[Jaaanosik (OP)]

Is horizontal component slowing down the ship?

Yes. All of the kinetic energy possessed by the ship and balls is stored in the springs at the end of the interaction. Keep in mind that the springs are technically being pressed from both the bottom (due to the ship's velocity) and the top (due to the ball's velocity). An equal amount of energy is being absorbed from both the ship and the balls in the process because both the balls and the ship have the same mass.

No, the horizontal component is not going to slow down the spaceship.
No work is done to slow down the spaceship.
How do we know?
Because work is a dot product of F and s.
The force is 90 degrees to the trajectory of the spaceship, no work is done.
F*s = 0 (as a dot product)
Jano

[Jaaanosik (OP)]

Now to continue along the line.
When the ball pushes the horizontal spring shaft then it is doing a work.
The trajectory s is horizontal and the inertia of the ball is pushing the shaft - the ball is doing work F*s.
The ball is losing its kinetic energy, transferred to the horizontal spring potential energy,
... but it is NOT slowing down the ship!
Jano
 

[Kryptid]

No, the horizontal component is not going to slow down the spaceship.
No work is done to slow down the spaceship.
How do we know?
Because work is a dot product of F and s.
The force is 90 degrees to the trajectory of the spaceship, no work is done.
F*s = 0 (as a dot product)
Jano

If no work is being done to slow down the ship, then no work is being done to slow down the balls either. Remember, just as much energy entering the springs is coming from the ship as is coming from the balls. The fact that kinetic energy is being removed from the balls and the ship to compress the springs means that both must be slowed down.

Now to continue along the line.
When the ball pushes the horizontal spring shaft then it is doing a work.

And when the ship is pushing the spring against the ball, it is doing work as well.

The trajectory s is horizontal and the inertia of the ball is pushing the shaft - the ball is doing work F*s.
The ball is losing its kinetic energy, transferred to the horizontal spring potential energy,
... but it is NOT slowing down the ship!

If the balls are losing kinetic energy, then the ship is too. Remember, the situation is perfectly symmetrical. From the reference frame of the balls, the balls are sitting still and the springs are moving towards them. From the balls' point of view, the kinetic energy of the ship-spring system is what is compressing the springs because the balls have no kinetic energy in their own reference frame. From the reference frame of the barycenter, energy from both the balls and the ship are being used to compress the springs.

[Jaaanosik (OP)]

No, the horizontal component is not going to slow down the spaceship.
No work is done to slow down the spaceship.
How do we know?
Because work is a dot product of F and s.
The force is 90 degrees to the trajectory of the spaceship, no work is done.
F*s = 0 (as a dot product)
Jano

If no work is being done to slow down the ship, then no work is being done to slow down the balls either. Remember, just as much energy entering the springs is coming from the ship as is coming from the balls. The fact that kinetic energy is being removed from the balls and the ship to compress the springs means that both must be slowed down.

Now to continue along the line.
When the ball pushes the horizontal spring shaft then it is doing a work.

And when the ship is pushing the spring against the ball, it is doing work as well.

The trajectory s is horizontal and the inertia of the ball is pushing the shaft - the ball is doing work F*s.
The ball is losing its kinetic energy, transferred to the horizontal spring potential energy,
... but it is NOT slowing down the ship!

If the balls are losing kinetic energy, then the ship is too. Remember, the situation is perfectly symmetrical. From the reference frame of the balls, the balls are sitting still and the springs are moving towards them. From the balls' point of view, the kinetic energy of the ship-spring system is what is compressing the springs because the balls have no kinetic energy in their own reference frame. From the reference frame of the barycenter, energy from both the balls and the ship are being used to compress the springs.

Kryptid,
The balls start to rotate in the barycenter frame.
The balls velocity component down is getting smaller because of this rotation in the barycenter frame.
The spaceship velocity component up is not getting smaller because the spaceship does not rotate in the barycenter frame.



If you look at the figure. The 'ideal' absorber is stiff, does not bend, just provides deflection.
When the deflection happens the spring is wind-up and locked.
If we pair the left absorber with the same type absorber on the other side of the spaceship then the spaceship will not rotate.
The spaceship stays inertial and the balls start to rotate in the barycenter frame.
Why?

Because, the work done on the pair of springs in the figure above is the same as in the figure below.
If the spaceship system with balls is moving upwards the motion of the balls have no effect on the upward velocity.
The constraint forces, 90 degrees to the velocity.



Going back to the deflected ball.
The short time after the deflection the ball is still free-flying but on a different trajectory.
The work done on the spring did not change the spaceship velocity/momentum in the barycenter frame.
The deflected free-flying ball has smaller velocity/momentum in the downward direction because the velocity vector direction change does not come free, the angular momentum does not come free.
I hope this helps,
Jano

[Kryptid]

The balls velocity component down is getting smaller because of this rotation in the barycenter frame.

No, it's getting smaller because it's meeting resistance. The act of compressing a spring creates a force against whatever is compressing it. So you can just as easily redesign the system where the balls are prevented from rotating and you get the same result.

The spaceship velocity component up is not getting smaller because the spaceship does not rotate in the barycenter frame.

Again, the resistance caused by the spring is what causes the ship to slow, not rotation.

The work done on the spring did not change the spaceship velocity/momentum in the barycenter frame.

Yes it did, for reasons I've mentioned.

I hope this helps,

It doesn't because it's wrong. You can't break the law of conservation of momentum.

[Jaaanosik (OP)]

Kryptid,
The spaceship moves upwards/forward.
Are you saying that the horizontal motion will slow down the spaceship?
Are you saying that winding-up the springs on the absorbers will slow down the spaceship?
Jano

[Kryptid]

Kryptid,
The spaceship moves upwards/forward.
Are you saying that the horizontal motion will slow down the spaceship?
Are you saying that winding-up the springs on the absorbers will slow down the spaceship?
Jano

In this most recent image of yours, there is no upward movement. The balls are moving to the side. So it isn't akin to the previous version. In your earlier version, the spring paddles are at a 45 degree angle to the trajectory of the balls. This means that both a horizontal and a vertical component to the force will be present when the ball hits the paddle. The horizontal component will go into compressing the spring, whereas the vertical component will be carried through the paddle and spring to the wall of the ship where the spring is attached. It is this vertical component that slows down the ship.

We could spend all day talking about various designs, but the fact of the matter is that the laws of physics will not allow them to work. We know before we begin any kind of analysis that the total momentum of the system must be identical at all stages of the machine's working. If you discover at the end of your analysis that the total momentum has changed, then you must have made an error in your analysis somewhere. This is demanded by conservation of momentum. Conservation of momentum, in turn, is demanded by Noether's theorem: https://en.wikipedia.org/wiki/Noether%27s_theorem

Take note how Noether's theorem is a theorem and not a theory. A theory is supported by scientific evidence, whereas a theorem is supported by mathematical proof: https://en.wikipedia.org/wiki/Theorem

[Jaaanosik (OP)]

Kryptid,
Please, have a look here: https://en.wikipedia.org/wiki/Momentum#Multiple_dimensions



I rotated the figure to follow wiki example.
How big momentum goes to the bottom absorber (on the right now)?



Do you have a new theory about momentum?
Jano

[Kryptid]

How big momentum goes to the bottom absorber (on the right now)?

All of the ball's forward momentum goes into it.

Do you have a new theory about momentum?

No. I have no need for it. The existing one is good enough.

[Jaaanosik (OP)]

How big momentum goes to the bottom absorber (on the right now)?

All of the ball's forward momentum goes into it.

Do you have a new theory about momentum?

No. I have no need for it. The existing one is good enough.

Kryptid,
The bold part, you are not serious, are you?
Jano

[Kryptid]

Kryptid,
The bold part, you are not serious, are you?
Jano

On second thought, perhaps not. I imagine some of the forward momentum could be transmitted to the ship floor through the bottom spring (not by compressing the bottom spring, mind you, but by applying a sideways force through the rod connecting it to the floor). The exact ratio of how much of the forward momentum goes into compressing the right spring and how much gets transmitted through the rod holding the bottom spring, I do not know. It ultimately doesn't matter though, as the total must necessarily be equal and opposite to the amount of the ship's momentum (due to Newton's third law) it cancels out. If the ball comes to a complete stop, then the ship has to as well. That's Newton's third law.

[Jaaanosik (OP)]

Kryptid,
The bold part, you are not serious, are you?
Jano

On second thought, perhaps not. I imagine some of the forward momentum could be transmitted to the ship floor through the bottom spring (not by compressing the bottom spring, mind you, but by applying a sideways force through the rod connecting it to the floor). The exact ratio of how much of the forward momentum goes into compressing the right spring and how much gets transmitted through the rod holding the bottom spring, I do not know. It ultimately doesn't matter though, as the total must necessarily be equal and opposite to the amount of the ship's momentum (due to Newton's third law) it cancels out. If the ball comes to a complete stop, then the ship has to as well. That's Newton's third law.

Kryptid,
there is nothing wrong to follow the free body diagram.
1/2 of the initial momentum stays in the ball and 1/2 goes to the tilted plate.
1/2 of the tilted plate momentum (1/4 of the original momentum) goes to the side spring and stays there locked.
The second 1/4 goes to the bottom spring, it can be locked as well.
The cycle continues, the ball will hit another pair of absorbers, then another, ...
We can have an array of this deflectors.

The end result is obvious.
A significant amount of the original ball kinetic energy is locked in the side springs.
Not all energy goes to the bottom springs.
This is obvious now, I hope.
We have a forward net momentum.
The pressure on the sides is not going to slow down the spaceship forward motion,
Jano

[Kryptid]

We have a forward net momentum.

I think you missed this:

We could spend all day talking about various designs, but the fact of the matter is that the laws of physics will not allow them to work. We know before we begin any kind of analysis that the total momentum of the system must be identical at all stages of the machine's working. If you discover at the end of your analysis that the total momentum has changed, then you must have made an error in your analysis somewhere. This is demanded by conservation of momentum. Conservation of momentum, in turn, is demanded by Noether's theorem: https://en.wikipedia.org/wiki/Noether%27s_theorem

Take note how Noether's theorem is a theorem and not a theory. A theory is supported by scientific evidence, whereas a theorem is supported by mathematical proof: https://en.wikipedia.org/wiki/Theorem

[Jaaanosik (OP)]

We have a forward net momentum.

I think you missed this:

We could spend all day talking about various designs, but the fact of the matter is that the laws of physics will not allow them to work. We know before we begin any kind of analysis that the total momentum of the system must be identical at all stages of the machine's working. If you discover at the end of your analysis that the total momentum has changed, then you must have made an error in your analysis somewhere. This is demanded by conservation of momentum. Conservation of momentum, in turn, is demanded by Noether's theorem: https://en.wikipedia.org/wiki/Noether%27s_theorem

Take note how Noether's theorem is a theorem and not a theory. A theory is supported by scientific evidence, whereas a theorem is supported by mathematical proof: https://en.wikipedia.org/wiki/Theorem

Where did I break the conservation of energy or conservation of momentum?
What is wrong with changing the linear momentum to angular momentum?
Jano

[Kryptid]

Where did I break the conservation of energy or conservation of momentum?

When the spacecraft starts off, it is stationary. The total momentum of the system is zero. So if the total momentum ever changes from zero, then conservation of momentum has been violated. You claim that your system creates net momentum and therefore you claim that your system can violate conservation of momentum.

What is wrong with changing the linear momentum to angular momentum?

Linear momentum and angular momentum are both their own, conserved phenomena. They are not interchangeable. If the linear momentum and angular momentum both start off at zero, then both must remain at zero.

[Jaaanosik (OP)]

Where did I break the conservation of energy or conservation of momentum?

When the spacecraft starts off, it is stationary. The total momentum of the system is zero. So if the total momentum ever changes from zero, then conservation of momentum has been violated. You claim that your system creates net momentum and therefore you claim that your system can violate conservation of momentum.

What is wrong with changing the linear momentum to angular momentum?

Linear momentum and angular momentum are both their own, conserved phenomena. They are not interchangeable. If the linear momentum and angular momentum both start off at zero, then both must remain at zero.

Kryptid,
we can transform kinetic energy to rotational energy but we cannot transform linear momentum to angular momentum?
Please, remember what I said.
A spaceship collects the interstellar hydrogen and helium would be fused with huge amount of excess energy.
The hydrogen potential energy is incoming into the system, no physical objects are ejected out (radiation is different).
So the increase of the internal kinetic energy cannot be transformed to external kinetic energy?
The work energy principle does not apply, F*s (dot product) is not good, correct?

Linear momentum and angular momentum are both their own, conserved phenomena. They are not interchangeable. If the linear momentum and angular momentum both start off at zero, then both must remain at zero.

This is important!
Are you sure the linear momentum cannot be converted to angular momentum?
My original proposal revolves around 'bending' the laws of physics.
The external potential energy transforms into linear kinetic energy at the front of the spaceship.
The balls/cylinders are thrown back and the kinetic energy is transformed into rotational energy.
The balls/cylinders can generate electricity till they stop at the back of the spaceship. The electricity can generate a heat and it can be radiated outside at the back.
Then they can be transferred to the front of the spaceship in a manner that they do not pickup rotational energy.
The front: hydrogen -> potential energy -> electricity -> gun -> linear kinetic energy
The back: linear kinetic energy -> rotational energy -> electricity -> heat -> radiation
Where is the conservation of energy broken here?
The most important step here is the incoming linear kinetic energy = outgoing kinetic energy + rotational energy.
Does energy rule or not?
Jano

[Kryptid]

we can transform kinetic energy to rotational energy but we cannot transform linear momentum to angular momentum?

No, you can't: https://van.physics.illinois.edu/qa/listing.php?id=24173&t=is-linear-momentum-converted-to-angular-momentum

So the increase of the internal kinetic energy cannot be transformed to external kinetic energy?

It can't produce net momentum, no.

Are you sure the linear momentum cannot be converted to angular momentum?

Yes. See the link above.

Where is the conservation of energy broken here?

It isn't. Conservation of momentum is what is broken.

[Jaaanosik (OP)]

we can transform kinetic energy to rotational energy but we cannot transform linear momentum to angular momentum?

No, you can't: https://van.physics.illinois.edu/qa/listing.php?id=24173&t=is-linear-momentum-converted-to-angular-momentum

So the increase of the internal kinetic energy cannot be transformed to external kinetic energy?

It can't produce net momentum, no.

Are you sure the linear momentum cannot be converted to angular momentum?

Yes. See the link above.

Where is the conservation of energy broken here?

It isn't. Conservation of momentum is what is broken.

Kryptid,
No, there is only one momentum, angular momentum.
The linear momentum is angular momentum!!!!
The linear momentum is angular momentum that has infinite radius, the axis of rotation is infinitely far away,
Jano

[Jaaanosik (OP)]

Kryptid,
you do not trust me?
Here: https://www.khanacademy.org/science/ap-physics-1/ap-torque-angular-momentum/conservation-of-angular-momentum-ap/v/ball-hits-rod-angular-momentum-example

Jano

[Jaaanosik (OP)]

This is not new theory, this is physics!
Jano