but rather let it arise
naturally in the context of a particular problem - in
other words derive it whenever you need it. Under no
circumstances should you write it down in a lecture and
underline it or draw a box around it!

I ask my first year students to derive everything they
need from first principles. They don't all do it, of
course. I don't let them have a formula sheet on
examinations as some of my colleagues do, and my
students constantly complain that there is too much to
memorize, to which I respond "You're right; there is
too much to memorize. Perhaps it would be better for
you to understand it."

Some of my students understand this and appreciate it,
but this is not the royal road to popularity.

Leigh