Understanding Gravitational Potential Energy (GPE)

Gravitational Potential Energy (GPE) is the energy an object has because of where it is positioned compared to other objects.

You can use this simple formula to calculate GPE:

$$GPE = mgh$$

Here’s what the letters mean:

• $m$ = mass of the object (measured in kilograms)
• $g$ = gravity's pull (which is about $9.81 \, \text{m/s}^2$ on Earth)
• $h$ = height above the ground (measured in meters)

Examples from Everyday Life

1. Dropping a Ball:
   Imagine you have a 2 kg ball that you drop from a height of 5 meters. To find its gravitational potential energy before it falls, you can use the formula:

   • Mass ($m$) = 2 kg
   • Height ($h$) = 5 m

   So, the calculation would look like this:

   $$GPE = 2 \times 9.81 \times 5 = 98.1 \, \text{Joules}$$

2. Hydroelectric Power:
   In a hydroelectric dam, water is stored high up, giving it gravitational potential energy. This energy can be turned into electricity. For example, if there is 100,000 kg of water held at a height of 120 meters, you can find its GPE:

   • Mass ($m$) = 100,000 kg
   • Height ($h$) = 120 m

   The calculation is:

   $$GPE = 100,000 \times 9.81 \times 120 = 117,720,000 \, \text{Joules} \, (or \, 117.72 \, \text{MJ})$$

3. Toolbox on a Scaffold:
   If a toolbox that weighs 15 kg is sitting on a scaffold 10 meters high, its GPE would be calculated like this:

   • Mass ($m$) = 15 kg
   • Height ($h$) = 10 m

   The math here is:

   $$GPE = 15 \times 9.81 \times 10 = 1,471.5 \, \text{Joules}$$

Conclusion

These examples show how we can calculate gravitational potential energy in different situations. Understanding GPE is important in our daily lives and in many engineering projects.