Did not have much time to react.
Lloyd wrote: ↑Fri Mar 20, 2020 4:15 pm
I wanted to see if an imploding filament would produce enough pressure to cause fusion of heavy elements from light elements, esp. hydrogen. Lightning seems to cause a small amount of fusion sometimes, esp. in the Sun's photosphere, I guess. One website says "Pressure squeezes the hydrogen atoms together. They must be within 1x10^-15 meters of each other to fuse." This site
https://physics.stackexchange.com/quest ... emperature says 10^21 or 10^28 Pa is needed to produce fusion.
Ok that is clearer.
In my experience the pressure varies a lot when electric fields/currents are involved.
Fusion shows up in lightning and Fusors with ease.
Anyway, here is how I would calculate it:
First try to find the average force that most of the object will encounter.
I will criticize this approach below.
Average force and pressure of 2 Colliding objects:
If two objects collide and merge, you have a distance over which they merge.
Let's say that is R (radius), and they approach with speed V.
The de-acceleration (a) stops the movement.
This happens with a short time (T).
R= 0.5 * a * T^2
In the same time (T) the de-acceleration reduces V to zero.
V= a * T
(so: T= V/a)
We try to get acceleration (a) from the equation.
R = 0.5 * a * (V/a)^2
R = 0.5 * (V^2) / a
a = 0.5 * (V^2) / R
From acceleration (a) we can get the force (F) and the pressure (P)
F = m*a ,where m is mass of object.
P = F / Area ,where Area is surface area where objects touch each other.
Area goes from 0 to (PI * R^2)
For the average force, we may get PI*R^2
So:
Average P = ( m / Area ) * (0.5) * (V^2) / R
Average P = ( 0.5 * m * V^2 ) / ( Area * R )
With your data:
Using c= 3E8 [m/s] and converting [km] to [m].
Estimate R= 0.66E8 [m]
P= 0.5 * 2E30 [kg] * (0.85* 3E8 [m/s] )^2 / ( 1.5E12 *1E6 [m^2] * 0.66E8 [m] )
P= 1E30 * ( 1.7^2 ) * 1E16 / ( 1E26 )
P= (~3) *1E46 / 1E26 = 3E20 [Pascal]
Criticism and correction:
This pressure is certainly not constant during the collision.
The Area varies during the merging of the 2 objects.
The front ends of the objects get a sudden shock, because the front end
has a very small R, and small A.
The way the material compresses is also important, as gas will
compress a lot easier than liquid or solid. This reduces the mass
in the equation.
But you could try to calculate how a square meter of the front surface would behave when
it collides onto the other surface.
Now you get more the pressure equation that you described in your first post,
where the gas gets compressed into a very small volume.
But this only becomes a lot more than the above equation, when
there is both a gas and liquid/solid state.
But in reality gets far more complex.
The shock will cause a strong shock-wave, and that will cause an explosion.
Also the compression and resistance will suddenly increase the heat of of the front of the object.
These super-sonic shocks will have far higher pressure than shown.
It will work like a meteoroid that explodes in the atmosphere,
before it reaches the surface.
This explosive collision is the most interesting part of the collision
and is far too difficult to calculate.
Instead simulators are used to calculate the effects of such collisions.
Did not have much time to react.
[quote=Lloyd post_id=1564 time=1584720924 user_id=184]
I wanted to see if an imploding filament would produce enough pressure to cause fusion of heavy elements from light elements, esp. hydrogen. Lightning seems to cause a small amount of fusion sometimes, esp. in the Sun's photosphere, I guess. One website says "Pressure squeezes the hydrogen atoms together. They must be within 1x10^-15 meters of each other to fuse." This site https://physics.stackexchange.com/questions/281082/nuclear-fusion-with-extremely-high-pressure-and-low-temperature says 10^21 or 10^28 Pa is needed to produce fusion.
[/quote]
Ok that is clearer.
In my experience the pressure varies a lot when electric fields/currents are involved.
Fusion shows up in lightning and Fusors with ease.
Anyway, here is how I would calculate it:
First try to find the average force that most of the object will encounter.
I will criticize this approach below.
[b]Average force and pressure of 2 Colliding objects:[/b]
If two objects collide and merge, you have a distance over which they merge.
Let's say that is R (radius), and they approach with speed V.
The de-acceleration (a) stops the movement.
This happens with a short time (T).
R= 0.5 * a * T^2
In the same time (T) the de-acceleration reduces V to zero.
V= a * T
(so: T= V/a)
We try to get acceleration (a) from the equation.
R = 0.5 * a * (V/a)^2
R = 0.5 * (V^2) / a
a = 0.5 * (V^2) / R
From acceleration (a) we can get the force (F) and the pressure (P)
F = m*a ,where m is mass of object.
P = F / Area ,where Area is surface area where objects touch each other.
Area goes from 0 to (PI * R^2)
For the average force, we may get PI*R^2
So:
Average P = ( m / Area ) * (0.5) * (V^2) / R
Average P = ( 0.5 * m * V^2 ) / ( Area * R )
With your data:
Using c= 3E8 [m/s] and converting [km] to [m].
Estimate R= 0.66E8 [m]
P= 0.5 * 2E30 [kg] * (0.85* 3E8 [m/s] )^2 / ( 1.5E12 *1E6 [m^2] * 0.66E8 [m] )
P= 1E30 * ( 1.7^2 ) * 1E16 / ( 1E26 )
P= (~3) *1E46 / 1E26 = 3E20 [Pascal]
[b]Criticism and correction:[/b]
This pressure is certainly not constant during the collision.
The Area varies during the merging of the 2 objects.
The front ends of the objects get a sudden shock, because the front end
has a very small R, and small A.
The way the material compresses is also important, as gas will
compress a lot easier than liquid or solid. This reduces the mass
in the equation.
But you could try to calculate how a square meter of the front surface would behave when
it collides onto the other surface.
Now you get more the pressure equation that you described in your first post,
where the gas gets compressed into a very small volume.
But this only becomes a lot more than the above equation, when
there is both a gas and liquid/solid state.
But in reality gets far more complex.
The shock will cause a strong shock-wave, and that will cause an explosion.
Also the compression and resistance will suddenly increase the heat of of the front of the object.
These super-sonic shocks will have far higher pressure than shown.
It will work like a meteoroid that explodes in the atmosphere,
before it reaches the surface.
This explosive collision is the most interesting part of the collision
and is far too difficult to calculate.
Instead simulators are used to calculate the effects of such collisions.