XPost: sci.physics, alt.sci.physics, uk.politics.misc
On Mon, 09 Jan 2023 09:07:50 +0100
Thomas Heger <
ttt_heg@web.de> wrote:
Am 08.01.2023 um 10:36 schrieb Dave:
Is it v or v^2?
Is this formula E=0.5mv^2 correct, or is it more like E= mv?
That should depend on the used units for E, m and v.
As unit systems have different degrees of internal consistency, you
should certainly be able to find an example for both factors.
I usually use SI units only and would get 0.5 as factor, but have not verified the exponent 2 myself.
In general I would prefer the quantity momentum over energy, because
v is frame dependent, hence also kinetic energy.
Then I would like to compare conservation of momentum and
conservation of energy, but suggest choosing conservation of momentum
over conservation of energy.
TH
The whole question revolves around kinetic energy being a different
thing from momentum, not just being a different word for it. To begin
with, we have no idea of the absolute kinetic energy or the absolute
momentum of an object, because we have no idea how fast an object is
moving, and according Einstein, we never can know it. So we work on
relative quantities, generally relative to 'stationary with respect to
the bit of Earth's surface where the action takes place'.
The kinetic energy of an object of mass m moving at velocity v is the
amount of energy required to raise the mass from a stationary position
to the velocity v, or to slow it down to stationary. You can start from
first principles with length and time, going through force,
acceleration and work, or you can work directly with velocity as the independent variable.
The integral of momentum mv from zero to v with respect to v is 0.5 * m
* v^2. It's a definite integral, over a particular range, so there is no constant of integration.
The same principle applies to other forms of 'moving', such as the
current in an inductor and the voltage change across a capacitor. The
energy stored in the former is 0.5 * L * i^2, in the latter is 0.5 * C
* V^2. Both arise from the same kinds of integral, calculating the
total energy required to achieve a particular voltage or current
value. In the latter case, there is a quantity called 'charge', which
is equal to C * V and is analogous to mechanical momentum.
Momentum is useful in particular situations, for example solving
problems involving snooker balls. Anything involving resonance is best understood in terms of energy, as resonance is the repeated conversion
of one type of energy to another, and back again.
Almost all mechanical, electric or electronic engineering would simply
not work if engineers did not know how to calculate energy, as the OP
suggests.
--
Joe
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)