Lesson 7: Basic Units

In this lesson we will discuss the seven basic units of the metric system. These units can be combined with each other to define any quantity mankind knows of so far so as velocity which is meters per second or force which is kilogram meters per second squared. These units are used in almost every field such as chemistry, engineering, physics, and mathematics.

1. The first and most obvious basic unit is length. In the metric system, this unit is the meter.
2. Next is mass. This expresses the amount of acceleration an object acquires when subjected to a given force. The standard unit for this quantity is the kilogram. This is equal to 1000 grams.
3. Temperature expresses how hot or cold something is. In the metric system, the Kelvin is used. These units are equal to the Celius scale minus 273.15 degrees. This is due to the fact that the Kelvin scale is absolute, which means that 0 Kelvin is absolute zero and the object is as cold as it can possibly get which means it has absolutely no thermodynamic energy.
4. Electrical current in the metric system is expressed in amps. These units are typically seen on electrical devices along with a given voltage (which is a compound unit and will be covered later).
5. Luminous intensity is expressed by the candela. These units describe how bright a light source is such as a flashlight or spotlight.
6. The amount of matter in an object is expressed by the mol. This quantity is frequently used in chemistry.
7. Last but not least is time, which is expressed in seconds. I won't go into detail here because everyone has had experience with this unit.

With these units, any quantity imaginable can be described. They are extremely necessary in any field of work. So, think of a few objects and think of what units you would need to describe its parameters with.

For further information check out http://en.wikipedia.org/wiki/Metric_units

Lesson 6: Precision

Often, many people don't know that a single number not only descibes a quantity, but also the amount of precision which it is associated with. the number 200 is less precise than the number 200.0 You might be asking yourself why the same two numbers can have different precisions but the answer lies in where the decimal is placed and how many numbers are around it.

Lets first look at the number 200. (period, not a decimal) It is relatively uncertain because there is no decimal place. 200 could have been 249 so the person making the measurement could have just rounded it down or the number could have been 150 and the person making the measurement could have rounded it up. So, 200 is only accurate only to the hundred digit.

200.0 on the other hand is more precise because the decimal after the zero indicates that the number was not rounded in the hundreds digit. However, there could still likely be some rounding going on in this figure. However, due to the decimal place and the zero to the right of it, we know the rounding occured in the tenths place. The number could have been 200.04 or 199.95.

This is a particularly useful aspect to remember about measurements, especially in the modern world. Precision applies to almost every field. It is seen frequently in the news or in arguemental literature. So, when you are given a figure or measurement, take a moment to think about how precise the figure is and how significantly it could have been rounded.

Lesson 5: Scientific Notation

In the technical world, when extremely large or small numbers need to be expressed, a technique called scientific notation is often used to simplify writing these numbers.

In scientific notation, a number is simplified by moving the decimal place around until only one nonzero digit is to the left of it. Then, the number of digits the decimal was moved is compensated by multiplying the new number by some power of ten. This is a confusing concept to understand at first so if you are confused, just stick with it because the examples will help clarify what is going on.

Let's think of the number 2 000 000 000. In scientific notation, this can be expressed as 2.0 * 10^9 (two times ten to the nineth power). So what is happening here, is that the number 2 is being multiplied by 10 to the ninth power which equals 2 000 000 000. Lets take this process step by step so we can see what is happening.

1. We take 2 000 000 000 and move the decimal place over to the left until we have only 1 nonzero digit to the left of the decimal place. So now we have 2.000 000 000 which can be simplified to 2.0
2. We take note that we move the decimal place over 9 digits so then we multiply 2.0 by 10^9. The original number was made smaller so we must make the exponent on the ten larger.
3. Now, we have our final product which is 2.0*10^9 and is exactly equal to 2 000 000 000.

This process can work the other way. We can use this notation to make extremely small numbers easier to write. Lets go through an example to illustrate this. We will use .0000007

1. We will shift the decimal to the right seven places which will give us 7.0
2. We next multiply 7.0 by 10^-7 because we moved the decimal place 7 places to the right. We made the original number bigger so we must make the exponent smaller.
3. This then gives us 7.0*10^-7.

It is important to remember a few things when using this notation. The modified number should always have a decimal in it in order to indicate the amount of precision of the measurement (We will cover this in more detail later), and when we move the decimal to the left, or make the number smaller, the exponent on the ten must get bigger. In contrast, when we move the decimal place to the left, or make the number bigger, the decimal must get smaller.

Lesson 4: Applications of Newton's Laws

So far, through our lessons, we have covered all of Newton's laws. So, in order to get a better understanding of why they are important to us, let us look at a few examples and applications.

First, lets find out how to calculate our mass given our weight. This task is relatively simple when dealing with pounds in the English system because pounds of force is equal to pounds of mass on Earth. However, in the metric system, there is a more striking difference between weight and mass. Think of weight as the force you apply on the ground when you stand on it. Mass on the other hand is a quantity which is consistent with or without the presence of gravity.

So, let's say someone weights 200 Newton's. In order to find mass, we have to use Newton's second law which states, Force = Mass * Acceleration. On Earth, the gravitational acceleration is 9.8 (m/s squared) So, we plug in 200 (Newton's) = Mass * 9.8 (m/s squared) and solve for mass. If you aren't sure how to solve for mass, all we do is divide both sides of the equation by 9.8. So, this particular person's mass is 20.4 kg.

In another example we can find out how much force we have to apply to accelerate an object to some given acceleration. So, for example, we want to accelerate a hockey puck at 10 m/s squared. We will say a hockey puck has a mass of .1 kg. So, we use Newton's second law and plug the values in. Force = (.1 kg) * (10 m/s squared) The force we would have to apply would be 1 Newton.

Now, it is important to remember to keep our units consistent. When inputting values into our equations, we must use meters per second squared, kilograms, and Newtons to maintain simplicity. If you have units that are different, use conversions to convert them. Conversions can be readily found using major search engines.

So, try a few of these on your own. If you aren't sure what the specific measurements are of the particular situation you are analyzing, just ballpark the measurements for practice.

Lesson 3: Newton's Third Law

In continuation with our small series, today we will cover Newton's third law. This is the hardest law to conceptualize but with a bit of explanation, it will become clear.

Newton's third law states that for every force applied to an object, there is an equal force directed in the opposite direction. Contrary to what you might have heard, this law states that when you push something, it pushes back.

Now you might be thinking, how can we ever get something to move, if it pushes back when we push it? The catch is, multiple things get different pushes. To visualize this, the picture below illustrates a few examples.



First, the table exerts and equal force in the opposite direction of gravity to hold the bowling ball up. This is a simple illustration of what Newton's third law states. the negative sign in the equation means the forces oppose one another.

To illustrate this further, with more practicality, a boat towing another boat is illustrated. Each arrow represents the forces being applied along with their opposites. The tug exerts a forward force and an opposing force is seen in the water which is propelled backwards. The large boat is being pulled by the tug but is being opposed by the resistance of the water.

So image you are walking down the street. Your legs are pushing you forward but there is always an opposite force. The ground is actually pushing back (we will cover this in more detail later). This is what keeps your foot still and in this instance is in the form of friction.

This is a tough concept to fully learn and ingest. So just take a few minutes to think about some actions and opposing actions which you encounter every day and hopefully it should start to make more sense. If you are still having trouble, leave me a comment about what you are having trouble with and I will try to clear up the confusion.

This concludes the learning portion of our mini series. In the next few lessons we will apply what we have just learned to some practical, real life instances so you can get a greater understanding of the importance and uses of these concepts.

Lesson 2: Forces and Newton's Second Law

In our first lesson, we discussed Newton's first law and how it states that an object's motion only changes when a force acts upon that object. Today, we will cover Newton's second law.

This law states that the rate at which an object's momentum changes is equal to the force acting on the object. All this really means is that if we have an object and we apply a force to it, there is a direct relationship between the amount of force with which we push with on the object and how fast it ends up going.

Think of it this way. We have a light ball, and we softly push it across a table. It will go slowly across the surface of the table. If we take that light ball and push it extremely hard, the ball will speed across the top of the table. Now we take a heavier ball and push extremely hard. This time, however, the heavier ball has more mass and it rolls across the table slower because we have to push harder to make it go as fast as the light ball.

The length of the arrows in this picture represent approximate quantities. The longer the arrow, the larger the quantity is.



This law basically describes a relationship in terms of numbers. Don't get skittish because this is an extremely easy equation. All Newton's second law says is:

Force = (the mass of the object) multiplied by (the acceleration of the object)

So think of it this way. If we have a 1 kilogram ball and we want to accelerate it by 1 meter per second squared (this is the metric unit for acceleration and means that the ball will go 1 meter per second faster every second), we would have to apply 1 Newton (this is the metric unit of force and is acceleration times mass) of force with our arm.

And with that, we will end our lesson for today. So today, think of a few objects and try to imagine how much for it would take to get them moving in a certain direction.

Lesson 1: Forces and Newton's First Law

Forces can be thought of as a push or a pull. They involve one object acting upon another, like a pool ball hitting another pool ball, or the gravity of the Earth pulling us all down toward the ground. We all have had countless experiences with forces, whether we like it or not, like falling off of a ladder and being kindly welcomed by the pleasing hardness of the ground below us.

Isaac Newton, analyzed forces and motion and describes them in three simple laws. Now if you are getting at all finicky, don't worry, these are way easier to learn than you think.

Today we will start off with the first of three laws and we will cover the next two laws in the next two days and we will look at a few applications after that. With that being said lets begin.

Newton says that if an object is in motion, it will stay in motion, or if an object is not moving, it will stay still unless forces act upon it. At first glance this does not seem quite right because when you kick a ball, it eventually stops, or when a tool is set still on a slanted roof, it might slide off. However, we have to understand that it is extremely hard to find a place where no forces act on an object. On Earth, we have the force of friction that will slow that ball down after it is kicked, or we have the force of gravity which will pull the tool down off of the roof and towards the ground.

Think about it for a while, if we were in space and we were far away from everything, we would just float there. We wouldn't spontaneously start flying around because what would push us? This is the same for something that is in motion. If it is moving, what would be around to stop it? There would be no air resistance, friction, or gravity.

So for today, think about Newton's First law and try to imagine what would happen to the world if we took forces away such as gravity or friction.

With that we will end our first lesson and i will see you tomorrow for lesson 2.