Re: Can a system's mass vary?

["Shapiro, Mark" <mshapiro@EXCHANGE.FULLERTON.EDU>]

No, you are just properly accounting for the change in momentum of the
material being added to the car.  Think about moving along in a
reference frame that is moving with the same velocity of the car.
Compute the momentum of a bit of material dropping from the elevator in
this frame BEFORE and AFTER it hits the car.  The conclusion you come to
is that F=dp/dt works just fine.

Dr. Mark H. Shapiro
Professor of Physics, Emeritus
California State University, Fullerton
Phone: 714 278-3884
FAX: 714 278-5810
email: mshapiro@fullerton.edu
web: http://chaos.fullerton.edu/Shapiro.html
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http://community.webshots.com/user/mhshapiro 
 
 

-----Original Message-----
From: Robert Cohen [mailto:Robert.Cohen@PO-BOX.ESU.EDU] 
Sent: Sunday, November 09, 2003 10:17 AM
To: PHYS-L@lists.nau.edu
Subject: Re: Can a system's mass vary?

I asked:

> Does it matter what the speed of your inertial reference=20
> frame is?  In other words, does it still work if you observe=20
> the grain elevator/hopper car system from a moving train?

to which Mark Shapiro replied:

> Not if you are careful to properly identify v as the relative=20
> velocity of the car and the grain elevator.

What is it about applying dp/dt with the mass varying
that requires v to be the relative velocity?

It seems to me that you aren't really using dp/dt with
the mass varying.  Rather, you are applying Newton's
second law twice - once to the grain and once to the
hopper - with the provision that the grain's initial
momentum is zero.  The end result:

0 =3D m dv/dt + v dm/dt

"looks" like you've applied dp/dt with the mass varying
but is that really what you've done?

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301