Chapter 17: Gravitational Potential Energy

17.1 Introduction to Gravitational Potential Energy (GPE)

In this chapter, we will discuss another essential form of energy—gravitational potential energy. Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. This energy is “stored” energy which can be converted into other forms of energy.

17.2 Formula for GPE

Gravitational potential energy is associated with the gravitational force acting on an object . The force of gravity is always acting on an object near the Earth’s surface, attempting to pull it towards the center of the Earth. Consequently, when an object is lifted to a certain height, it gains potential energy because work has been done against gravity.

The gravitational potential energy (GPE) of an object can be calculated using the following formula:

where is the gravitational potential energy, is the object’s mass, is the acceleration due to gravity (approximately on Earth), and is the height of the object above a reference point (usually the ground).

17.3 Example Calculations

17.3.1 Numerical Example #1:

Let’s consider an example. Suppose a 5 kg box is lifted to a height of 2 meters above the ground. To find the gravitational potential energy, we can use the equation:

Thus, the box has 98.1 Joules of gravitational potential energy at a height of 2 meters above the ground. However, this energy is just realtive to our chosen reference point.

17.3.2 Numerical Example #2:

Suppose we have the same 5 kg box, but this time we are at the top of a ten-story building. Let’s choose our reference point to be the street, say 30 meters below us. Again we lift the box 2 meters up. So, in total, the box has a height of 32 meters above the reference point. Thus:

However, we could just as easily choose our reference point to be the bottom of the 10th floor of the building. Then the gravitational potential energy will still be 98.1 Joules.

17.3.3 Numerical Example #3:

Finall, let’s suppose that we once again lift the 5 kg box 2 meters off the ground. This time, we will take the reference point to be the ceiling, say 1 meter above the box. Thus:

The truth is, it doesn’t matter where you put your reference point, but some choices make more sense than others. GPE is relative to the reference point. Thus is can be positive or negative unlike kinetic energy which can only be positive.

17.4 Conservation of Energy

The concept of gravitational potential energy is essential in understanding energy conservation in systems involving height changes or forces acting against gravity. When an object falls, its gravitational potential energy is converted into kinetic energy. Conversely, when an object is lifted or thrown upwards, its kinetic energy is converted into gravitational potential energy.

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Continue to Chapter 18: Elastic Potential Energy

Back to Chapter 16: Kinetic Energy

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