Springs Physics

Springs - Definition and Meaning

Springs are elastic and can store energy.

Properties of Springs in Physics

In physics, springs have the following basic properties:

• They are elastic, meaning they return to their original shape after being deformed by a force.
• They store potential energy.
• The force the spring exerts increases as the distance it is stretched/compressed increases.

Types of Springs

The most common spring, especially in physics problems, is a simple metal coil spring. This is what you probably think of when you think of the word spring, like slinkies or the springs in pens. However, there are many different types of springs. Anything that has the properties we mentioned above technically counts as a spring. For example, if you hold a plastic ruler on the end of your desk, bend it downwards, and release it, it will spring back and forth until it becomes straight again. Therefore, the ruler acts as a spring.

Even within coil springs, there are different types for different applications. The two most common types of coil springs are compression springs and extension springs. Compression springs are designed such that they have the most potential energy when they are compressed, and they have space to be compressed, such as the spring in a pogo stick. Extension springs have the most potential energy when extended and typically don't have much space for compression, such as the springs on a trampoline. There are also torsion springs that are used in rotation, such as the spring in a mousetrap.

Even though springs come in many shapes and sizes, all springs have similar characteristics and exert the same type of force.

Spring Force

Let's define and discuss spring forces.

If you squish a spring between your fingers, you can feel it fighting back against the force you apply; this is the spring force. The spring force acts in the direction opposite of the compression or extension of the spring.

The spring force is sometimes referred to as a restoring force because it wants to restore itself to its relaxed position.

Spring Force Equation - Hooke's Law

The equation for spring force is known as Hooke's Law:

$$F_\mathrm{s}=-kx$$

The variable \( k \) represents the spring constant, which depends on the stiffness of the spring. The stiffer the spring, the larger the spring constant, the larger the spring force. The spring constant depends on the spring's material properties, the thickness of the spring, and--for coil springs--how many coils it has. It has units of \( \mathrm{\frac{N}{m}} \).

The variable \( x \) represents the distance the spring has been compressed or extended. The larger the distance, the larger the spring force. Since the spring constant is always the same for a single spring, springs will extend or compress linearly with the amount of force applied to them.

The negative in the equation tells us that the spring force acts in the opposite direction of the displacement of the spring. We might also see the spring force equation as follows:

$$\left| F_\mathrm{s} \right |=-k\left | x \right |$$

The absolute values just indicate that the magnitude of the force increases as the magnitude of the distance increases. Hooke's law applies to all springs as long as they aren't stretched farther than their elastic zones (if you stretch a spring so far that it doesn't return back to its correct shape, the equation doesn't work as exactly).

The Spring Force is Caused by Interatomic Electric Forces

The spring force is a contact force (because something has to come into contact with the spring for there to be a force), and all contact forces are caused by interatomic electric forces. Microscopically, springs are made up of many atoms and molecules that are bonded together. The atoms of a spring prefer to stay in their natural state. When the spring is compressed, the interatomic electric forces push out, and when the spring is stretched, the electric forces pull back to keep the atoms and their bonds at their proper distance.

Spring Force Examples - Mass Without Motion

To look at examples using the spring force, we will use a mass attached to a common coil spring.

Mass on a Spring Attached to a Wall

First, we consider an example of a block on a spring hoving horizontally.

Mass Hanging from a Spring

What happens when the mass is instead hanging vertically?