When we talk about potential energy in physics, it's important to understand two types: elastic potential energy and gravitational potential energy. Both types of energy relate to the position of an object but come from different situations.

Gravitational Potential Energy (GPE) is the energy an object has because of its height in a gravitational field. This is usually about how high something is above the ground.

The formula for gravitational potential energy is:

$$PE_g = mgh$$

Here’s what the letters mean:

• $PE_g$ is gravitational potential energy.
• $m$ is the mass of the object, measured in kilograms.
• $g$ is the acceleration due to gravity, which is about 9.81 m/s² near the Earth's surface.
• $h$ is the height of the object above the ground, measured in meters.

From this equation, we can see that gravitational potential energy increases when either the mass of the object or its height goes up.

Elastic Potential Energy (EPE) is the energy saved in objects that can stretch or squeeze, like springs or rubber bands. This energy builds up when the object is changed from its normal shape and can do work when it goes back to that shape. The formula for elastic potential energy in a spring is:

$$PE_e = \frac{1}{2} k x^2$$

In this equation:

• $PE_e$ is elastic potential energy.
• $k$ is the spring constant, which tells us how stiff the spring is.
• $x$ is how much the spring is stretched or squeezed from its normal shape, also measured in meters.

Unlike gravitational potential energy, elastic potential energy depends only on how much the spring is changed and how stiff it is.

Key Differences:

1. Where They Come From:

   • GPE is about how high something is and the gravitational pull on it.
   • EPE comes from how much elastic materials are stretched or compressed.

2. What Affects Them:

   • GPE changes with the object's mass and height; if you increase either, you get more energy.
   • EPE changes with how much the spring is deformed and how stiff it is; more deformation or a stiffer spring means more energy can be stored.

3. Forces:

   • GPE comes from gravity, which always pulls objects downwards.
   • EPE comes from elastic forces that can either pull together or push apart, depending on how the material is changed.

4. Where We See Them:

   • GPE is seen in things like roller coasters, falling objects, or anything up high.
   • EPE is found in things like catapults, bows, and even shock absorbers, showing how this energy can help things move.

In summary, both elastic potential energy and gravitational potential energy are important for understanding energy in different situations. Even though they are different types of energy, knowing how they work helps us understand energy in nature and in things we create.