Potential Energy Calculator
Calculate gravitational potential energy, mass, or height using the formula: PE = mgh
Step-by-Step Solution:
1. Using the potential energy formula: PE = m × g × h
2. Substitute the values:
PE = 10 kg × 9.81 m/s² × 5 m
3. Calculate:
PE = 490.5 kg·(m/s²)·m
What is Potential Energy?
Gravitational potential energy is the energy stored in an object due to its position above a reference point. The higher an object is and the more massive it is, the more potential energy it has. When released, this stored energy converts into kinetic energy as the object falls.
Potential Energy Formula:
PE = m × g × h
where: - PE = gravitational potential energy (measured in joules) - m = mass of the object (measured in kilograms) - g = acceleration due to gravity (9.81 m/s² on Earth) - h = height above the reference point (measured in meters)
This formula can be rearranged: - Mass: m = PE / (g × h) - Height: h = PE / (m × g)
How to Calculate Potential Energy
To find gravitational potential energy, follow these steps:
-
Determine the mass: Measure the object's mass in kilograms
-
Know the gravitational acceleration: Use 9.81 m/s² for Earth (or the value for another body)
-
Measure the height: Determine the height above your chosen reference point
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Multiply all three: Use the formula PE = m × g × h
Example: A 5 kg book sits on a shelf 2 meters above the floor. - PE = 5 kg × 9.81 m/s² × 2 m = 98.1 J
Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed. In a closed system without friction:
KE + PE = constant
As an object falls: - PE decreases (it loses height) - KE increases (it gains speed) - Total mechanical energy stays the same
A roller coaster perfectly demonstrates this — potential energy at the top converts to kinetic energy at the bottom.
Gravity on Different Bodies
The gravitational acceleration (g) varies by location:
| Body | g (m/s²) | g (ft/s²) |
|---|---|---|
| Earth | 9.81 | 32.17 |
| Moon | 1.62 | 5.32 |
| Mars | 3.72 | 12.2 |
| Jupiter | 24.79 | 81.3 |
| Sun | 274 | 899 |
The same object has different potential energy on different planets because g changes.
Types of Potential Energy
Gravitational PE: Energy due to height in a gravitational field (PE = mgh). This is what the calculator above computes.
Elastic PE: Energy stored in stretched or compressed springs (PE = ½kx²).
Chemical PE: Energy stored in molecular bonds (fuels, food, batteries).
Electrical PE: Energy due to position in an electric field.
Real-World Applications of Potential Energy
- Hydroelectric dams: Water at height has PE that converts to electricity when released
- Roller coasters: Design relies on PE-to-KE conversion for thrilling rides
- Construction: Calculating energy of objects at height for safety analysis
- Space missions: Computing the energy needed to reach orbit (escaping Earth's gravity)
- Pendulum clocks: Operate by converting PE to KE and back
- Skiing and sledding: Gravitational PE converts to kinetic energy going downhill
Common Questions About Potential Energy
What is the formula for gravitational potential energy?
The gravitational potential energy formula is PE = mgh, where PE is potential energy, m is mass, g is gravitational acceleration (9.81 m/s² on Earth), and h is height above the reference point.
What is potential energy?
Potential energy is stored energy due to an object's position or configuration. Gravitational potential energy depends on an object's height and mass — the higher and heavier it is, the more potential energy it has.
What is g in the potential energy formula?
In PE = mgh, g is the acceleration due to gravity. On Earth's surface, g ≈ 9.81 m/s² (or 32.17 ft/s²). On the Moon, g ≈ 1.62 m/s², and on Mars, g ≈ 3.72 m/s².
How are potential and kinetic energy related?
Potential and kinetic energy can convert into each other. As an object falls, its potential energy decreases while its kinetic energy increases. In an ideal system (no friction), the total mechanical energy (KE + PE) stays constant.