Kinetic Energy formula check - a series of short burn rockets, and see how the velocity adds up.

[Dave]

Kinetic Energy formula check - a series of short burn rockets, and see
how the velocity adds up.

Is it v or v^2?

Is this formula E=0.5mv^2 correct, or is it more like E= mv?

Also can calculate the kinetic energy before and after each stage -
check velocity from the experimental apparatus.

Ideally use an airtrack - no rotational inertia to be concerned with.
Needs good design so each rocket burn adds the same energy.

Remember this correction is for basic, military and professional
education - nothing to do with university.

This is bread and butter basic physics.

Copyright release on the above in exact and equivalent:
(and rights and patents) all public domain - attribution annon.:

[Dave]

Post by Dave
Kinetic Energy formula check - a series of short burn rockets, and see
how the velocity adds up.
Is it v or v^2?
Is this formula E=0.5mv^2 correct, or is it more like E= mv?
Also can calculate the kinetic energy before and after each stage -
check velocity from the experimental apparatus.
Ideally use an airtrack - no rotational inertia to be concerned with.
Needs good design so each rocket burn adds the same energy.
Remember this correction is for basic, military and professional
education - nothing to do with university.
This is bread and butter basic physics.

Is this one of the reasons why France split between Engineering Schools
and universities? Likely universities are constituted to teach whatever
they like. Let the students deal with this.

[Jim Pennino]

Post by Dave
Kinetic Energy formula check - a series of short burn rockets, and see
how the velocity adds up.
Is it v or v^2?
Is this formula E=0.5mv^2 correct, or is it more like E= mv?

Read:

https://www.toppr.com/guides/physics/motion/equations-of-motion/

and learn how the derivation of the equations of motion is done using
the algebraic method, the graphical method, and the calculus method.

No vacuum chambers or precision timers required, just the basic
assumptions that distances are meters, acceleration is constant and in
units of m/s^2 and time is in seconds.

<snip crackpot babble>

[Thomas Heger]

Post by 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

[Joe]

On Mon, 09 Jan 2023 09:07:50 +0100

Post by Thomas Heger

Post by 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.

[Thomas Heger]

Am 09.01.2023 um 15:13 schrieb Joe:
...

Post by Joe
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.

My problem with momentum and energy is, that momentum is known to be a
conserved quantity and energy assumed to be.

But momentum is m*v, while kinetic energy is 1/2 *m *v².

How could both quantities possibly be both conserved for the same
object, with same mass m and same velocity v, if one curve of that
quantity over v is linear with v and one quadratic ????

If v gets smaller a little, than both curves cannot possibly coincide
with their respective conservation curve, hence one quantity is not
conserved, if v is altered. But we can easily alter v, because v is
frame dependent. And choosing a different coordinate system should not
alter the state of an object, hence neither energy nor momentum.

TH

[Thomas Heger]

Post by Thomas Heger
...

Post by Joe
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.

My problem with momentum and energy is, that momentum is known to be a
conserved quantity and energy assumed to be.
But momentum is m*v, while kinetic energy is 1/2 *m *v².
How could both quantities possibly be both conserved for the same
object, with same mass m and same velocity v, if one curve of that
quantity over v is linear with v and one quadratic ????
If v gets smaller a little, than both curves cannot possibly coincide
with their respective conservation curve, hence one quantity is not
conserved, if v is altered. But we can easily alter v, because v is
frame dependent. And choosing a different coordinate system should not
alter the state of an object, hence neither energy nor momentum.

This is actually wrong, because momentum is not independent of the state
of an object, against which a flying object hits. The velocity v is
therefore not arbitrary and should be relative to the stationary object,
which serves as target.

This is also the case for kinetic energy, which is also depending on the
state of motion of a possible target.


TH

[Sylvia Else]

Post by Dave
Kinetic Energy formula check - a series of short burn rockets, and see
how the velocity adds up.

During a rocket burn there is a frame dependent split between the energy
ending up the exhaust and the thing being propelled. So trying to
analyse kinetic energy by looking at rocket burns will get you nowhere.

Sylvia.