I am a biologist developing an interest in physics. I am struggling with the implications of changing reference frames on momentum, mechanical energy and work done calculations. I invented the situation in the diagrams below to try and work stuff out but the outcomes do not fit with what I believe are the correct physical principles. Can anyone assist me?
The diagrams show the situation. Starting in the ground reference frame I have first calculated velocity after collision via conservation of momentum and mechanical energy. I hope this is correct.
I believe that while the momentum and mechanical energy values will differ for different reference frames, the values should be conserved within a reference frame before and after an elastic collision. I have calculated momentum and kinetic energy values for the 2kg ball reference frame and momentum does not appear conserved in this scenario. I cannot figure out what my error is.
A final question. Imagine we have another ball to the left which is not involved in the collision and is stationary. In the ground reference frame the momentum and mechanical energy are both conserved. In the reference frame of the 2kg ball, neither momentum nor mechanical energy are conserved. Is this something wrong with the way I have defined the system as I could add any number of stationary objects fixed to the Earth which in the ground reference frame would have no momentum or mechanical energy but in the reference frame of the ball would have momentum and kinetic energy meaning the conservation principles do not work. In general I am unclear on the concept of system in mechanics. I have this working notion: In mechanics a system consists of an object or group of objects whose motion is being described.
The velocities in the 2kg reference frame examples should be correct based on the original velocities I stipulated in the ground reference frame. Any help would be much appreciated.