Introduction

We have been negligent to dive deeper into forces, despite introducing it briefly in the previous chapter. As a refresher, forces are simply a push or pull that may change motion. Again, they are not directly responsible for maintaining or causing motion, like we discussed in the previous lesson.

The Four Fundamental Forces

• Gravitational Force: This is a force that arises due to gravity. It is one of the forces that will be important to us. Gravity is a long-range force, since it requires bodies to have quite large masses in order to take any effect. There is a specific equation we can use to calculate it, but that comes later on. particle theorized to be the vector particle for the gravitational interaction is the graviton.

• Electromagnetic Forces: Virtually all the forces that we experience and see in the world fall under this category (e.g. friction, air resistance, etc.). If you know chemistry, you know there are electrons around the nucleus of the atom. All these forces are caused by repulsion of the electrons in objects when they come into “contact” with another. Again, this isn’t important for our purposes. Electromagnetic forces can actually be short-range or long-range, but for right now, most of them will be short-range, specifically in the form of contact forces, so we’ll treat them that way. The photon is the particle responsible for the electromagnetic interaction.

• Strong Forces: Not of too particular interest to us. It only happens at an atomic scale, and it is primarily responsible for holding the nucleus of an atom together. This is a short-range force, since it only happens within and between protons and neutrons (protons and neutrons are actually a composite of three quarks bound by the strong force). You can think of it this way—it only acts at distances of one femtometer ($10^{-15}~\textrm m$). Its vector particle is the gluon, and unlike the photon it has mass and contributes most of the mass of the proton and neutron.

• Weak Forces: This force also doesn’t show up until much later. It is the force that is behind nuclear fission and radioactive decay. Interestingly, it discriminates between left-handed (left-spimming) and right-handed particles. It is also a short-range atomic-level force, but unlike the strong force we can see it in action (for instance, in radioactive decay, which has very real consequences!) .It is interesting to note, however, that this force and the electromagnetic force become one at very high temperatures. The vector particles of this force are the $W+$, $W-$, and $Z$ bosons.

You don’t need to remember any of this particle exchange stuff for the actual lesson, but Eric finds it interesting, so it’s included in here. (Note from Eric: Edward just doesn’t understand it—at least not yet). The bolded parts are what are actually important for you to remember for our lesson, and just remember that all four of these forces are the four fundamental forces in nature.

IMPORTANT!! If a force does not fall under the category of any of those four forces, it does not exist (Note from Eric: sort of, but that will be taught later)!

The Gravitational Force

Firstly, there’s the gravitational force, but remember, that’s long range force. It is the primary long range interaction we will be dealing with in Newtonian mechanics. It is denoted as $F_G$ or $F_g$. Let’s start by considering an object in free fall, where the gravitational force is the only force acting on it, assuming no air resistance. Remember from kinematics that a body undergoing free-fall has acceleration equal to $g$, which is equal to $9.81~\textrm m /\textrm s$. $g$ is also sometimes called the gravitational field strength, and its units may also be denoted as $\textrm N /\textrm{kg}$. Thus, by Newton’s second law, the net force, or sum of all forces is equal to just $F_g$. But $F_g=ma$, and since we know the magnitude of acceleration to be $g$, $F_g=mg$. This is one of the primary forces that you will be dealing with.

Electromagnetic Forces

The Frictional Force

Note: Even though the title says "The Frictional Force", it's NOT a new "type" of force. Remember that frictional forces fall under the Electromagnetic forces category.

Frictional forces are contact forces exerted parallel to a surface. They are denoted by $F_f$ or sometimes simply $f$ (though, again, this is a letter used by other quantities as well). Friction is really quite a complex force resulting from microscopic interactions between the irregularities between surfaces. Even things that seem very smooth have many ridges and bumps at a microscopic level. Friction between surfaces is proportional to the normal force and a dimensionless constant known as the coefficient of friction, which varies between surfaces and for different modes of motion.

In general, there are two types of frictional forces: static and kinetic. Static friction acts when an object is still at rest relative to the surface it rests on. Kinetic friction acts when an object is in motion relative to the surface it rests on.

The coefficient of static friction is denoted as $\mu_s$ and kinetic friction $\mu_k$. Static friction is also sometimes written as $\mu_s^{MAX}$, and you will see why in a second. If both are equal, usually just $\mu$ is used for simplicity. The friction force is equal to $\mu \cdot F_N$ and is usually oppositely directed to any net applied force, but this doesn’t always hold true. The more general rule is that friction always opposes relative motion between two surfaces. This will become more prevalent later on when we teach free-body diagrams.

One really important concept that we recognize and clear out of the way for friction is how the frictional force actually works. Static friction is actually a force that will automatically adjust itself to match the applied force. However, there is a certain maximum for this. That's what $\mu_s$ is here for. The magnitude of the frictional force will always be $≤\mu_s F_N$, and so when you exceed that value, the frictional force turns into the kinetic frictional force, which is always constant value of $\mu_k \cdot F_N$. This means that the coefficient of static friction must be greater than the coefficient of kinetic friction!!

There's no doubt you've definitely tried to push something across a floor at some point in your life. You'll notice that it is actually harder to get the box moving at first, but once it is moving, it becomes a bit smoother sailing from there. What we just explained, if you think about it, perfectly matches up with this intuition!

A graph here to show what we mean:

Conclusion