Physics of roller coaster rides are based on the laws of classical physics or the newton laws of motion.
Imagine a roller coaster that goes down with the head pointing downwards. We all know that if we try to hang upside down, we will fall. Then why not we fall when the roller coaster goes down? There are two forces, one gravity, that will pull down the body, and the opposite force caused by the rotation of the amusement park, which balances down pull due to gravity.
Similarly, roller coasters are not controlled by external force when they go up. When the roller coaster travels upwards, it must go against the force of gravity that pulls it down. But the coaster does not use any motors or any fuel to push it up against gravity. In fact, when the roller coaster ride down it gains speed by virtue of the free fall. When this lowest point has a sufficient amount of energy that it receives through the natural movement down that ended the vertical segment without an additional external power source as combustion engine or fuel.
The beauty of roller coaster is something that follows the natural laws of the classical movement. Only at first some kind of external force must be supplied, when it prevails, that only the natural laws of motion.
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