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Physics is the nature of basic things such as motion, heat, energy, electricity, waves, and optics. It is the fundamental of all sciences. Biology breaks down into chemical reactions between cells and tissues. Chemistry breaks down into the physical laws that govern the atom. Those physical laws lie within the realm of physics and you cannot break down physics any further. It is the foundation of our Universe. In 320 B.C., Aristotle describes the motion of objects in terms of natural motion, and violent motion. Natural motion refered to an object's natural state of things. For example, a rock's natural state would be at rest on the ground, whereas the moon's natural state would be in the sky moving around the Earth. Each object had it's own unique natural state. Violent motion refered to moving an object out of it's natural state. So, throwing the rock or pushing the rock would be putting it into violent motion, and eventually the rock would return to its natural state of rest. In Aristotle's mind, most everyday objects subsisted in this natural state of rest. Afterall, whenever you would move something, it would always end up back at rest. The problem lies with the fact he didn't consider objects that move without the influence of the ground or table working agaisnt the object to slow it down to a stop. Aristotle was a brilliant who studied under Plato for 20 years, contributed to philosophy, science, and education. Unfortunately, his ideas of motion were left unchallenged for almost 2,000 years! Galileo Galilei comes on the scene in the early 1600's and challenges one of Aristotle's claims at the Leaning Tower of Pisa: do heavier objects fall faster than lighter objects? He went on to challenge many more things and was the first to advance our knowledge of physics, which had laid dorment all throughout the dark ages. However, this didn't go without a price. Because he taught counter to the Aristotlean views, and endorsed the Copernican theory of the sun-centered solar system rather than the earth-centered, the Church warned him not to advanced his teachings. Ultimately, he was put on house arrest, but he finished his writings, and had them smuggled from Italy so that they could be puplished in Holland.
Thanks to Galileo, science as we know it emerges. Science can be defined as: a systematic way of collecting, analyzing, and interpreting data in order to draw conclusions about how the Universe works.
Unfortunately, there are some misconceptions about science and physics that I want to
address. I will begin with my version of the scientific method and build from there.
Pretend you are an alien with no knowledge of the Earth and its inhabitants. You have no idea about cars, stoplights, and traffic rules, and you happen to land your ship next to an intersection with four stoplights. As a scientist, you are intrigued by this and decided to investigate. 1. Observe a Problem You notice that there are three different colored lights, there are moving objects that move, slow down, and stop. (Assume this is a law abidding corner). Pretend that each car has tinted windows so that you cannot see the people inside, and you are not aware of the fact the cars have engines. You just think these are moving objects, that appear to stop and go according to the lights. So, a problem might be: How do the lights affect the movement of the objects if they do at all? The problem is simply a question you want to answer, and it must be one that you can actually test or observe in order to answer. Otherwise, what would be the point? 2. Make a Hypothesis The next step is to make a hypothesis, which is simply an educated guess. An educated guess is a prediction of the outcome to your question based on previous knowledge and experience. In other words, a hypothesis must have a reason based on logic or existing facts. In this situation, the hypothesis might be: The different colored lights dictate the different movements
Notice how the hypothesis answers the problem. Also, if the hypothesis is not testable, it is not scientific. It must be testabel! (Technically, the problem and hypthesis are a little too broad, and in real situations would need to be more specific and refined, but these examples are used for the purpose of introducing the steps).
3. Design an experiment and Observe/Take Data After establishing the question and making a prediction, it is time to design an experiment that will enable you to obtain the necessary data to answer your question. Obviously once you have designed your methods, it is time to collect data. There are two kinds of data: quantitative and qualitative. Quantitative Data is that which consists of numbers. Qualitative Data consists of description of the the qualities, such as size, color, and texture to name a few. Obviously, you would observe all cars stopping on red, unless of course they turn right, slowing down on yellow, and going on green. Again, pretend this is a law abidding corner. For this type of data, you might have constructed a chart that kept track of what the objects did for each color. 4. Organize and Analyze/Interpret the Data At this point, you are ready to analyze the data. This is done by usually organizing it into tables or graphs. From these tables or graphs, one can see patterns, trends, or relationships. The data in our scenario will definitely show strong trends between the colors and the object's movements. (Recognizing patterns and relationships from graphs will be covered later.) 5. Make conclusions by forming the simplest general rule Here is where you take the interpretation of the data and formulate the simplest general rule for the phenomenon. In this situation, there could be three rules:
1. All objects stop on red, unless they turn right.
When does something become a law? Does it have to become a principle first? Is there a difference between a scientific law, principle, or fact? The answer to the last two questions is a resounding no! All three have the same status. A law is no stronger or no better than a principle or a fact. They are used interchangeably. So, the question is: when does something become a law? It wouldn't happen with our scenario even if we did it for 100 days. In order for something to become a law (from here on out, I will only refer to it as a law even though it could be a principle or fact) it has to be tested by other scientists in other settings, and they must all agree on the results. If an experiment isn't duplicable, it isn't scientific. Any scientist should be able to read your report, set up the experiment exactly like yours, and achieve the same results. Only then can it become a law. A scientific law is defined as: a generally close agreement by competent observers of an observation of a naturally occurring phenomenon. Let's say that other alien scientists did land at other intersections and they found the same results. Therefore, the three rules established earlier have now become a scientific law. Scientific Theory Question: Does a Scientific Theory have the same status, lesser status, or greater status as a law? This is where most people go awry. Most people would say that a scientific theory is just somebody's idea and it has not been proven yet. In other words, it has a lesser status than a law, principle, or fact. However, this is not the case. It is true that a theory is someone's idea. But, it is an idea that gives an interpretation of a set of proven laws. A theory must be tested and proven correct before it is accepted as a "scientific theory." For example, Einstein's special theory of Relativity is an interpretation of a certain set of laws; one law being that the speed of light is constant regardless of your reference frame. It was a radical theory that was not fully accepted until it was tested. It stands today as the second most tested theory. It is proven thousands of times a day in particle accelerators. In our scenario, a theory could be that the red light produces a field that prohibits the objects from moving, the yellow light produces a field but it is weaker, so they only slow down, and the green light means the field is gone. We could go even further and say the objects have a constant desire to move, and only stop because of the field. Of course, we would attempt to detect this field to see if it actually exists, but the point is for our example: the theory helps to unify the three laws under one umbrella so to speak. It explains them and connects them by a common thread in the way of a field. Question: Can a Theory or Law be modified or thrown out altogether? Let's say one day while you were observing another intersection trying to detect the field, you notice a car run a red light. This would really shake you up since it goes agaisnt your scientific Law and Theory. Can you go back and change the law or theory? Not only can you, but you have to if you find new evidence that contradicts them. This happens all the time in science. For example, as technology gets better, we are better able to see things that were previously unseen. It was only a little over a hundred years ago we thought the atom was the smallest building block of matter. However, as we advanced, we were able to "see" inside and notice the atom was made up of smaller pieces. What happens when we as aliens get the technology to actually look into the objects? We would see people and an engine, which would greatly complicate matters, and pose contradictions to our established theory. When this happens in science, one of two things happen: either the theory or law is modified to stay consistant with the new observations, or they are completely discarded because they are not compatable with the new data. Which brings up a good question. Question: Can you know for sure whether or not a theory is correct? Here is why I used the scenario. Let's go back to the point where we never saw a contradiction to our original three laws and theory. Even though we know that isn't the way cars work in an intersection, would the aliens know that? How could they? All they know is what they see. So, if for one hundred years every observation made at any intersection agrees with the established laws and theory, the alien's have no choice but to accept them as correct, even though they really aren't. The point of this was to show that even though a scientific theory may predict every outcome, we can never know if it is actually how nature works. Only God knows that. So, how do we know for sure? We don't worry about it. Science is not interested in trying to prove something that cannot be proven. It is interested in predicting outcomes. If every outcome is predicted by a certain theory, then it is accepted as the way it is regardless if God actually has it another way, because we would never know anyway. What we see is what we get.
Significant digits  Notice that the ruler has centimeters, designated by the larger tick marks, and millimeters, which are denoted by the smaller tick marks. The rod definitely without a doubt is longer than 2 centimeters. It is also without a doubt longer than 2.2 cm. However, after the .2 millimeters, we are not sure because the ruler doesn't have a smaller measurement. Therefore, we estimate that last digit. There are two rules for estimating:
1. If the object is close to or almost half way to the next tick mark, the last digit is zero.
 As a result, this number has three significant digits, with the last digit of zero being the most uncertain. It actually represents the limit of our measuring tool. The ruler can only accurately measure objects to the millimeter. Anything beyond between the millimeter tick marks is an estimate, and anything beyond that estimate between two millimeter marks is completely meaningless.
Determining Significant Digits  Conversions More to be added later. Speed Speed is defined by how much distance you cover per unit of time. So if you say your speed is 10 miles/hour, it means you are traveling a distance of 10 miles in a time of one hour. Average Speed: Average speed is just that, an average of the speed over a certain period of time. The way to find average speed is to take the total distance traveled and divide by the total time in which it took to do it. For example, if you travel across town which is 5.0 miles long and it takes you 20.0 minutes to do it, then you would write: This says that it took you one hour to go .25 hours. Now, that doesn't mean you didn't go faster than that at any given time during the trip. The speed limit may have been 30 mph and you probably went that speed between stoplights. However, you had to speed up to 30 mph and you had to slow down to a stop several times along the way because of those stoplights. You also had to wait for extended amounts of time. So, average speed takes into account all of those starts, stops, and down times. Instantaneous Speed Instantaneous speed is what most people are familiar with. It is the speed that you are going at that instant. It is the speed that the speedometer on the car reads when you look at it. So, while you were driving across town, your instantaneous speed was 30 mph for some of the time and 0-mph for the times you were stopped at the light. Displacement Now is a good time to distinguish between distance and displacement. Distance is something everyone is familiar with. It is how far you travel. It is a length. Displacement is a little different. Displacement is how far you end up from your original position. For example, look at the picture below.  In this picture our guy walks from d=0 to a point 10 meters away. His distance is 10 meters because he walked 10 meters, and his displacement is 10 meters because he is 10 meters from his starting position. Now, if he walks back to the starting point again as shown in the next picture, what is the overall total distance he has now walked? What is the overall total displacement?  His overall distance walked is now 20 meters because you have to count the 10 meters walking away from the starting position, and the 10 meters walking back to the starting position. What would be the overall displacement? If you guessed zero then you are correct! He ended up zero meters from his starting position. Velocity We had to introduce displacement before we hit velocity. Speed was distance divided by time which means velocity is displacement divided by time. You might be able to see where speed and velocity will be the same thing but can you see where they would be different? Let's return to the picture only this time we will include times.  Here the man walks the same 10 meters only this time we have timed him. It has taken him 5 seconds to walk that distance. So the speed would be given by: The average velocity would be the displacement divided by time: Now let's see what happens when he walks back to the starting position. Let's say at the t = 5 s mark he immediately turned around and walked back taking another 5 seconds which would total 10 seconds for the entire trip.  The average speed would be the total distance, 20 meters, divided by the total time, 10 seconds: Can you guess what the average velocity would be? The total displacement is zero that means the velocity also has to be zero! Now let's see if you can figure out the average speed and average velocity of the next picture.  O.K. We need to define the distance traveled in this picture. If the man went North for three meters and then West for four meters, his overall distance would be 3 + 4 meters, which is 7 meters. Since it took him 5 seconds to complete his trip, his speed would be 7 divided by 5 or 1.4 m/s. What is the man's displacement? From the picture, you can see that there is an arrow that connects the starting point with the finishing point directly. That arrow's length is 5 meters. Therefore, the displacement is 5 meters and the velocity is 5 divided by 5 or 1 m/s! Even though the person actually walked north and then west, the velocity is still dependent on the displacement. In fact, when representing the velocity, you have to include a direction because it is a vector quantity. We will talk about vectors more next chapter. For now, just know that the velocity needs a direction, which is why there is an angle, labeled on the diagram. The correct way to express the velocity in this picture would be to say 1 m/s 53 degrees west of North. The interesting thing about speed and velocity is that no matter which one you use, the person will start from the starting point and end at the finish point at the same exact time. For example, if one person started walking north and then west at 1.4 m/s and another person started walking 1 m/s 53 degrees west of north, they would meet at the finish point at the same time. They both express the same outcome two different ways. It is convenient to use velocity because it includes the direction of travel, speed does not. Acceleration Acceleration by definition is the change in velocity divided by the time during that change. Notice it is not the change in speed divided by time. So, can a vehicle be traveling at a constant speed and still be accelerating? The answer is yes! Remember that velocity includes a direction. So, if you are changing direction while going a constant speed, you are still changing velocity, which means you have to be accelerating. This will make more sense when we talk about circular motion. Let's focus now on changing speed. If a car started at rest and accelerated to a speed of 10 m/s in 5 seconds, we could easily calculate its acceleration:  Notice the second squared in the answer. Another way of saying it would be 2 meters per second per second. Here is why the seconds are squared. It took the car 5 seconds to reach a speed of 10 m/s. That means that the car increased its speed 2 m/s every second. So, after three seconds, the car would have an instantaneous speed of 6 m/s, because it is 2 m/s every second for three seconds. See how the word second occurs twice? That is why it is seconds squared in the equation. Direction Direction is a very important key to acceleration, velocity, and displacement. When problems involve motion along the same line, in other words the object is not traveling north and then turns to travel west, it is useful to use positive and negative to denote the direction of an the object. For me, it is easiest to use direction to the right, (as seen from a chalkboard for example), as positive, and direction to the left as negative. When dealing with up or down, I make down negative and up positive, which we will deal with later in this chapter. I bring this up because it is possible to have a negative displacement. That just means you end up to the left of your starting point for example. Also, it is imperative that you understand that having a negative acceleration does not always mean you are slowing down! The rule is, if the velocity is in the same direction of the acceleration, you are speeding up. So, if the object is traveling to the left, negative velocity, and the acceleration is to the left, negative acceleration, then the object is speeding up. Whenever the velocity and the acceleration have opposite directions, the object will be slowing down. Kinematic Equations There are a set of equations that involve displacement, velocity, acceleration, and time. They are called kinematic equations because the term kinematics means the study of motion with no regard to mass and force. These equations are useful because they allow you to solve for a variety of problems that give you different pieces of information. For example, you may be given velocity and displacement but no time, and the problem may ask for the acceleration. You could not solve that with the equations above. Here is the list of widely used kinematic equations.  The Vf's are the final velocities. The Vo's (pronounced V naught) are the initial velocities. The arrows above the variables denote a vector value which we will address next chapter. Right now, all the arrows mean is you have to include a plus or negative sign depending on the direction. If there are not any arrows above the variables, you do not have to worry about the sign. Before considering the example below, I recommend that you read over the problem solving steps under the homework tips page. When dealing with problems that require you to utilize equations, it is best to follow those five steps to ensure success. I will outline those steps with the following example. A car has an initial velocity of 30.0 m/s and an acceleration of -1.0 m/s^2. Find its velocity after 10.0 seconds. The problem is dealing with velocity and acceleration. It is asking for a final velocity. Givens: Vo = 30.0 m/s a = -1.0 m/s^s t = 10.0 s Vf = ? All information is in meters and seconds. If the velocity was given in miles per hour and acceleration was given in m/s^s, then I would have to convert. Here is where you look at the given information and refer to your kinematics list to see which equation will work. In this situation, the first one will suffice. Plugging in the numbers we have, Which equals 20.0 m/s. We did not get a ridiculously large or small number, so it seems reasonable. These steps should be followed every time when dealing with problems that deal with equations. For the sake of time and space, I am not going to outline those steps every time. Now let's find the displacement of the car after 10.0 seconds. Since I now need displacement and I am given Vf, Vo from the problem above, and time, there is only one equation I can use. Plugging in the numbers gives, Which yields an answer of + 250 meters. How far will the car travel when it comes to a complete stop? A new given here will be the final velocity which is zero, because it is at a stop. Notice we are not given time, so we need to use the equation that has x,Vf,Vo, and a. Plugging in the numbers gives, solving for x yields + 450 meters. There are other problems to work through in the archive page under Chapter One. |