- The total mechanical energy (kinetic + potential) of the roller coaster car is conserved if we assume no friction or air resistance.
- At the top of the first hill, the car has initial kinetic energy (1/2)mv₀² and potential energy mgh.
- At point A, which is at the same height h as the starting point, the potential energy is again mgh. By conservation of energy, the kinetic energy must be the same as at the start, so the speed at A equals v₀.
- At point B, which is at height h/2, the potential energy is mg(h/2). Since total energy is conserved, the kinetic energy at B is greater than at A. Specifically, it gains kinetic energy equal to the loss in potential energy: mg(h - h/2) = mgh/2. So the speed at B is greater than v₀.
- At point C, which is at the bottom (height 0), the potential energy is zero. All the initial mechanical energy is now kinetic. The kinetic energy at C is (1/2)mv₀² + mgh, so the speed at C is the highest of all points.
- Therefore, ranking the speeds from greatest to least: C > B > A.
Parent Tip: Review the logic above to help your child master the concept of conservation of mechanical energy worksheet.
