Solving the Spaceship Problem: Comparing Forces

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The discussion centers on the physics of two identical spaceships, one stationary and the other moving at a constant speed, both starting their engines simultaneously. Participants debate whether the spaceship traveling at a higher initial speed experiences a different force compared to the stationary one. The consensus leans towards the idea that both spaceships feel the same force due to the principle of Galilean relativity, which states that initial speed does not affect the force experienced during acceleration. The reasoning emphasizes that both spaceships will accelerate equally, leading to the same force being felt by their occupants. Ultimately, the conclusion is that initial speed is irrelevant when both spaceships accelerate simultaneously.
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dear friends, days ago on a physics forum I saw this interesting question regarding fixed power and speed of a spaceship. After thinking for a while I came up with my answer but I am not really sure its correct.So please tell me what you think the answer is.

The question is: imagine there are 2 identical spaceship(with 2 identical engines),1 in stationary state,other travels at constant speed in a straight direction.Now 2 engines starts, how do people in different spaceship feel about the force(or the acceleration)?

some people believe that the one with higher initial speed(lets call it spaceship B) "feels" more force acting on it, becoz of the formula p=fv(since p is fixed, f decreases while v increases).

Somehow I disagree with it.(tell me if i am wrong:))
here is my reasoning:
since the way spaceship's engine works is to utilise the reaction force of its emitted gas(i don't know how to describe it but i assume you understand:)), so the velocity in the formula has something to do with the gas.Since both spaceships A and B was in balanced state, after the engines starts(assuming they start at the same time), A and B would travel at the same accelerating speed at any given time(take their emitted gas as reference frame).since p=fv, f is the same.
so my conclusion is people in both spaceship would feel the same force when the engines start at the same time. If i am wrong about this, please tell me why.
 
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The "one with the higher initial speed" thinks that the other one is the one with the initial speed. Each spaceship thinks that they are the one that is stationary. And so each spaceship uses "v=0" in their own equation.

mrhoneycinnamo said:
so my conclusion is people in both spaceship would feel the same force when the engines start at the same time. If i am wrong about this, please tell me why.

Yes, I believe this conclusion is correct. (I didn't completely follow your reasoning, though.)
 
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"Force equals mass times acceleration". With the same acceleration, the same force will be felt. Initial speed is irrelevant. That goes back to "Gallilean relativity".
 
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