Chapter 18: Elastic Potential Energy

18.1 Introduction to Elastic (Spring) Potential Energy

In this chapter, we will explore another form of potential energy, known as elastic potential energy. Elastic potential energy (also known as spring potential energy) is the energy stored in an object when it is deformed, such as when a spring is compressed or stretched. We will discuss the properties of elastic potential energy as well as its relation to Hooke’s Law.

18.2 Hooke’s Law

When dealing with elastic potential energy, Hooke’s Law is an essential principle that describes the relationship between the force applied to a spring and the spring’s displacement from its equilibrium position. Hooke’s Law states that the force needed to compress or extend a spring is directly proportional to the displacement from the equilibrium position. Mathematically, Hooke’s Law can be written as:

where is the force applied to the spring, is the spring constant (a measure of the stiffness of the spring), and is the displacement of the spring from its equilibrium position. The negative sign indicates that the force applied is in the opposite direction of the displacement. This is why we sometimes refer to a spring force as a restoring force—it tries to restore the spring to its equilibrium position.

18.3 Elastic Potential Energy

The elastic potential energy (EPE) stored in a compressed or extended spring can be calculated using the following formula:

where is the elastic potential energy, is the spring constant, and is the displacement of the spring from its equilibrium position.

Let’s consider an example. Suppose a spring with a spring constant of 200 N/m is compressed by 0.1 meters. To find the elastic potential energy, we can use the equation:

Thus, the spring stores 1 Joule of elastic potential energy when compressed by 0.1 meters (10 centimeters). Consider how this is similar to gravitational potential energy in the fact that it is another “stored” form of energy.

18.4 Energy Conservation in Elastic Systems

Elastic potential energy plays a crucial role in understanding energy conservation in systems involving elastic deformation. When a spring is compressed or extended and then released, its elastic potential energy is converted into kinetic energy. Conversely, when an object collides with a spring and compresses or extends it, the object’s kinetic energy is converted into elastic potential energy. These conversions are essential in solving for the motion of many physical systems.

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Continue to Chapter 19: Thermal Energy

Back to Chapter 17: Gravitational Potential Energy

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