Understanding Elastic Potential Energy in Springs

When you compress a spring, you are applying a force over a distance. This process involves doing work on the spring. According to the work-energy theorem, the work done on a system changes its energy. In the case of a spring, the work done against the restoring force of the spring is stored as elastic potential energy.

Elastic potential energy is the energy stored in an elastic material, such as a spring, when it is deformed (stretched or compressed) from its equilibrium position. The amount of elastic potential energy stored depends on the stiffness of the spring and the amount of deformation.

Let's consider what happens during compression:

• Initially, the spring is at its equilibrium position, where its elastic potential energy is typically considered zero.
• As you compress the spring, you are moving its coils closer together, away from the equilibrium state.
• You have to apply a force to overcome the spring's tendency to return to its original shape.
• The work you do against this restoring force is converted into stored energy within the spring.
• The more you compress the spring (the greater the displacement from equilibrium), the more work you do, and therefore, the more elastic potential energy is stored.

The formula for elastic potential energy ($U$) stored in a spring with spring constant $k$ when displaced by a distance $x$ from its equilibrium position is given by:

\(U = \frac{1}{2} k x^2\)

Here, $k$ is a constant for a given spring, and $x$ is the displacement (compression or stretching) from the equilibrium position. When you compress the spring, $x$ increases from zero (at equilibrium) to some non-zero value. Since $x$ is squared, the elastic potential energy $U$ is always non-negative and increases as the magnitude of displacement ($|x|$) increases.

Therefore, when you compress a spring, doing work on it, the energy is stored as elastic potential energy, causing it to increase.

Let's look at the options:

• Increases: This aligns with the principle that work done on an elastic system against the restoring force is stored as elastic potential energy, which increases with deformation.
• Disappears: Energy is conserved. Work done on the spring is converted to potential energy, not disappeared.
• Remains constant: Since work is done on the spring, its energy state changes, meaning the potential energy cannot remain constant.
• Decreases: Compressing the spring requires work input, which adds energy to the system, causing the potential energy to increase, not decrease.

Based on the physics principles, the elastic potential energy of the spring increases when it is compressed because work is done on it, and this work is stored as potential energy.