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Consider the situation: a body slides down on a wedge with only gravitational force as an external force. I calculate the the velocity of the body in the wedge's frame using work energy theorem. Now I use this velocity of the body to find the velocity of the wedge in ground frame using conservation of momentum. The point is that can I do this? That is, can I use two separate frames to find different quantities and then relate both to find something else?

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You can do this, with some caveats:

  • Some frames of reference will show objects as having different velocities. You will need to convert the velocity into the new frame to continue.
  • Some values, such as energy, are conserved within a frame but are not conserved when changing frames of reference. Thus, you can use energy to calculate the velocity within the wedge frame, but you would get in trouble if you calculated the energy of the body in one frame, and then used that energy number to do conservation of energy calculations in another frame.
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The first place you're going wrong is that you're talking about velocity at a place the only thing you can talk about is acceleration. If you're talking of a time dependant expression for velocity, then I suggest that you use acceleration to avoid ambiguity. Now, coming to you using the Conservational Law of Momentum: think if you can apply that to a system where external forces are influencing the bodies' motion. Hope this helps.

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