# Some Physics (rather long)

```WARNING: This mail only contains some physics stuff. It is not directly
related to dinosaurs, but was triggered by recent physics discussions.

In the last few days, there was some confusion about the correct
definitions of masses, densities and relativity. It seems that also this
is not really related to dinosaurs, some people are interested. So, as a
physicist, I add my .02\$ here:

Definitions of units:
The Volume units like liter are derived from the length unit; one liter is
a volume of a cube of side length 10cm*10cm*10cm.
The correct definition of the meter does not involve the wavelength of
atomic radiation anymore; it is rather defined as 1/299792800 of the
distance passed by light within a second. (The reason is that this can be
measured more exactly and that in this way the meter definition is tied to
a constant of nature - and the definition of a second, which is still
defined by atomic radiation). There is no relation to water here.

I am not sure what the exact definition of the kilogram is. Until ten
years ago (when I studied physics and had to lean this stuff) it was
defined as the mass of a certain piece of matter, the "ur-Kilogram" in
Paris, which was made of a special alloy to be as insensitive to external
influences as possible. This ur-Kilogram was at the time made to have the
mass of a liter of water (I believe at 14.5 degree Celsius) , but as
measuring precision increases, there are
slight differences now. The reason why water was not used directly for
this definition is that the density of water is too temperature-dependent.

So water has a density of 1000kg/cube-meter approximately, but not
exactly.

Notes on relativity:
There is some confusion  even under physicists about the correct meaning
of E=mc2.
The story is like this:
As you may have heard, the mass of a particle changes with velocity,
according to the formula m = m0 / sqrt(1- (v/c)**2)
where sqrt means square root and **2 means power of two, and m0 is the
mass you measure when the particle is at rest relative to you.
Now, if you use this velocity-depending mass, E=mc**2 is an EXACT formula.
This is the way people in high-energy-physics use it, who deal with
particle that are extremely close to the speed of light and have a mass
that is several hundred times their rest mass.
If, however, the speeds are small, you may use the rest mass of the
Then, in a first approximation, you get
E=m0c**2;
including the next-hgher order term gives
E= m0 c**2 + 0.5 m0 c**2 *(v/c)**2,
which gives
E = m0 c**2 + 0.5 m0 * v**2
The second term is the standard kinetic energy term you may remember from
school - where of course nobody is interested in the rest mass energy,
because in daily life it always stays constant.
Finally, including the next-higher order gives an additional term
.75 m0 c**2 (v/c)**4 = 0.75 m0 v**4 / c**2
(I hope I got the constant right)
This can usually be neglected, becase (v**2/c) is very small. (For
instance, it is 0.0003 for the speed of sound; and it gets squared again
in the formula!)

To have a completely correct value, one should use the
formula with the square root shown above, and then everything is fine
again.

Sorry, if this was off-topic. It's like when you hear people talk about
dinosaurs, who make slight mistakes: There is always the urge to give
people a better understanding of a topic we love.

P.S.: I will be away for two weeks, so I will not be able to answer any
mail for a while.

Dr. Martin Baeker
Institut fuer Werkstoffe
Langer Kamp 8
38106 Braunschweig
Germany
Tel.: 00-49-531-391-3066
Fax   00-49-531-391-3058
e-mail <martin.baeker@tu-bs.de>

```