This chapter covers a few basic areas of physics and mathematics that are important for science and engineering, namely, temperature, force, pressure, and some general algebra/statistics concepts. Why are these areas so important? Because they govern the physical world and how many things work or behave. Understanding of these tools can provide the background to ways of improving life, increasing energy efficiency, improving products, increasing safety, and other innumerable facets of life.
Temperature
Temperature is a measure of a physical property of all matter, and it represents a level of internal energy the object or material contains. Another way of looking at temperature is a comparison of energy levels within or between objects or materials. For example, a hot object has more internal energy than a cold object. In theory, at a temperature of absolute zero, there is no energy.
There are two temperature scales (English and Metric) used, and they have both a full-scale component and a scale that is used for everyday temperature measurements. The following equations highlight various conversions of 32 degrees Fahrenheit or the freezing point of water to other temperature scales:
32°F + 459.67 = 491.67°R
(32°F − 32) × 5/9 = 0°C
0°C + 273.15 = 273.15°K
Temperature is a key measure in how weather works and plays a significant role in our comfort. It is amazing how we are heating or cooling our home, to control its temperature, sometimes doing both in the same day!
Force
What does force really mean and why is it critical to everything we do?
An object will not move from a state of rest unless a force acts upon it. Putting it simply, no movement occurs unless a force is generated by some means, and that force pushes or pulls an object. For example, as a baby learns to walk, she gains a very real lesson on how to control all facets of force and balance in order to get from the table to her mother. As she starts out, she must pay attention to the force needed to move forward. Otherwise, she may lose her balance and fall down. If the floor is slippery and she fails to keep her weight over her feet, she may not be able to keep from slipping and will fall down. If she does not keep moving and slows down, she may not be able to keep her balance, and she falls down. Over time we do these things without consciously thinking about them and are able to walk from point A to point B without incident. These basic constraints are inescapable and continually govern many aspects of our daily life.
Pressure
Diagram Showing Pressure
Pressure = Force/Area, abbreviated as P=F/A
Metric system: Pressure = N/m2 (Newton per square meter)
English system: Pressure = lbs/in2 or psi (pounds per sq. inch)
Why is pressure important? It is a measure of true exerted force. An experiment later in the book shows how changing the surface area can really change the force an object experiences. Think about when an apple is being cut. When the point of the knife is poked through the skin, the applied pressure at the point of the knife is very high. However, it is very hard to cut through the skin of an apple using the whole length of the blade.
Basic Concept of Algebra
Distributive property
Multiplying A by the expression in the parenthesis:
A × (B +C) = A × B + A × C
Manipulating an equation
A variable can be subtracted from or added to both sides of the equation:
If A + B = C + D + B
subtracting B from both sides yields
A = C + D
Also, a variable can be multiplied or divided on both sides of the equation:
7 × A = B
Then dividing by 7 on both sides yields
A = B/7
While these operations seem simple, they form the basis of setting up equations to solve many different variables. Using these operations provides a number of ways to resolve and answer many scientific or engineering questions.
Statistical Concepts
The authors do not go into great detail regarding statistics in this book, but this section is included to highlight some important basics of this important tool. Statistics is a method that is used to analyze the variability of data and research meaningful trends of large groups of data.
Xaverage = (X1+X2+X3+…)/quantity of values of X
Std Dev = Square root of (1/N x ∑ (( Xi – Mean)2))
What is happening in the standard deviation equation? For each value, a difference is found from the mean value. Those differences are squared and summed, and finally the square root of that number is found. What is this actually telling us? The equation establishes a value for an expected “deviation” from the mean. When the analyst is looking at additional data gathered and sees a significant difference in standard deviation, it may indicate there is a problem somewhere.
Statistics is a very complex subject, and the preceding concepts are the basics. They do provide the groundwork for most of statistical analysis. If the reader is exploring a scientific or engineering career, they are encouraged to explore statistics in greater detail, in particular, hypothesis testing.
Direct Compared to Inferred Measurements
A direct measurement is a measure of the item of interest. An example of a direct measurement is a voltmeter measuring voltage. An example of an inferred measurement is when another aspect is measured and the item of interest is inferred from what can be measured. In many cases, the sensors in this book like the MCP9700 transistor temperature sensor actually provide an output voltage based on the temperature at the sensor. The temperature is an inferred measurement.
Summary
The world is a very unique place, and the concepts outlined in this chapter provide the basics of some of the most important engineering tools and scientific concepts. The reader is encouraged to explore them further in later chapters along with advanced classes and studies.