I had crap science teachers so forces in physics never really made sense to me. I understand that my momentum has a kind of energy to it…so if I stop myself on the slide where does that energy go?
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A small amount of the energy could be lost to heat if you held your hands at a static location to your sides, but the overwhelming majority of energy transferred will not be due to this. Your hands have to be slipping for anything to be lost this way, and that was not stipulated in the OP.
If you gripped the edges of the slide, and reversed the arrow of time, what would the interaction look like? You pulling yourself up the slide. Where does the energy come from? Your muscles. In the forward direction of time, with anchored hands, it’s actually the same thing. At some point while you are decelerating, your hands will stop slipping and this state will apply.
You’re using your muscles to accelerate your body relative to an anchored point, the slide, whether your hands are slipping or anchored. Newton’s Third Law, the force applied to you is the same as applied to the slide, and so you do “transfer” some energy into the Earth this way.
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