The roller coaster ride starts from rest at point A. Assume friction is negligible. Rank the following quantities from greatest to least at each point.
a.   PE
b.   KE
c.   Speed
The Correct Answer and Explanation is :.
Assumptions:
- Friction is negligible, so mechanical energy (PE + KE) is conserved.
- The roller coaster starts from rest at point A (PE is maximum, KE is zero).
Points:
Let’s assume there are three main points in the ride: Point A (start), a point at the highest peak, and a point at the lowest dip.
1. At Point A (Starting Point):
- Potential Energy (PE): At the highest point, PE is at its maximum because the roller coaster has the most height relative to the ground.
- Kinetic Energy (KE): Since the ride starts from rest, KE is zero.
- Speed: Since KE = 1/2mv², if KE is zero, the speed is also zero.
2. At the Highest Point (e.g., after a hill or peak):
- PE: Still relatively high, but less than at Point A, because the coaster has descended a bit.
- KE: As the car moves downwards from the peak, some PE is converted into KE, so KE increases.
- Speed: Speed increases as KE increases, but since the coaster is still relatively high, the speed might not be at its greatest yet.
3. At the Lowest Point (e.g., at the bottom of a dip):
- PE: PE is at its minimum because the roller coaster is at its lowest height.
- KE: KE is at its maximum because almost all the initial PE has been converted to KE.
- Speed: Since KE = 1/2mv², the speed will be at its greatest, because KE is maximized.
Ranking:
- PE (Potential Energy): Greatest at Point A > Highest Peak > Lowest Dip.
- KE (Kinetic Energy): Greatest at Lowest Dip > Highest Peak > Point A.
- Speed: Greatest at Lowest Dip > Highest Peak > Point A.
This explanation follows from the principle of conservation of mechanical energy, where the total energy (PE + KE) remains constant throughout the ride, but energy continuously transforms between potential and kinetic forms depending on the height of the coaster.