Physci text 00
Introduction
SC 130 Physical Science is a residential laboratory science course focused on three core areas: science as discovered explanations, the mathematical models that power those explanations, and writing skills. The course is centered on the laboratory experiences. Science is not memorized facts but a system of exploring the natural world and generating explanations for observations. In physical science, those explanations are mathematical models.
Course Learning Outcomes
The student will be able to:
Explore physical science systems through experimentally based laboratories using scientific methodologies
Define and explain concepts, theories, and laws in physical science.
Generate mathematical models for physical science systems and use appropriate mathematical techniques and concepts to obtain quantitative solutions to problems in physical science.
Demonstrate basic communication skills by working in groups on laboratory experiments and by writing up the result of experiments, including thoughtful discussion and interpretation of data, in a formal format using spreadsheet and word processing software.
Units of measurement
In physical science there is space, time, and matter. Space has three dimensions - think in terms of left and right, forward and backward, up and down. Time has one dimension and, for us, only goes in one direction. Forward, ever forward in time. Never backward. Matter has no dimensions.
Space measures length, height, width, distance, depth, altitude. Space also measures areas and volumes. Time measures duration. Matter is mass, the amount of stuff in an object.
Space answers questions of how - how far, how high, how deep, how wide, how small, how large. Time answers questions of when - when did something occur. Matter answers questions what - what stuff is present and in what quantity.
Space is measured in meters and centimeters.
Time is measured in seconds.
Matter is measured by mass in kilograms and grams.
The two metric systems are referred to as CGS and MKS.
Role of mathematics in physical science and mathematical models
In physical science a "relationship" means how one variable changes with respect to another variable. This change is described using mathematical equations. Math is the language in which physics is "spoken."
Galileo Galilei spoke of science as "natural philosophy," a term the Greek philosopher Aristotle also used for science. Galileo noted that the universe around us is "written" in the language of mathematics:
La filosofia è scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico l' Universo'), ma non si può intendere, se prima non il sapere a intender la lingua, e conoscer i caratteri ne quali è scritto. Egli è scritto in lingua matematica,...
which might be translated as:
[Science] is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language,... – Galileo Galilei
Physicist Freeman Dyson, who studied subatomic physics in the 20th century, echoed Galileo:
For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. I mean, the fact that nature talks mathematics, I find it miraculous. I mean, I spent my early days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too. – Physicist Freeman Dyson
A core concept in the physical sciences is the idea that physical systems obey mathematical equations. The mathematical equations are also called mathematical models or mathematical relationships.. If two variables are related by a mathematical equation, then predictions can be made about that physical system. Physics, engineering, and chemistry all depend on predictable results. When something is done in the same way twice, the same result should occur.
One way to begin to find the mathematical equation that relates two variables is to make an xy scatter graph. The graph will help indicate whether a relation exists between the variables. The graph will also help us determine the nature of the relationship. By nature we mean whether the relationship is linear or non-linear.
If the relationship between variables is linear or non-linear, then the system behaves in a predictable manner. Given the value of one variable, we can predict the value of the other variable. In this class we will only try to make predictions for linear relationships. Non-linear relationships are also predictable, but the mathematics is beyond the scope of this course.
If the relationship is linear, then the equation has the form y = startValue + Rate ∙ x. You may be more familiar with the form y = mx + b. In physics the slope m is often a rate of change and the y-intercept b is often a startValue. The y-intercept is not always the startValue, but for many systems the y-intercept, where x = 0, is a starting place for a system.
If we find that a relationship does form a roughly straight line, then we will try to find the slope and intercept.
The following graphs show the different types of relationship that might exist between two variables.
To decide on whether a relationship exists between two variables, start with an xy scattergraph. Looking at the graph, consider the following questions:
Does the data form a roughly straight line?
Does the data form a smooth curve?
Does the (data form no pattern, scattering randomly on the chart?
If the data points form roughly a straight line, then a linear model can be used to model the relationship. If the data points form a smooth curve, then the relationship is a non-linear relationship. If the data points form no pattern, then there is no relationship between the variables being studied.
The following decision flow chart is a map of the flow of decisions described above.
Desmos graphing calculator can be used to explore how well mathematical models fit the data.
If the data points form a line, then we can find a line through the points. This line that best goes through the data points is called a best fit line, trend line, or a linear regression.
Note that because of uncertainty in primary measurements and error, data is considered linear even when the data falls only roughly along a straight line. The data does not have to fall exactly in a straight line. The issue of how close data comes to a straight line is part of the study of correlation in statistics.
Technology
Science uses technology. Technologies such as Desmos above are an integral part of exploring the physical world and making sense of the physical world.