## Thursday, September 16, 2021

### Understanding Vectors and Vector Math

Where are we going with this? The information on this page relates to the skills needed to investigate and evaluate the graphical and mathematical relationship (using either manual graphing or computers) of one-dimensional kinematic parameters (distance, displacement, speed, velocity, acceleration) with respect to an object's position, direction of motion, and time.

Understanding Vectors and Vector Math
(Oh brother! What now?)

In THIS, the concepts of vectors were looked at "from a distance" and by example. Here, we'll try to get a little closer and start thinking more about the math… Examples seem like a good idea, though, so… Yeah…

Let's begin with this little reprise:

The study of objects in motion and forces acting upon them relies heavily on using vectors. Thus, having an understanding of vectors is very important. So… we should talk about this…

A vector is a concept connected to quantities that specifies a magnitude and a direction.  Answering many physics questions about the world around us best done by using vectors.

Representing Vectors

It is very, very common to draw diagrams showing how vector quantities are acting on an object. Usually, there will be some sort of reference thing… the horizon… the plane of a ramp… often, the x-y axis thingy. (Thingy? Really? That's the best you can do?)

Vectors, in the diagrams, are represented by arrows.
• The direction that the arrow points indicates the vector's… direction.
• The length of the arrow represents its magnitude.
Vector arrows have a tail and a head. The pointy end is the head.

Strictly depicted, the length of the arrows should be drawn exactly in proportion to their lengths. So, a vector with a magnitude of 4 would be twice as long as one with a magnitude of 2 and half as long as one with a magnitude of 8. NOTE: any illustrations on this page are NOT strictly depicted!

Likewise, the angles should correctly represent the angle at which the vector operates on the object being observed.

Working With Vectors: The Big Picture

When more than one vectors of any give quantity (e.g. force, velocity, acceleration) operate on an object within some frame of reference, their effect combines. The the vector that results in the combination of each of the component vectors.

Component vector: Any individual vector having magnitude and direction within a given frame of reference.

Component vectors can be combined into a resulting vector (or the resultant vector).

A resultant vector can be broken down into its component vectors.

Working With Vectors: Graphical Conceptualization

Working with strictly depicted vector diagrams, all of the component vectors working on a single object can be rearranged such that they create a depiction of the resultant vector.

To do this, any of the vectors can, IF THEIR ANGLE WITHIN THE FRAME OF REFERENCE DOES NOT CHANGE, be moved so that its tail connects to head of the second vector. All of the vectors in the system can be moved in this same manner. This only works if the moved vector remains parallel to its original direction. (That is the same as saying that the angle does not change.)

A line from the tail of the first vector to the head of the last vector represents the resultant vector.

Moving a vector so that its origin is in a different place, but without changing its direction or magnitude is called vector translation.

Finding a resultant vector by translating component vectors is a process that is sometimes called "The Triangle Method."

 The blue vector is translated to the end of the green vector, andthe red vector is the resultant vector.

The order in which the vectors are rearranged does not matter. (This will be true when we look at the math process, too.) This is true combining vectors is essentially adding their effects, and since there's some fancy name (the commutative property) for math that says it doesn't matter what order we do addition.

 Source
Also, since… all that about adding their effects… if vectors point in opposite directions, their effects reduce each other, even to the point of cancelling totally. This is easily observed when two vectors are operating on a single line.

Think tug-of-war; two force vectors are pulling in opposite directions. When evenly matched, both forces have the same magnitude, but in opposite directions. Hence, the effect of the force does not result in the flag moving.

So (jumping ahead to math approaches), when operating in opposite directions, one vector can be thought of as positive and the other negative.

Working With Vectors: Math Processes

Mathematically, working with vectors begins with nearly trivial simplicity, then becomes more and more complex. The simplest situations involve vectors on a single line / axis. Next up are vectors at right angles. Finally, when the vector is some arbitrary angle to the axes, the math becomes most complicated.

Vectors On One Line

When vectors lay on a single axis, all that is necessary is to assign positivity and negativity to the directions. Left is negative, right is positive. Right is negative, left is positive. Up is positive, down is negative. Something like that…

The resultant vector is the sum of the signed component vectors.

A box moves from a point of origin 10 meters left, then 4 meters right, then 2 meters left, then 3 meters right. Where is the box in relationship to the point of origin.

∆d = d1 + d2 + d3 + d4

Where left is positive and right is negative,

d1 = 10 m
d2 = -4 m
d3 = 2 m
d4 = -3 m

∆d = (10 + (-4) + (2) + (-3)) m
∆d = 5 m left

Vectors At Right Angles To Each Other

In the case where more than one vector acts on an object and they are at right angles, the process is fairly easy.

The first thing to do is create a diagram aligning the vectors with the vertical and horizontal axes (x and y). If the vectors are perpendicular, one of them will align with each axis.

Then, translate one of the vectors so that its origin moves to the head of the other one.

The resultant vector will be the hypotenuse of the triangle formed.
• Its magnitude can be found using the Pythagorean Theorem.
• Its angle can be found using arctan (inverse tangent).

If you have several vectors that act on the same line, you can combine them into a single resultant vector. Once you have two perpendicular vectors, you can find the resultant (as above).

vector is some arbitrary angle to the axes

MORE TO COME!

## Wednesday, September 15, 2021

### ATP Quick Look: Adenosine Triphosphate-Cellular Energy

Where are we going with this? The information on this page should increase understanding related to this standard:  Evaluate comparative models of various cell type…Evaluate eukaryotic and prokaryotic cells.

ATP Quick Look
(So… We're really doing this?)

Okay… cells need energy… and… the mitochondrion creates it…

…in the form of adenosine triphosphate (ATP). It's actually a fairly easy concept, although the bio-chemistry behind it is fairly detailed. (Promises, promises!)

Cells need energy for a number of different functions (e.g. cell metabolism, transportation across membranes, moving muscles).

Energy in cells is stored as lipids (fats) and is made ready for use as carbohydrates (sugars). The ready-to-use sugars, however, are further processed into ATP by the mitochondrion. "ATP then serves as a shuttle, delivering energy to places within the cell where energy-consuming activities are taking place" [1].

ATP has two main parts:

The triphosphate part is made of… three phosphates in a chain.

It is this phosphate chain wherein the energy is stored.

Before we go any further, let's define some things.

So… what happens is this…

It's actually a cycle in which ATP gives off energy to become ADP or (sometimes AMP) and then later, becomes ATP again.

In the mitochondria, ATP is formed, and then shipped out to the cell to do some work. Where work needs to be done, one of the phosphates is broken off from the ATP.

Since energy is stored in chemical bonds and since the phosphate bond has a relatively impressive bonding energy, the breaking of the phosphate bond gives off a lot of energy—energy that the cell needs for the various functions mentioned earlier.

Back in the mitochondria, energy from sugar (to keep it simple) is used to reform that phosphate bond. In this way ATP is prepared for the next occasion that it is needed.

The ATP --> ADP --> ATP --> ADP… cycle goes on and one. (Likewise, if it's a case of breaking two bonds to become AMP, it's a cycle.)

To say it another way…

…sugar gets "burned" to provide energy to jam a phosphate onto an ADP making it an ATP.
…ATP goes out into the cell from the mitochondria.
…one of the phosphate bonds breaks releasing energy to power cell functioning.
…repeat

That's it… As a quick look, this is how ATP serves as the source of energy for cells.

Granted, this leaves out a LOT of details. More can be learned from the linked resources and many, many others.

## Tuesday, September 14, 2021

### Overviewing Vectors

Physics Index

Where are we going with this? The information on this page relates to the skills needed to investigate and evaluate the graphical and mathematical relationship (using either manual graphing or computers) of one-dimensional kinematic parameters (distance, displacement, speed, velocity, acceleration) with respect to an object's position, direction of motion, and time.

Overviewing Vectors
(Oh brother! What now?)

The study of objects in motion and forces acting upon them relies heavily on using vectors. Thus, having an understanding of vectors is very important. So… we should talk about this…

A vector is a concept connected to quantities that specifies a magnitude and a direction.  Answering many physics questions about the world around us best done by using vectors.

Understanding by example…

Whereas distance traveled is just a number and a distance unit… The race car driver drove 500 miles to win the race… displacement is a number and a distance unit AND a direction.

The box moved 20 m to the left.

The boxed changed position ( ∆x ) by a magnitude of 20 m and in the direction of left.

Working in 2D motion, the concept of vectors was assumed when positive and negative values were assigned to thing happening in opposite directions. When motion was to the right and acceleration was to the left, their magnitudes were given different signs. Likewise for up and down.

EXAMPLE 1
Working with Directions on the SAME line.

A ball with an initial velocity of 9 m/s is thrown directly upward on a planet where acceleration due to gravity is 3 m/s2. How long will it rise before stopping?

Solving this is simple (making it a fitting example):

Find t

Where
vi = 9 m/s
a = 3 m/s2
vf = 0 m/s

and where

vf = vi + at

Before solving, we need to "vectorize" the quantities. What's positive and what's negative? So… 2nd round…

Find t

Where
vi = 9 m/s up
a = 3 m/sdown
vf = 0 m/s up

and where

vf = vi + at

Not done yet… We need get the directions worked out so that we can math them! It's a nit that we usually do mentally, but… 3rd round…

Find t

Where up is positive

vi = 9 m/s up
a = 3 m/sdown  = -3 m/sup
vf = 0 m/s up

and where

vf = vi + at

Now, we can solve… easy!

vf = vi + at
0 = 9 m/s + (-3 m/s2 )(t)
-9 m/s = (-3 m/s2 )(t)
3 s = t

While that solution is relatively intuitive (up and down are in opposite directions; naturally, the ball will slow down), others (that will emerge in more complex situations) require the rigor of the formality in the 3rd round.

Moving on into 2 dimensions, we'll stick with displacement as the quantity…

EXAMPLE 2
Pizza Delivery Route as Vectors

Suppose a city laid out in perfect blocks (like graph paper where the lines are roads).

Okay, at point A is some dude or dudette who wants to get to point B. To do so, travel must result in TWO displacements (ish… Just hang in here as we develop the concept.)

The TOTAL displacement to the right has to be 3 blocks.

The TOTAL displacement up has to be 3 blocks, also.

Okay… suppose…

A pizza deliver robot is at point A. It sets out to delver a pizza by moving as follows:

1 block right…
2 blocks up…
1 block right…
1 block up…
1 block right.

Does it reach the customer at point B?

If you trace the path, you'll find out that, indeed, the pizza was delivered!

Okay… Let's ruin this…

Think x axis and y axis… meaning that (normally) right is positive and up is positive.

So, the total displacement is the total change in position… Let's go with

∆P

Therefore conceptually

∆P = ∆x + ∆y (ish, not exactly, but we're getting there…

So, ∆x is how much did it move on the x axis. ∆y is how much did it move on the y axis.

Let's grab those movements from above… and sort them…

2 blocks up
1 block up

1 block right
1 block right
1 block right

So, up is y and right is x…

∆x = 1 block + 1 block + 1 block
∆y = 2 blocks + 1 block

So, the total motion is (sticking with intuition, not formal math)

∆P = 3 blocks up + 3 blocks right

or

∆P = 3 blocks(y) + 3 blocks(x)

What just happened?

We took all of the x vectors and added them, then we took all of the y vectors and added them. Bam!

Okay, so… what if we wanted to get a little more formal?

We can do that…

Component vector: Any individual vector having magnitude and direction within a given frame of reference.

Component vectors can be combined into a resulting vector (or the resultant vector).

A resultant vector can be broken down into its component vectors.

Now, some caveats… common sense that needs to be outed…

1. Within a frame of reference (for simplicity, let's say the x-y axis frame of reference), component vectors have magnitudes ONLY on one axis.

2. The frame of reference will assign positive and negative to some direction on each axis; usually, up on the y axis is positive and right on the x axis is positive.

 fig 3
3. The resultant vector can be described as the sum of the x components and the sum of the y components.

4. However, it can also be described by its own (resultant) magnitude and an angle with respect to one of the axes (frequently, with respect to the x axis).

Returning to the pizza deliver (fig 3) robot, the blue line represents the resultant vector

While we can say that the total displacement is…

3 blocks right and 3 blocks up

we could also go with the x-y axis thing and say…

∆x = 3; ∆y = 3

Woh… that got mathy fast!

or we could say:

The resultant vector is some magnitude at some angle to the x axis.

Using the Pythagorean theorem, the blue line has a length that is the square root of 18. Geometry tells us that the angle of a triangle with two equal sides is 45°.

So…the resulting vector is

√18 = blocks long in a direction that is 45° above the x axis.

Enough, already… really! What happened to the pizza?

5. When "doing the math" you can't combine vectors of different quantities. For instance, you can't combine velocity vectors with acceleration vectors directly. They operate on an object differently.

6. Many different paths to deliver the pizza can end up at the same place. The robot could go 10 to the right, 10 up, then 7 left and 7 down. The sum of these component vectors would yield the same displacement:

∆x = 3; ∆y = 3

EXAMPLE 3
The 1100 mile per hour pitch.

In this example we are emphasizing the frame of reference. And… the math will be scant… so…

A really good baseball pitcher can hurl a ball at around 100 mph.

The earth rotates, completing approximately 24,000 miles in approximately 24 hours; hence, a point on the surface of the earth has a velocity of 1000 mph.

So, some alien orbiting the sun at the same rate as planet earth is looking through a telescope tuned to ONLY see the baseball.

From the frame of reference where the sun is not moving, then the velocity of the baseball (if thrown with the rotation of the earth is the sum of the pitch plus the velocity of a point on the surface of the earth.

Back up some… The sun is moving through the galaxy which is moving through the universe. Assuming that the universe is not moving, the velocity of the baseball is the sum of…

the pitch
the rotation of the earth
the motion of earth around the sun
the motion of the sun moving through the galaxy
and the motion of the galaxy through the universe…

Each of those component velocities could be added together to find the resultant velocity of the baseball.

## Wednesday, September 8, 2021

### Cell Organelles

Biology Index

Where are we going with this? The information on this page should increase understanding related to this standard:  Evaluate comparative models of various cell type…Evaluate eukaryotic and prokaryotic cells.

Article includes ideas, images, and content from Troy Smigielski (2021-09)

Cell Organelles

(Do they play music??)

Okay… starting with cell theory, we are expected to agree that…

Wait, we did that already! Okay, what next?

Let's look at those organelles we find inside the cells!

"An organelle (think of it as a cell’s internal organ) is a membrane bound structure found within a cell.

Just like cells have membranes to hold everything in, these mini-organs are also bound in a double layer of phospholipids to insulate their little compartments within the larger cells. You can think of organelles as smaller rooms within the factory, with specialized conditions to help these rooms carry out their specific task (like a break room stocked with goodies or a research room with cool gadgets and a special air filter). These organelles are found in the cytoplasm, a viscous liquid found within the cell membrane that houses the organelles and is the location of most of the action happening in a cell."

Nucleus

The nucleus houses the cell’s DNA in chromosomes (chromatin) and controls cell activities. The nucleus protects the DNA. If the DNA was not kept safe inside the nucleus, it would be vulnerable to damage from other things.

Not all cells have a nucleus. For instance, red blood cells do not. The function of red blood cells is to carry oxygen throughout the organism. Without a nucleus, they can carry ore oxygen.

So, does this make red blood cells prokaryotic? Not actually. They start out as eukaryotic cells, but as they develop, the get rid of their nucleus.

 Source, 2021-09

Consider this: Some breeds of dogs have their tails cropped-off routinely. Removing a part of the tail does not cause them to stop being dogs. In the same way, "cropping off" the nucleus does not cause a red blood cell to stop being eukaryotic.

But back to that genetic information in the nucleus… In the nucleus, the genetic information (DNA double helix) is packaged by special proteins (histones) to form a complex called chromatin. The chromatin undergoes further condensation to form the chromosome.

So, to sum it up a little, the nucleus houses the genetic information in chromosomes.

Nucleolus

The nucleolus is located inside the nucleus of a cell. The nucleolus is not bound by a membrane, so it actually isn't an organelle, but it is notable enough to warrant discussion.

The nucleolus is a space that forms near the DNA and there, it makes ribosomal subunits. Ribosomes are assembled in the nucleolus and exit the nucleus through openings called nuclear pores.

Ribosomes

Ribosome parts are built in the nucleolus. Both prokaryotic cells and eukaryotic cells have ribosomes.

The function of ribosomes is to build proteins.

Rough Endoplasmic Reticulum

Rough endoplasmic reticulum helps fold and modify proteins. It is studded with ribosomes.

This is the assembly line of the cell that has ribosomes as the workers.

Smooth Endoplasmic Reticulum

Smooth endoplasmic reticulum makes lipids, steroid hormones, and it helps in the detoxification of byproducts. It does not have ribosomes.

Golgi Apparatus (AKA Golgi Body)

Packages and ships proteins once they are made.

A Golgi body, also known as a Golgi apparatus, is a cell organelle that helps process and package proteins and lipid molecules, especially proteins destined to be exported from the cell.

Lysosome and Peroxisome

Have digestive enzymes that break down waste, food particles, and/or bacteria or viruses.

Mitochondrion (POWERHOUSE OF THE CELL)

The mitochondrion has the function in the cell to make ATP (adenosine 5'-triphosphate, cellular energy).  More on that can be found HERE.

The mitochondrion is the site of cellular respiration.

Vesicles

Molecules used for transport.

These are the "boxes" that proteins get packed into.

Plasma Membrane

Both prokaryotic cells and eukaryotic cells have a plasma membrane. It is also called a cell membrane or cytoplasmic membrane

Controls what enters and exits the cell.

The plasma membrane is made up of a phospholipid bilayer.

Cytoplasm

Surrounding all of the organelles within the cell is a fluid-like material called cytoplasm.

Putting it all together…

Well, cells vary in composition based on their function within the organism, but, a good, general picture of a cell includes ten key organelles, plus the cytoplasm in which they all are arranged.

Working together, all of the organelles carry out the work needing to be performed by the cell.

The Cell in Action

Thinking about how the cells carry out their work, it is convenient to think of some organelles as systems working closely together. One set of organelles forms what is called the endomembrane system.

The endomembrane system consists of the endoplasmic reticulum, the Golgi apparatus, and the vesicles.

These three organelles work together to make, package, and transport proteins.

Plant Cells

Plant cells have a few additional organelles. These organelles have important functions in plants, and are not found in animals.

Vacuole

"A vacuole is a membrane-bound cell organelle. In animal cells, vacuoles are generally small and help sequester waste products. In plant cells, vacuoles help maintain water balance. Sometimes a single vacuole can take up most of the interior space of the plant cell."

Plant cells have an organelle for storage. The large central, vacuole functions to store materials like water, sugar, or waste.

Some animal cells also have vacuoles.  However, in animals, vacuoles are smaller than their plant counterparts. However, in animals, vacuoles also usually appear in greater numbers.  There are also animal cells that do not have any vacuoles.

Chloroplast

The chloroplast is the site of photosynthesis, which makes sugar for the plant.

 275 ' Tall Tree

Cell Wall

The cell wall of plant cells functions to give structure and rigidity to cell. It also provides protection. It is made of cellulose (a carbohydrate, a polysaccharide).

The cell wall’s rigidity allows trees to grow up to 400 feet tall without falling over.

Mitochondrion vs. Chloroplast

The mitochondrion is site of cellular respiration and creates energy in the form of ATP.  The chloroplast is the site of photosynthesis and creates energy in the form of glucose (or other sugars).

Both animal and plant cells have mitochondria.

Both animal and plant cells need ATP.

However, only plants have chloroplasts. Animals do not carry out photosynthesis; the chloroplasts function as the location whereby photosynthesis takes place in plants.

How about a chart? That would be cool!

Cell Organelles and their Functions

 Function Organelle • houses the cell’s DNA inchromosomes (chromatin).• controls cell activities Nucleus • makes ribosomal subunits Nucleolus • build proteins Ribosomes • allows ribosomal subunits to exit the nucleus Nuclear Pores • helps fold and modify proteins. • studded with ribosomes Rough Endoplasmic Reticulum • makes lipids, steroids and hormones.• helps in the detoxification of byproducts. • does not have ribosomes. Smooth Endoplasmic Reticulum • packages and ships proteins once they are made. Golgi Apparatus • have digestive enzymes that break down waste, food particles, and/or bacteria or viruses. Lysosome and Peroxisome • makes ATP• site of cellular respiration Mitochondrion • molecules used for transport. Vesicles • controls what enters and exits the cell.• made up of a phospholipid bilayer. Plasma Membrane • a fluid-like material that surrounds all of the organelles within the cell. Cytoplasm • the site of photosynthesis, which makes sugar Chloroplast (plants only) • gives structure and rigidity to cell Cell Wall (plants only) • store materials like water, sugar, or waste. Vacuole (plants only)

## Tuesday, September 7, 2021

### Eukaryotic and Prokaryotic Cells

Biology Index

Where are we going with this? The information on this page should increase understanding related to this standard:  Evaluate comparative models of various cell type…Evaluate eukaryotic and prokaryotic cells.

Article includes ideas, images, and content from Troy Smigielski (2021-09)

Eukaryotic and Prokaryotic Cells
(Hmm… What now?)

Okay… starting with cell theory, we are expected to agree that:
1. All living organisms are made up of cells.
2. Cells are the basic unit of life.
3. All cells come from pre-existing cell.

Furthermore, all cells are made up from four basic biomolecules.

But all cells are not the same. There are two basic types of cells: eukaryotic and prokaryotic.

Eukaryotic Cells

The first type of cell we will discuss are called eukaryotic cells. To begin with, eukaryotic cells have a nucleus and membrane-bound organelles.

So, just what are membrane-bound organelles?

A membrane is an outer lining or covering.

Organelles are the smaller parts of the cell that have specific functions.

For example, the nucleus or the mitochondria are membrane-bound organelles. The organelles are the parts that make up a cell.

Secondly, eukaryotic cells have ribosomes, which are organelles that make proteins.

Additionally, eukaryotic cells are larger and more complex than prokaryotic cells. Prokaryotic cells  are between 1 µm and 10 µm while eukaryotic cells are between 10 µm and 100 µm in size.

It is worth nothing here that plant cells have a cell wall whereas animal cells do not. So, eukaryotic cells occur both with and without cell walls.

Based on having eukaryotic cells, some organisms are classified as eukaryotes.

If an organism has eukaryotic cells, it is said to be a eukaryote. Alternately, if an organism has prokaryotic cells, it is said to be a prokaryote.

Okay, cool…

Eukaryotes are generally multicellular although they can be unicellular. For instance, diatoms are unicellular eukaryotes that produce ~20% of earth’s oxygen.

Examples of eukaryotes include animals, plants, and fungi.

 By File:Osmia rufa couple (aka).jpg: André KarwathFile:Boletus edulis (Tillegem).jpg: Hans HillewaertFile:Volvocales.png: Aurora M. NedelcuFile:Lightmatter chimp.jpg: Aaron LoganFile:Ranunculus asiaticus4LEST.jpg: Leif StridvallFile:Isotricha intestinalis.jpg: Agricultural Research ServiceCompilation: Vojtěch Dostál - File:Osmia rufa couple (aka).jpgFile:Boletus edulis (Tillegem).jpgFile:Volvocales.pngFile:Lightmatter chimp.jpgFile:Ranunculus asiaticus4LEST.jpgFile:Isotricha intestinalis.jpg, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=5321214

Some eukaryotic cells will have flagella and/or cilia. These function in cellular movement.

In eukaryotes, DNA is housed in the nucleus in structures called chromosomes (chromatin).

Eukaryotic Cells Summary:
• Eukaryotic cells have a nucleus and membrane-bound organelles.
• Eukaryotic cells have ribosomes, which are organelles that make proteins.
• Eukaryotic cells are larger and more complex than prokaryotic cells.
• Based on having eukaryotic cells, some organisms are classified as eukaryotes.
• DNA is housed in the nucleus in structures called chromosomes (chromatin).

Prokaryotic Cells

The next type of cell we will discuss are called prokaryotic cells. Prokaryotic cells do NOT have a nucleus and do NOT have membrane-bound organelles.

All prokaryotes have a cell wall.

Prokaryotic cells also have ribosomes.

Prokaryotic cells are smaller and less complex than eukaryotes.

Organisms made up of prokaryotic cells are called prokaryotes.

Prokaryotes are usually unicellular although there is some debate that they can be multicellular.

Examples of prokaryotes are bacteria and archaea.

Another difference between eukaryotes and prokaryotes is found in the way they arrange their DNA. Recall that in eukaryotes, DNA is housed in the nucleus in structures called chromosomes (chromatin). In prokaryotes, DNA is floating freely in one chromosome and is circular in shape.

There are extra pieces of DNA called plasmids that can be transferred to other prokaryotes. These typically carry favorable genes like antibiotic resistance.

Prokaryotic Cells Summary:
• All prokaryotes have a cell wall.
• Prokaryotic cells also have ribosomes.
• Prokaryotic cells are smaller and less complex than eukaryotes.
• Organisms made up of prokaryotic cells are called prokaryotes.
• Prokaryotes are usually unicellular, although there is some debate that they can be multicellular.
• DNA is floating freely in one chromosome and is circular in shape.

__________________________

The Endosymbiotic Theory

 Source
If all cells come from other cells… where did the original cells come from? In an attempt to explain a process that would explain the presence of the existing variances in cells, biologists have constructed a theory.

"The endosymbiotic theory states that some of the organelles in today's eukaryotic cells were once prokaryotic microbes. In this theory, the first eukaryotic cell was probably an amoeba-like cell that got nutrients by phagocytosis and contained a nucleus that formed when a piece of the cytoplasmic membrane pinched off around the chromosomes. Some of these amoeba-like organisms ingested prokaryotic cells that then survived within the organism and developed a symbiotic relationship. Mitochondria formed when bacteria capable of aerobic respiration were ingested; chloroplasts formed when photosynthetic bacteria were ingested. They eventually lost their cell wall and much of their DNA because they were not of benefit within the host cell. Mitochondria and chloroplasts cannot grow outside their host cell." (Source, 2021-09-07)

According to the endosymbiotic theory one ancestral prokaryote (with no membrane bound organelles) ingested a mitochondrion.

Rather than the mitochondrion being broken down, the two cells began to live in symbiosis which is where they help each other out.

 https://ib.bioninja.com.au/standard-level/topic-1-cell-biology/15-the-origin-of-cells/endosymbiosis.html

This process continued until the modern-day eukaryote evolved with many organelles.

So, according to the theory, the complex arrangement of the eukaryotic cells resulted from the happenstance merger of smaller prokaryotic cells that resulted in a symbiotic relationship. The repeated occurrence of these mergers eventually produced the various, specific-functioning cells we can identify now.

__________________________

Wow! That's a lot of stuff about something so small! Seriously… How about a chart?

Comparison of Eukaryotic and Prokaryotic Cells

 Prokaryotic Eukaryotic Nucleus? No Yes Membrane-bound organelles? No Yes Cell wall? Yes Animal - NoPlant - Yes General Cell Type Unicellular Multicellular Cell size Smaller Larger, more complex DNA Location Floating freely Within nucleus Examples Bacteria AnimalsPlants.