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Old Nov 1st 2017, 01:34 PM   #1
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Physics Contrast of Meanings: mass = const with dm/dt = 0

Help on this idea will be appreciated...

In HS physics the idea "Conservation of Mass" is taught as "mass is constant" stated mathematically as:
1) m = const.

In freshman physics "Conservation of Mass" is taught as "mass is constant" with a new math statement.
2) dm/dt = 0

Statements 1) and 2) "are" and "are not" equivalent. They "are" for any specific case but 2) alone
is correct for any case and also all other cases (some kind of universality). In math 1) is a non-homogeneous
eqn whereas 2) is homogeneous eqn. The power of 2) over 1) has something to do with this math
characteristic - its a perspective.

Also with mass conservation there is momentum, energy et al.. What is this connection. How do you see it?

Thank you, jp

Last edited by THERMO Spoken Here; Nov 1st 2017 at 01:38 PM. Reason: spelling
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Old Nov 1st 2017, 02:04 PM   #2
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I don't follow your reasoning. Clearly if m = constant then simply take the derivative with respect to time and you get dm/dt = 0. If you take dm/dt = 0 and integrate you get m = constant. In each case the constant is determined by initial conditions. Perhaps you're confusing the form of the equations with their physical implications?

I also don't understand what you mean by Also with mass conservation there is momentum, energy et al.. What is this connection. Can you be more specific?

Note: Not all physics texts state the conservation of mass in the same way. For example: the physics text by Knight phrases it as "The total mass in a closed system is constant. Mathematically M_f = M_i"

Gotta go. My cat Scooter is demanding that I clean his kitty litter. Yep. He has a certain meow which means I either clean his litter or he'll "go" elsewhere.

Last edited by Pmb; Nov 1st 2017 at 02:20 PM.
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Old Nov 1st 2017, 02:13 PM   #3
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Not having the benefit of an American education some context would be appreciated.

You are usually interested in thermodynamic/fluid mechanic issues is this the case here and are you talking about what we call the steady flow equation?

H1 + (c1)^2 +Q = H2 + (c2)^2 +W

or perhaps the continuity equation

dm/dt = AC/V

BTW you don't seem to visit so often these days which is a pity IMHO.

I would not like to see d(Thermospokenhere)/dt reduce.


Last edited by studiot; Nov 1st 2017 at 02:16 PM.
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Old Nov 1st 2017, 02:17 PM   #4
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I was going to give a more elementary response until I checked who was posting.

Conservation of mass, conservation of momentum, conservation of energy. Three pillars of modern Physics. In SR two of these are combined: conservation of momentum and energy, though the details are slightly different. Why? Because when we add a "time" component E/c to the momentum 3-vector we get a momentum-energy 4-vector that is conserved overall. That is, the momentum-energy 4-vector can be written as $\displaystyle \left ( \frac{E}{c}, ~ p_x, ~ p_y, ~ p_z \right )$ This means that energy and momentum can change in a closed system subject to conservation of the energy-momentum 4-vector. Specifically $\displaystyle \frac{E^2}{c^2} - \textbf{p}^2 c^2 = m^2 c^2$. (The inner product of a 4-vector with itself is a constant.) So energy and momentum are not quite conserved in SR.

I'm not sure what you mean by m = constant and dm/dt = 0 aren't the same? The only thing that I can think of is that we may have a constant of integration, that is the derivative equation gives $\displaystyle m = m(0) + \text{arbitrary constant}$ . I can't think of any circumstance where the arbitrary constant can't be defined as contributing to $\displaystyle m_0$. (m(0) is the mass at t = 0 and $\displaystyle m_0$ would be the rest mass.)

Between the three of us (studiot and Pmb both responded as I typed this) did we answer your question?

-Dan
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Old Nov 1st 2017, 02:39 PM   #5
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Thanks for the thoughtful replys:

I asked about what I do not understand. I posed a vague question.
You made the best of it you could. I'll read and reread. Thanks.
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Old Nov 1st 2017, 06:31 PM   #6
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Red face

Both these bare equations have little meaning, without context.

Certainly if I drew a graph of mass verses distance between the door and the window in this room, it would not be constant.

Similarly the total mass in this room is about to change (dm/dt), as I am about to sign off and go to my bedroom.

Goodnight.
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