Final answer:
Possible locations of static equilibrium on a roller-coaster track can be stable, unstable or neutral. Stable equilibrium occurs at the bottom of a deep curve or loop, while unstable equilibrium occurs at the top of a hill or steep incline. Neutral equilibrium can be found at the highest point of a loop.
Step-by-step explanation:
When considering static equilibrium for a roller-coaster car on a portion of the track, candidate locations can be identified based on the forces acting on the car. Stable equilibrium occurs when a car is in a position where it will return to its original position if slightly displaced. Unstable equilibrium occurs when a car is in a position where it will move away from its original position if slightly displaced. Neutral equilibrium occurs when a car is in a position where it will remain in that position if slightly displaced.
In the case of the roller-coaster track, possible locations of stable equilibrium are at the bottom of a deep curve or loop, where the gravitational force keeps the car in position. Unstable equilibrium can be found at the top of a hill or steep incline, where the car is prone to rolling back down. Neutral equilibrium can occur at the highest point of a loop, where the car experiences minimal net force.