Final answer:
Using the formula for potential energy, the objects arranged from least to greatest potential energy are the 1-kilogram ball at 20 meters, 25-kilogram box of books at 2 meters, 15-kilogram stone at 3 meters, and 10 kilograms of water at 9 meters.
Step-by-step explanation:
To arrange the objects in order from least to greatest potential energy, we use the formula PE = m × g × h, where 'PE' stands for potential energy, 'm' is mass in kilograms, 'g' is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and 'h' is the height in meters. We'll calculate the potential energy for each of the given objects and then compare the values.
- 15-kilogram stone at a height of 3 meters: PE = 15 kg × 9.81 m/s² × 3 m = 441.45 J
- 10 kilograms of water stored at a height of 9 meters: PE = 10 kg × 9.81 m/s² × 9 m = 882.9 J
- 1-kilogram ball located 20 meters in the air: PE = 1 kg × 9.81 m/s² × 20 m = 196.2 J
- 25-kilogram box of books placed on a shelf 2 meters high: PE = 25 kg × 9.81 m/s² × 2 m = 490.5 J
Arranged from least to greatest potential energy, the order is:
- 1-kilogram ball at 20 meters: 196.2 J
- 25-kilogram box of books at 2 meters: 490.5 J
- 15-kilogram stone at 3 meters: 441.45 J
- 10 kilograms of water at 9 meters: 882.9 J