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MechanicsPotential Energy Calculator
Potential Energy (PE) = mgh
Practical Examples:
Example 1: Water Tower
A water tower has a mass of 100,000 kg and is 30 meters tall. Calculate the potential energy of the water in the tower.
Solution: PE = mgh = 100,000 kg × 9.8 m/s² × 30 m = 2,940,000 J
Example 2: Roller Coaster
A roller coaster car has a mass of 500 kg and is lifted to a height of 50 meters at the top of a hill. Calculate the potential energy of the car at the top of the hill.
Solution: PE = mgh = 500 kg × 9.8 m/s² × 50 m = 245,000 J
Example 3: Hydroelectric Power Plant
A hydroelectric power plant has a dam that stores water at a height of 100 meters above the turbine. The water flows down to the turbine, generating electricity. If the mass of water flowing through the turbine is 10,000 kg per second, calculate the potential energy of the water per second.
Solution: PE = mgh = 10,000 kg/s × 9
Example 4: Skyscraper
A skyscraper has a mass of 50,000 kg (including the building's structure, occupants, and contents) and is 200 meters tall. Calculate the potential energy of the skyscraper.
Solution: PE = mgh = 50,000 kg × 9.8 m/s² × 200 m = 98,000,000 J
Example 5: Mountain Climbing
A climber with a mass of 70 kg is ascending a mountain and reaches a height of 2,000 meters above sea level. Calculate the potential energy of the climber at this height.
Solution: PE = mgh = 70 kg × 9.8 m/s² × 2,000 m = 1,372,000 J
