PhysicsLAB Resource Lesson
What is Mass?

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Welcome to physics! Once you defined matter as anything that has mass and occupies space. You also learned that atoms are composed of protons, neutrons, and electrons. Now you are going to be exposed to further details regarding the constituent particles forming matter.
Currently we now know that atoms are composed of leptons and quarks organized into three families called the Standard Model. Ordinary matter is composed of quarks in the first generation. Recent discoveries at the Large Hadron Collider at CERN during the summer of 2012 have shown critical support for the Standard Model with the discovery of “events that look like the Higgs mechanism” - a process which gives unique masses to each type of subatomic particle. The Nobel Prize in 2013 was awarded to Francois Englert and Peter Higgs for the theory they proposed in 1964 regarding the existence of a particle that would explain why other particles have a mass. The current Standard Model, formulated during the 1960-1970’s, states that protons are composed of three quarks: up, up, down and that neutrons are also composed of three quarks: down, down, up, along with the strong force carriers, gluons.

But notice how mass is measured in the chart below. It is not presented in terms of kilograms (kg) but in terms of energy (MeV) and the speed of light (c). An up quark is approximately 2.3 MeV/c2), while a down quark is approximaely 4.8 MeV/c2 and an electron is 0.511 MeV/c2. How are those units related to our everyday kilograms? Dimensionally, MeV/c2 equals kilograms according to Einstein's equation relating mass and energy proposed in his Special Theory of Relativity, ΔE = (Δm)c2.

The unit MeV measures energy and representing 1.6 X 10-13 Joules. Using Newton's 2nd law of motion, net F = ma, a Joule (J) is a derived unit which represents a kg (m/sec)2. The unit c is the speed of light through a vacuum and represents 3 x 108 m/sec. Putting all of this together we get

Therefore they are stating the particle's mass, but just in a unit more convenient to particle physics.
Returning to the chart, notice that the quarks carry “fractional” electric charge: an UP quark has a charge of +2/3 and a DOWN quark has a charge of -1/3. But +2/3 and -1/3 of what? They are fractions of the fundamental unit of charge which is carried by an electron. The magnitude of this charge is 1.6 x 10-19 coulombs, where the unit is in honor of Charles Coulomb, a French physicist (1738-1806) who formulated the definition of electrostatic force of attraction and repulsion.
Examining the quark composition of a proton, we see that the two up quarks each has +2/3 and the single down quark has a charge of -1/3 which adds to a charge of +1. Similarly, a neutron being composed of two down quarks each having a charge of -1/3 and one up quark having a charge of +2/3 yields a neutral particle.
But a single quark has never been “seen” they always come in sets of three quarks (hadrons) or two quarks (mesons). And yes, there is such a thing as antimatter. Every quarks and lepton has its antimatter partner. Antimatter has the same mass but carries the opposite charge. So an anti-electron, or positron, has the same mass as an electron but is positively charged. Positrons were predicted by Paul Dirac in 1928 and were discovered in 1932 by Carl Anderson while studying cosmic rays collisions in a cloud chamber.

Not only do these quarks have unique masses, they also come in three "colors." Although their intrinsic color property is not actually red, green, and blue - the quarks always pair up with each other to form "white" particles (a study called quantum chromodyanmics). Moreover, each quark has an anti-quark which carries its complementary color (cyan, yellow, or magenta). Consequently, subatomic particles are formed from either three quarks or a quark and antiquark.

Each family or generation in the Standard Model contains two leptons which are indivisible and carry the fundamental electric charge, e, as discussed earlier. The muon and the tau are "heavy" electrons - meaning they have the same charge as an electron but are more massive. Once again, the Higgs mechanism is critical in determining their unique masses.

The chart of the the Standard Model also includes the bosons whic are excitations in their respective fields. Currently we state that there are four fundamental forces in nature:
  • the strong nuclear force - carried by the gluons linking the quarks and found in the nucleus
  • the weak nuclear force - carried by the W+, W-, and Z0 bosons that are responsible for natural radioactive decay allowing one type of quark to transmute into another
  • the electromagntic force - carried by the chargeless, massless photons that are the boson for electrostatic attraction and repulsion
  • the gravitational force - carried by gravitons and first observed during the summer of 2016 the LIGO "chirp" when the gravity waves between two black holes collided.
These forces have specific distances, or ranges, over which they are felt.
  • The strong force acts solely within the nucleus. So its range is only a few femtometers. (10-15 meters)
  • The weak force acts within the atom. So its range is on the order of angstroms (10-10 meters).
  • The electromagnetic force is infinite is range and is predominately responsible for most of the phenomena we observe in our everyday life. Its force constant is very large (9 x 109 N m2/C2).
  • The gravitational force is also infinite in range, but has an extremely small force constant (6.67 x 10-11 Nm2/kg2) resulting in this force only being applicable when involving enormously large masses.
The force of universal gravitation has yet to be mathematically "attached" to the Standard Model. When it does, the model will mature into the "TOE" or the Theory of Everything - a quest Einstein never achieved but spent his last years pursuing. The Theory of Everything will unite the behavior of all four fundamental forces dealing with matter and energy.

Welcome to the 21st century!

As far as we are concerned, we are going to start our discussion with gravitational mass and inertial mass - terms that may or may be familiar to you.
  • Gravitational mass is a measure of the amount of matter present in an object based on its gravitational attraction to another object - in our case, the Earth. This deals with the object’s weight.
  • Inertial mass is a measure of an object’s resistance to being accelerated; that is, how hard it is to change either the speed or the direction an object is moving.
One of your first experiments will compare these two “types of mass” and let you discover that they yield the same numerical result for an object’s mass. The adjectives are employed when you want to describe the basis of how the mass is being measured or unitized in a particular situation. Always remember that mass and weight are NOT the same!
A second introductory lab will instruct you in the difference between an object's gravitational mass and its weight.

A third measure of mass which we will examine during our study of rotational motion is an object’s moment of inertia. This measurement calculates the resistance a rigid body has to changing its state of rotation about a specified axis. The amount of rotational inertia depends not only on the amount of mass, but also on the distribution of that mass about the specified axis.

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