(a) To find the potential energy of the roller coaster car at points A and B, we can use the equation:
Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
1. At point A:
- Mass (m) = 1000 kg
- Acceleration due to gravity (g) = 9.8 m/s² (assuming Earth's gravity)
- Height (h) = 0 ft (since point B is chosen as the zero configuration for gravitational potential energy)
Using the formula, the potential energy at point A is:
PE_A = 1000 kg * 9.8 m/s² * 0 ft
= 0 Joules
2. At point B:
- Mass (m) = 1000 kg
- Acceleration due to gravity (g) = 9.8 m/s²
- Height (h) = 135 ft
Converting the height to meters:
135 ft * 0.3048 m/ft = 41.148 m
Using the formula, the potential energy at point B is:
PE_B = 1000 kg * 9.8 m/s² * 41.148 m
= 404,060 Joules (rounded to the nearest whole number)
3. To find the change in potential energy as the car moves from point A to point B:
Change in PE = PE_B - PE_A
= 404,060 Joules - 0 Joules
= 404,060 Joules
Therefore, the potential energy of the roller coaster car at point A is 0 Joules, at point B is 404,060 Joules, and the change in potential energy as the car moves between these points is 404,060 Joules.
(b) If we set the zero configuration with the car at point A, the potential energy at point A would be considered zero.
1. At point B:
- Mass (m) = 1000 kg
- Acceleration due to gravity (g) = 9.8 m/s²
- Height (h) = 135 ft
Converting the height to meters:
135 ft * 0.3048 m/ft = 41.148 m
Using the formula, the potential energy at point B is:
PE_B = 1000 kg * 9.8 m/s² * 41.148 m
= 404,060 Joules (rounded to the nearest whole number)
2. To find the change in potential energy as the car moves from point A to point B:
Change in PE = PE_B - 0 Joules
= 404,060 Joules - 0 Joules
= 404,060 Joules
Therefore, the potential energy of the roller coaster car at point A is considered zero, at point B is 404,060 Joules, and the change in potential energy as the car moves between these points is 404,060 Joules.