Can you provide a source that gives an scientifically sound experiment where this was proven?
Yep. Your 32 oz. cup experiment does a fine job demonstrating FE's failure. The classic boy on a sled experiment also provides a great proof. You'll find it in almost all high school physics textbooks, usually in the chapter on friction.
Your boy on a sled experiment proved nothing. When I asked you where the 'missing energy' in the FE model goes, you did not respond. In the boy on a sled experiment, the energy does not just disappear, it goes to a different location.
Well, equal forces was your asserting, so the burden to show that that is yours. If you don't understand that, then you'd don't debating. If you believe that all energy goes to work, then you don't understand physics. Oh, the little brother on the sled does prove that two different mechanisms can achieve the same work with different amounts of force.
Believe what you want TomG, but matter and energy cannot be created or destroyed last time I checked. Even if it's a different mechanism, the energy still has to go somewhere. You continue to not tell me where the energy goes. I would like to know, because if I'm wrong then I can learn. Could you explain where it went?
Well, let's start with your understanding of matter and energy being created and destroyed. Neither energy or matter can be created or destroyed in a closed system except from one to another as given by Einstein's famous equation: E=mc
2.
Next, you're arguing that the force must be the same. You have the burden of proof.
Finally, let's go over work and energy. Work is the productive expenditure of energy. All mechanical systems are inefficient. Some energy is wasted, converted to heat through friction or to noise or to moving the item in the wrong direction. In the case of your little brother on the sled, you waste energy melting the ice under the runners. In the RE case of tides, the Moon "wastes energy" in creating tides by the friction of the ocean over the ocean floor. In the FE case of tides, the moving of the FE wastes energy tilting the whole Earth, not just the ocean. To argue that the force in both cases must be equal is supportable--until you calculate the energy required to tilt the FE (The energy wasted by the Moon has long been calculated.). I don't believe that you'll ever be able to determine the energy required to tilt the FE until FE states the mass of the FE.