Question

A 900-kg roller coaster car is initially at the top of a rise, at point A. It then meves 145ft, at an angle of 40.0⁰ on below the horiesinta, to a lower point X. Choose the car at point R to be the zero configuration for gravitationai potential enerwy of the roller coasiter-Earth system, Find the potential energr of the syitem mhen the car is at points (A) and (R), and the change in botential energy at the coaster moves between these points.

Answer 1

The potential energy at point A is calculated using the mass of the roller coaster, the height from point R, and the acceleration due to gravity. Point R has zero potential energy. The change in potential energy is the difference between the potential energy at point A and point R.

Step-by-step explanation:

The potential energy (PE) of the roller-coaster-Earth system when the car is at point A can be found using the equation PEA = mghA, where m is the mass of the roller coaster car, g is the acceleration due to gravity (9.8 m/s2), and hA is the height of point A from the reference point R. Since point R is the zero configuration for gravitational potential energy, the potential energy at point R is PER = 0.

To find the height hA when the car moves down to point X, we can use trigonometry. The car moves down at an angle of 40.0° to a distance of 145 ft, which must be converted into meters for consistency with SI units (1 ft = 0.3048 m). The height hA is then given by hA = 145 ft × sin(40.0°). The change in potential energy as the coaster moves between these points (ΔPE) is the difference in potential energy at point A and point R, which is ΔPE = PEA - PER.