Ball and Spring Model

Page created by Ashley Fleck.

Short Description of Topic

Introduction

Everything that has mass (solids, liquids, gases, etc.) is made of matter, which is made up of atoms. Each atom is composed of a dense positively charged nucleus and a much less dense negatively charged electron cloud (1). [Insert picture of a breakdown of an atom]. The charges of the atom affect how they interact with other atoms. Simply, the positive charge of one positively charged nucleus of one atom is attracted to the negatively charged electron cloud of the other atom, which bounds the two atoms together. This interaction is known as the electric force. However, this attraction only occurs up to a specific point. Once the atoms near too close to one another, the attractive forces of the nucleus and electron cloud are outweighed by the repulsive forces of the two atoms’ electron clouds (while opposite charges attract, negative charges repel). Therefore, if the atoms are pushed too close to one another, they will repel each other rather than attract. (1).

The Main Idea

These interactions can be modeled using a familiar object: a spring! Every spring has a relaxed length. Once the spring is stretched past this relaxed length, the spring exerts a force inward in order to restore it to its original, relaxed length. If the spring is compressed smaller than the relaxed length, then it exerts a force outward in order to restore it to its original, relaxed length. Atoms can be modeled in the same way. Suppose two balls represent two atoms. These two atoms are connected by a spring, which represents the chemical bond (a bond between atoms that is a result of electric forces that bind protons and electrons to each other) between the two atoms (5).

This simple model of just two atoms connected by a spring can then be extended to represent an entire solid! If each atom was connected to six atoms (each at a 90 degree angle to the others), it would form a cube, or what’s known as a simple cubic lattice. A simple cubic lattice is the simplest model of a solid. A model of this can be seen below. If one of the atoms is moved in any direction, it has a ripple effect with the other atoms (causing some to move away and some to come closer). Because they are all connected by these springs (which again, represents the electric forces between the atoms through a chemical bond), the movement of one atom affects all the other atoms (4).

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

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Connectedness

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History

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See also

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Further reading

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