Ubergeekian
Well-Known Member
Like I said, conseration of energy. The road has no energy in and of itself, only in relation to the cart. Honestly, if you step off the cart the road stops moving.
You're making the mistake of changing your reference frame. Think of it relative relative to the ground. When you step off the cart you slow down and the momentum you lose is transferred to the ground, which then speeds up. Bingo - energy transfer.
In practice the mass of the earth is so large that its velocity can be assumed to be unchanging, whichever reference frame you use. Note that in the boat case there will be significant energy transfers to and from the sea.
So using the road to power the cart is exactly the same as using the cart to power itself.
No.