1. What is a Gravitational Potential Energy Calculator?

Definition: This calculator computes gravitational potential energy (PE) or related variables (mass, gravitational acceleration, or height) using the formula \( PE = m \times g \times h \). It allows users to calculate PE given mass (m), gravitational acceleration (g), and height (h), or solve for m, g, or h when the other variables are known.

Purpose: It is used in physics and engineering to analyze the energy stored in an object due to its position in a gravitational field, with applications in hydropower, roller coaster design, and space exploration, inspired by tools like CalculatorSoup’s Gravitational Potential Energy Calculator.

2. How Does the Calculator Work?

The calculator supports four calculation modes based on the formula:

Unit Conversions:

• Energy: J, kJ (1 J = 0.001 kJ), MJ (1 J = 0.000001 MJ), Wh (1 J = 1/3600 Wh), kWh (1 J = 1/3600000 kWh), ft-lb (1 J = 0.73756214927727 ft-lb), kcal (1 J = 1/4184 kcal)
• Mass: μg (1 μg = 0.000000001 kg), mg (1 mg = 0.000001 kg), g (1 g = 0.001 kg), dag (1 dag = 0.01 kg), kg, t (1 t = 1000 kg), gr (1 gr = 0.00006479891 kg), dr (1 dr = 0.0017718452 kg), oz (1 oz = 0.028349523 kg), lb (1 lb = 0.45359237 kg), st (1 st = 6.35029318 kg)
• Gravitational Acceleration: m/s², cm/s² (1 cm/s² = 0.01 m/s²), ft/s² (1 ft/s² = 0.3048 m/s²)
• Height: mm (1 mm = 0.001 m), cm (1 cm = 0.01 m), m, in (1 in = 0.0254 m), ft (1 ft = 0.3048 m)

Explanation: Inputs are converted to SI units (J for energy, kg for mass, m/s² for g, m for height), the selected variable is calculated, and the result is converted to the chosen output unit. Results use scientific notation for values < 0.0001 or > 100,000.

3. Importance of Gravitational Potential Energy Calculation

Details: Calculating gravitational potential energy is crucial for designing energy systems like hydropower plants, ensuring safety in amusement park rides, and understanding energy requirements in space missions.

4. Using the Calculator

Tips: Select the calculation mode, enter the required inputs with their units (e.g., mass in kg, height in m), ensuring mass, potential energy, and gravitational acceleration are positive, and height is non-negative for PE calculations (positive for m or g). Click “Calculate” to get the result in the selected unit. The result uses scientific notation for very small (< 0.0001) or large (> 100,000) values.

5. Example

Given (Calculate PE, Large Values): Mass = 1000 kg, Gravitational Acceleration = 9.81 m/s², Height = 150 m.
Calculation: Convert units (all in SI): \( m = 1000 \, \text{kg} \), \( g = 9.81 \, \text{m/s}^2 \), \( h = 150 \, \text{m} \).
- \( PE = 1000 \times 9.81 \times 150 = 1471500 \, \text{J} \)
- In MJ: \( PE = 1471500 \times 0.000001 = 1.4715 \, \text{MJ} \)
- In kWh: \( PE = 1471500 \times (1/3600000) \approx 0.409 \, \text{kWh} \)
Result (> 100,000 for J): 1.471500e+06 J, 1.472 MJ, 0.409 kWh.

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