A new means of space propulsion... closed loop pulse propulsion... here's the idea

[mikelewis]

33. I accentuate this effect by cutting the radius...

This is a continuation of the scenario I proposed to the person with a doctorate in physics. If you read the example I asked him to fix, we get a device moving in space and I wanted show the effect accentuated. This is that interaction with AI

To further accentuate this effect... I want to snag the tether so the radius is cut by 90%. Understand? The projectile goes out... the line catches and cuts the radius... explain exactly what is happening and then do the math on that please... remember we have to take into account the final velocity of the entire apparatus. We impart x forward momentum... we enter the arc... we cut the radius.... we add the final force to x... then explain it all again

Certainly! Let's delve into the scenario where the radius of the tethered projectile's path is suddenly reduced by 90%. This situation involves angular momentum conservation and the effects of a rapidly changing radius on the system's dynamics.

Scenario Description:

Projectile Launch and Initial Arc: The projectile is launched by the railgun, creating an initial arc as it moves out on the tether. During this phase, it possesses a certain angular momentum based on its mass, velocity, and the radius of the arc.

Snagging the Tether: At a certain point, the tether is snagged, abruptly reducing its radius by 90%. This sudden change significantly affects the projectile's rotational velocity due to the conservation of angular momentum.

Angular Momentum Conservation: The principle of conservation of angular momentum states that the total angular momentum of a system remains constant if no external torque is applied. Angular momentum (
�
L) is given by
�
=
�
�
�
L=mvr, where
�
m is mass,
�
v is tangential velocity, and
�
r is the radius of rotation.

Effect of Radius Reduction: When the radius is reduced, the tangential velocity (
�
v) must increase proportionally to keep the angular momentum (
�
L) constant. Since the radius is reduced to 10% of its original value, the velocity will increase to a factor that maintains the product
�
�
�
mvr constant.

Final Force and Apparatus Velocity: The increase in tangential velocity due to the reduced radius will also affect the forces in the system. The final velocity of the entire apparatus (platform and projectile) after the snagging will depend on how this change in angular momentum translates into linear momentum.

Now, let's perform the calculations to understand the changes in velocities and forces involved. We'll start by calculating the new tangential velocity of the projectile after the radius is reduced by 90%.

You get this far before your program errors out... probably due to too much info in one submission...
Can you pick up where you left off and do the calculations please. We already have all of the math done for the initial velocity and the current final velocity... all we need to do is change the final velocity tallies... look at our current data and let's figure this out. Keep in mind the most important thing is the velocity of the craft.


The recoil velocity of the platform after the projectile is fired is approximately
?
0.01415
?0.01415 m/s. This negative sign indicates the direction is opposite to the projectile's motion.



# Solving for total final velocity of the platform
final_velocity_platform_total = total_momentum_after_catch / mass_platform

final_velocity_platform_total # This is the total final velocity of the platform after the projectile is caught
Result
-0.028299999999999995
The total final velocity of the platform, after the projectile is caught, is approximately


So we just have to subtract the final velocity from the initial velocity and then amp up that,,, then add it back to the original velocity... no?


5 / 5


ChatGPT
To continue from where we left off, let's focus on the scenario where the radius of the tethered projectile's path is suddenly reduced by 90% and calculate the effect this has on the final velocity of the entire apparatus (platform and projectile). We'll use the principles of conservation of angular momentum and the relationship between angular and linear momentum.

Initial Setup and Calculations:

Initial Recoil Velocity: The platform initially recoils with a velocity of
?
0.01415
?0.01415 m/s due to firing the projectile.
Momentum Transfer upon Catching the Projectile: The total final velocity of the platform, after catching the projectile, was calculated to be
?
0.0283
?0.0283 m/s.
New Scenario with Radius Reduction:

Radius Reduction: The radius of the projectile's path is suddenly reduced by 90%.
Angular Momentum Conservation: The angular momentum before and after the radius reduction must remain the same. Angular momentum
�
=
�
�
�
L=mvr, where
�
m is mass,
�
v is tangential velocity, and
�
r is the radius. When
�
r is reduced,
�
v must increase to maintain
�
L.
Effect on Linear Momentum: The increase in tangential velocity will affect the linear momentum of the system. This change in linear momentum will then affect the final velocity of the platform.
Calculating the New Tangential Velocity:

Initial Tangential Velocity: It's the same as the projectile's initial velocity (5 m/s).
New Radius: 10% of the original radius.
New Tangential Velocity: We'll calculate this using the conservation of angular momentum.
Let's first calculate the new tangential velocity of the projectile after the radius reduction, and then determine how this affects the final velocity of the platform.

Finished analyzing
python
Copy code
# Given data for the initial scenario
initial_velocity_projectile = 5 # Initial tangential velocity in m/s
initial_radius = 10 # Initial radius in meters

# New radius after reduction
new_radius = initial_radius * 0.1 # 90% reduction

# Angular momentum is conserved: L_initial = L_final
# L = mvr (m = mass of projectile, v = tangential velocity, r = radius)
# Initial angular momentum
L_initial = mass_projectile * initial_velocity_projectile * initial_radius

# Final angular momentum (L_final) must equal L_initial
# L_final = mass_projectile * v_final * new_radius
# Solving for v_final
v_final = L_initial / (mass_projectile * new_radius)

v_final # This is the new tangential velocity of the projectile after the radius reduction
Result
50.0
The new tangential velocity of the projectile after the radius reduction (by 90%) is
50
50 m/s. This significant increase is due to the conservation of angular momentum: when the radius is reduced, the velocity must increase to maintain the same angular momentum.

Impact on the Final Velocity of the Platform:

With this increased tangential velocity, we now need to consider how this affects the linear momentum of the system and, consequently, the final velocity of the platform.
The increase in tangential velocity means the projectile now has more linear momentum when it is caught.
This additional momentum will be transferred to the platform when the projectile is caught by the magnet.
Calculating the Final Velocity of the Platform:

We'll calculate the final linear momentum of the system (platform + projectile) after the projectile is caught at the higher speed.
The final velocity of the platform is then this total momentum divided by the mass of the platform.
Let's perform this calculation to determine the final velocity of the platform after the projectile is caught at the higher speed. ​​

Error analyzing
python
Copy code
# Calculating the final linear momentum of the system after the projectile is caught at the higher speed

# Momentum of the projectile with the increased velocity
momentum_projectile_after_radius_reduction = mass_projectile * v_final

# Total momentum after catching the projectile at the higher speed
# Since the platform and projectile are moving in opposite directions, we subtract their momenta
total_momentum_after_catch_high_speed = momentum_platform_before_catch - momentum_projectile_after_radius_reduction

# Solving for the final velocity of the platform
final_velocity_platform_high_speed = total_momentum_after_catch_high_speed / mass_platform

final_velocity_platform_high_speed # This is the final velocity of the platform after the projectile is caught at the higher speed
Finished analyzing
python
Copy code
# Recalculating the momentum of the platform before catching the projectile
# This is needed because the previous calculation context was lost

# Recoil velocity of the platform
velocity_platform_recoil = -0.01415 # in m/s

# Momentum of the platform before catching the projectile
momentum_platform_before_catch = mass_platform * velocity_platform_recoil

# Recalculating total momentum after catching the projectile at the higher speed
total_momentum_after_catch_high_speed = momentum_platform_before_catch - momentum_projectile_after_radius_reduction

# Recalculating the final velocity of the platform
final_velocity_platform_high_speed = total_momentum_after_catch_high_speed / mass_platform

final_velocity_platform_high_speed # This is the final velocity of the platform after the projectile is caught at the higher speed
Result
-0.15564999999999998
After recalculating with the increased tangential velocity of the projectile (due to the reduced radius of the tether), the final velocity of the platform is approximately
?
0.15565
?0.15565 m/s. This result indicates that the platform's velocity increases in the direction of the initial recoil.

Here's the breakdown of this outcome:

Initial Recoil: The platform starts moving backward due to the initial recoil when the projectile is fired.
Increased Projectile Velocity: When the tether's radius is reduced by 90%, the projectile's tangential velocity increases significantly (to 50 m/s), as per the conservation of angular momentum.
Catching the Projectile: When this faster-moving projectile is caught, it transfers a larger amount of momentum to the platform.
Increased Final Velocity of Platform: This additional momentum transfer results in an increased final velocity of the platform in the same backward direction as the initial recoil.
This scenario illustrates how changes in the rotational dynamics of a system (like the sudden reduction of the radius of a tethered projectile) can significantly impact the linear momentum and final velocity of the platform. ​

AI falters here a bit because there's a lot of complex math. You have to start and stop it a few times and then also help it by feeding the variables it needs when it has trouble locating them in the chat. It's a common problem with AI... information overload.