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Re: momentum before force (was: friction)



Hi Gene Mosca and all-
You write:
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I have a problem with the statement F = dP/dt = m dv/dt + v dm/dt. If F,
m, and dv/dt are Galilean invarients and v is not, then this equation
cannot be correct. In fact, the rocket equation -m dv/dt = u dm/dt cannot
be derived from this statement. Note that in the rocket equation m, dv/dt
and u are Galilean invarients. For the original statement F = dP/dt = m
dv/dt + v dm/dt to be correct requires that the mass not be a scalar, as
is the case with the so called relativistic mass m/(1 - (v/c)^2)^1/2.
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Perhaps the following problem will help clarify the issue:
A little red wagon with a mass of 2 kg is filled with 5 kg of
sand. The sand is leaking out of a hole in the wagon at a rate of .q kg/s.
A motor attached to the wagon is pushing the wagon forward with a thrust
of 1 N. Calculate the acceleration of the wagoon as a function of t
before the sand is all gone. Assume that the wagon has an arbitrary
velocity v at t=0. Do the calculation both in the frames where the
where the initial velocity was v and where that velocity was 0.
Regards,
Jack