Energy question, what are the quantities conserved?

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The discussion centers on identifying conserved quantities in a physics problem involving a particle influenced by forces. The participant expresses uncertainty about the conservation of momentum and angular momentum due to the presence of force and torque acting on the particle. They conclude that energy is conserved along both the x and y axes, which helps them progress towards solving the problem. The equations of motion for the particle suggest that while momentum may not be conserved, energy conservation can still apply. Overall, the focus is on understanding the conservation laws relevant to the motion of the particle.
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Homework Statement


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Homework Equations

The Attempt at a Solution


I don't know how to do the last part. What are the additional conservation laws? I don't think momentum is conserved because there is force acting on the particle. I don't think angular momentum is conserved too because there is a torque acting on the particle.
Here is the numerical answer:
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Note that the equation for ##\ddot x## involves only ##x## (not ##y##). Similar comment for ##\ddot y##.

Imagine the x equation described a particle moving only along the x-axis. Anything conserved in this x-motion?
 
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TSny said:
Note that the equation for ##\ddot x## involves only ##x## (not ##y##). Similar comment for ##\ddot y##.

Imagine the x equation described a particle moving only along the x-axis. Anything conserved in this x-motion?
Thank you, I think the energy along x and y-axis are conserved too. Then I can find the answer.
 
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