The energy is converted to other types of energy, namely heat and sound. The steeper the slide and the faster you’re going, the more noticeable it will be. If you’ve ever dragged your bare skin while going down a slide and had a slight burn, or the loud squeaking your shoes make if you drag them to stop yourself.
I’m less certain about this part(high school physics was a long time ago), but I believe some of it would also be converted to potential energy. If you stopped yourself halfway down a steep slide, you would have to use some effort to hold yourself there because of gravity. As soon as you let go, you would start gaining momentum again(kinetic energy).
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.
All these answers about heat and sound are wrong.
In a theoretical, ideal scenario, momentum is conserved and simply transferred between objects in a system. In our case, our system includes you, the slide, and the rest of the earth. So when stopping yourself, your momentum is being transferred first to the slide and subsequently to the whole earth. In this ideal scenario, this is no different from just landing from a jump.
Because real life is messy, *some* of this momentum is lost due to heat and sound. Only some, though. Most of the momentum is just transferred to the earth, but since the earth is relatively ginormous, this has no measurable effect.
Astrophysics and Aerospace Engineering degree here. You talk about energy and momentum, so I’ll cover both. I’m also going to stay with Newtonian physics.
Assume the energy to start was the potential energy at the top of the slide. As you started to slide down, you gain equal kinetic energy from lost potential energy (minus friction). When you stop with your hands, you convert the gained kinetic energy to friction losses (heat and sound). You basically converted your distance from Earth’s gravity well for heat and sound.
Momentum is conserved with two momentums in opposite directions. When you climbed up the slide, you pushed off from the Earth’s mass. Both move, but you move far more because your mass is far smaller. When you slide down, you release a normal force that prevented the Earth and you from moving closer to each other from gravity. Again, you move far more in relation to the Earth. When you stop with your hands, you re-apply the normal force. Then, both you and Earth stop moving in relation to each other. People are saying that you slightly move Earth when you stop, but you actually stop slightly moving Earth when you stop.
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