物理101
Preface
The very framework of how to think about physics is the most helpful.
To understand how did the first scientists learn anything,
how did they change the way that they learned thing,
how did they change the framework of analysis over time as they learned one mode was batter than another.
If people really pay attention to physics 101, that is most valuable. – by Elon Musk
Introduction
In this text, you will begin to explore the history of the formal study of physics, beginning with natural philosophy and the ancient Greeks, and leading up through a review of Sir Isaac Newton and the laws of physics that bear his name. You will also be introduced to the standards scientists use when they study physical quantities and the interrelated system of measurements most of the scientific community uses to communicate in a single mathematical language.Finally, you will study the limits of our ability to be accurate and precise, and the reasons scientists go to painstaking lengths to be as clear as possible regarding their own limitations.
Physics: An Introduction
The unifying aspect of physical laws and the basic simplicity of nature form the underlying themes of this text. In learning to apply these laws, you will, of course, study the most important topics in physics. More importantly, you will gain analytical abilities that will enable you to apply these laws far beyond the scope of what can be included in a single book. These analytical skills will help you to excel academically, and they will also help you to think critically in any professional career you choose to pursue.
It is not necessary to formally study all applications of physics. What is most useful is knowledge of the basic laws of physics and a skill in the analytical methods for applying them. The study of physics also can improve your problem-solving skills. Furthermore, physics has retained the most basic aspects of science, so it is used by all of the sciences, and the study of physics makes other sciences easier to understand.
复杂的现象可以用简单的定律去解释
model
A model is a representation of something that is often too difficult (or impossible) to display directly. While a model is justified with experimental proof, it is only accurate under limited situations.
Physicists use models for a variety of purposes. For example, models can help physicists analyze a scenario and perform a calculation, or they can be used to represent a situation in the form of a computer simulation.
theory
A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers.
Some theories include models to help visualize phenomena, whereas others do not. Newton’s theory of gravity, for example, does not require a model or mental image, because we can observe the objects directly with our own senses. The kinetic theory of gases, on the other hand, is a model in which a gas is viewed as being composed of atoms and molecules.
laws
The laws of nature are concise descriptions of the universe around us; they are human statements of the underlying laws or rules that all natural processes follow. Such laws are intrinsic to the universe; humans did not create them and so cannot change them.
A law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments. Often, a law can be expressed in the form of a single mathematical equation.
Laws can never be known with absolute certainty because it is impossible to perform every imaginable experiment in order to confirm a law in every possible scenario.
principle
Less broadly applicable statements are usually called principles (such as Pascal’s principle, which is applicable only in fluids), but the distinction between laws and principles often is not carefully made.
The Scientific Method
This process typically begins with an observation and question that the scientist will research
the scientist typically performs some research about the topic and then devises a hypothesis
the scientist will test the hypothesis by performing an experiment
the scientist analyzes the results of the experiment and draws a conclusion
Classical physics VS Modern physics
Physics is the most basic of the sciences, concerning itself with energy, matter, space and time, and their interactions.
Classical physics is not an exact description of the universe, but it is an excellent approximation under the following conditions: Matter must be moving at speeds less than about 1% of the speed of light, the objects dealt with must be large enough to be seen with a microscope, and only weak gravitational fields, such as the field generated by the Earth, can be involved. Because humans live under such circumstances, classical physics seems intuitively reasonable, while many aspects of modern physics seem bizarre.
This is why models are so useful in modern physics—they let us conceptualize phenomena we do not ordinarily experience. We can relate to models in human terms and visualize what happens when objects move at high speeds or imagine what objects too small to observe with our senses might be like. For example, we can understand an atom’s properties because we can picture it in our minds, although we have never seen an atom with our eyes. New tools, of course, allow us to better picture phenomena we cannot see. In fact, new instrumentation has allowed us in recent years to actually “picture” the atom.
Modern physics itself consists of the two revolutionary theories, relativity and quantum mechanics. These theories deal with the very fast and the very small, respectively. Relativity must be used whenever an object is traveling at greater than about 1% of the speed of light or experiences a strong gravitational field such as that near the Sun. Quantum mechanics must be used for objects smaller than can be seen with a microscope. The combination of these two theories is relativistic quantum mechanics, and it describes the behavior of small objects traveling at high speeds or experiencing a strong gravitational field. Relativistic quantum mechanics is the best universally applicable theory we have. Because of its mathematical complexity, it is used only when necessary, and the other theories are used whenever they will produce sufficiently accurate results. We will find, however, that we can do a great deal of modern physics with the algebra and trigonometry used in this text.
虽然相对论量子力学可以解释一切，但是为了简单性，会用足够准确的其他理论解释
Physical Quantities and Units
The range of objects and phenomena studied in physics is immense, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. Giving numerical values for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitative description alone. To comprehend these vast ranges, we must also have accepted units in which to express them. And we shall find that (even in the potentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears—all physical quantities can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current.
We define a physical quantity either by specifying how it is measured（fundamental units） or by stating how it is calculated from other measurements（derived units）. For example, we define distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distance traveled divided by time of trave
用统一的物理量描述自然，能激活自己的想象力，便于表达和比较
Accuracy, Precision, and Significant Figures
Accuracy
Science is based on observation and experiment—that is, on measurements. Accuracy is how close a measurement is to the correct value for that measurement.
precision
The precision of a measurement system is refers to how close the agreement is between repeated measurements (which are repeated under the same conditions). The precision of the measurements refers to the spread of the measured values. One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values.
The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they are precise but not accurate.
uncertainty
The degree of accuracy and precision of a measuring system are related to the uncertainty in the measurements. Uncertainty is a quantitative measure of how much your measured values deviate from a standard or expected value.In more general terms, uncertainty can be thought of as a disclaimer for your measured values. In more general terms, uncertainty can be thought of as a disclaimer for your measured values.
The factors contributing to uncertainty in a measurement include:
- Limitations of the measuring device
- The skill of the person making the measurement
- Irregularities in the object being measured
- Any other factors that affect the outcome (highly dependent on the situation)
the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation.
significant figures
Significant figures indicate the precision of a measuring tool that was used to measure a value. Using the method of significant figures, the rule is that the last digit written down in a measurement is the first digit with some uncertainty.（尺子测量值在36.6和36.7之间，只能填36.6或36.7）
Zeros are significant except when they serve only as placekeepers.
When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value. There are two different rules, one for multiplication and division and the other for addition and subtract.
For multiplication and division:
The result should have the same number of significant figures as the quantity having the least significant figures entering into the calculation.For addition and subtraction
The answer can contain no more decimal places than the least precise measurement.
Finally, if a number is exact, such as the two in the formula for the circumference of a circle, c = 2πr, it does not affect the number of significant figures in a calculation.
Approximation
Many approximate numbers are based on formulae in which the input quantities are known only to a limited accuracy. As you develop problem-solving skills (that can be applied to a variety of fields through a study of physics), you will also develop skills at approximating. You will develop these skills through thinking more quantitatively, and by being willing to take risks. As with any endeavor, experience helps, as well as familiarity with units. These approximations allow us to rule out certain scenarios or unrealistic numbers. Approximations also allow us to challenge others and guide us in our approaches to our scientific world.