Introduction

Hello, and welcome to the statics and mechanics of materials guide. In this guide, we will break up the content into two main sections:

• Statics, and
• Mechanics of materials.

That is great, but you may be wondering what do these topics entail?

Great question! Statics is the study of physical systems that are not moving, either by translation or rotation. This means we will look a lot at free body diagrams (FBD), forces, and torque. Now, mechanics of materials relates to any temperature change, compression, tension, torsion, or shear force applied to a certain material. We will cover all this by the end of the guide!

Terminology

For this course, we will be using some terminology that would be good to define off the bat. First up is "particle" and "rigid body". Each definition can be found as:

• Particle - occupies a single point in space (no dimensions).
• Rigid Body - made up of several or more particles that have a fixed position relative to one another.

This is an important difference to consider, especially when we get into the materials section! Next up is "scalar" and "vector". They are defined as:

• Scalar - defined by magnitude only. (ie, mass, time, density, speed, temperature)
• Vector - defined by magnitude and direction. (ie, velocity, displacement, acceleration)

The difference between a scalar and vector is another important definition to remember. This importance will come in from the start when we work with free body diagrams. Now, speaking of free body diagrams, I would be remise if I did not mention Newton's contributions to physics starting with his three laws of motion:

• Law of Equilibrium - an object will stay in motion/rest unless acted upon by an external, unbalanced force.
• Law of Accelerated Motion - $ \Sigma \vec{F} = m \vec{a} $. In otherwords, the summation of all forces in a direction will equal the mass of the object times its acceleration.
• Action and Reaction - for every action, there is an equal and opposite reaction.

Now that we learned about Newton's Laws of Motion, lets learn about his law of gravitation!

Image of two spheres that have a gravitational attraction to one another.

Newton's Law of Gravitation says that $ F = G \frac{m_1 m_2}{r^2} $, where G is the gravitational constant, and $ G = 6.673E^{-11} \frac{m^3}{kg s^2} $. Now, remember Newton's 3rd law of motion? (We just learned it so hopefully so :) ) Well, a good example of that would be how if you press on a door with your weight, the door is pushing back on you with the same force applied by your hand. That is how you stay upright and not fall over!

However, in space when two bodies are attracted to one another, there is no gas medium or wall to resist the gravitational attraction. This is why the two masses have the same attractive force towards one another, even if one mass is significantly larger than the other; the smaller mass would simply accelerate faster than the larger mass!

Another interesting thing is weight on Earth and how that is measured. We actually use part of Newton's law of gravitation equation to calculate our weight. You see, we take the $ G \frac{m_e}{r_e^2} $, where $ m_e = 5.972E24 kg $ is the mass of the Earth and $ r_e = 6371 km $ is the radius of the Earth. All of these are constants, so we can simply plug them in to get the gravitational acceleration for Earth, which is $ g = 9.81 \frac{m}{s^2} $, or $ 32.2 \frac{ft}{s^2} $ for English units.

There are two more things I want to talk about before we called it a wrap on the introductory terminology. The difference between mass and weight:

• Mass - how much stuff makes up an object.
• Weight - the downward force acting on an object due to a gravitational force. (This is why we would weight less on the Moon, because there is a smaller gravitational acceleration)

The last thing we will touch on is units. Units help describe what type of properties a variable has. For example, we know if a variable has a unit of mass, then we know there the variable corresponds to some sort of mass, or if the variable has units of feet per second, then we know that variables describes a velocity.

There are two types of units, SI and English. SI units have base units of meter, second, and kilogram, where English units the base units of foot, second, and pound. We will practice both of these unit systems throughout the guide. Now, it is time to get started!