Biography Project

Part 0 – Basic Facts

When did this person live and die?

Where were they born, where did they work?

On March 23, 1882, Emmy Noether was born in Erlangen, which is a town in Bavaria. She taught at various universities, including the University of Erlangen, University of Göttingen, and the University of Moscow. She went on to work at Bryn Mawr in the United States. On April 14 1935, she died in after several tumors were discovered in her pelvis.

Part 1 – The Work. What did this person do?

What did they accomplish in their field?

Emmy Noether has become famous for her influence in the field of abstract algebra. In the history of mathematics, she has come to be regarded as one of the most influential women. All of her work was divided into “three epochs; the first dealing with invariant theory, the second commutative rings, and the third noncommutative algebra”. She proved Noether’s theorem, which

What did other scientists think of them?

Pavel Alexandrov and Hermann Weyl, who were her colleagues, and Albert Einstein all consider Noether to be “the greatest woman to ever work in the mathematics field”. The respect she garnered from her colleagues was evidenced when Albert Einstein asked her for assistance in the development of one of his theories; she was the only woman on the faculty. Respect was again shown to her in 1964 when she was the only woman honored at the World’s Fairs’ “Men of Modern Mathematics” exhibit.

Part 2 – The Person. Who was this person? How did he/she get that way?

What challenges did they overcome in their personal lives?

Emmy Noether struggled to gain respect from her male colleagues. During her lifetime, her field was dominated by the male sex. As a result, she pushed herself to work harder. She put herself in situations where she was the only female; working with Einstein and at the World’s Fair. Although she feared that she would not be received well by those around her, she did not let that stop her.

Emmy was also forced to deal with hatred from her society. She was living and working in Germany when the Nazi party came into power. She was Jewish and as a result her entire life was uprooted during World War II. Her brother, who was a professor like herself, moved his family to Siberia to protect himself. Emmy moved all the way to the United States, where she began working at Bryn Mawr, in order to stay safe. Although she enjoyed working with other females (Bryn Mawr is an all-female college), she was still saddened to have left her native homeland.

What kind of relationship did they have with their family members?

Although Emmy was the oldest of four children, she and her brother Fritz were the only ones who survived. Her interests aligned with her brother's, for he was also a mathematician. It is clear that they received their mathematical talents from their father, Max Noether, who was also a noted mathematician.

Part 3 – The Society. What kind of world did this person live in?

What were the usual expectations of women in this society? What limits were there? Emmy Noether lived in a time where women were considered second class citizens. They were treated as inferiors to men, and were expected to cook, clean, and care for children around the house. This was not what Emmy wanted to do. She was a hard-working female who was passionate about math. She did not wish to stay at home, caring for others. She wanted to forge ahead and do great things.

What were some of the biggest issues that people worried about at that time? Emmy was alive and working during the Second World War. It was hard because she was Jewish and was based in Germany. Hitler and his party expelled her from her job as a professor at the University of Gottingen. Luckily for Emmy, she was offered a position at Bryn Mawr, so she was able to flee to the United States. If she had not been granted this opportunity, there is a great possibility that she would have been taken to a concentration camp like millions of other Jews. Her passion for and skill in math saved her life.

Part 4 – Interactions. Consider how the work, the person, and the society influenced one another.
Did this person's work influence their family life, or vice versa? Because Emmy was an educated woman, she was able to secure good jobs for herself. She was not always graced with respect, but she always earned it eventually. Because of the Nazi Party in Germany during World War II, her family was forced to uproot their lives. Emmy's brother Fritz moved his family to Siberia to escape persecution and Emmy could have gone with him. Her knowledge and skill landed her a job in America though. Although she was safe, she was far from her family members. Her life was completely different from theirs.

Did the politics or values of his/her/our society influence this person's work, or vice versa? It is probably safe to say that the values of Emmy Noether's time, that men were superior to women, shaped her work. She expected her life to lead down a path where she taught a language, but instead she ended up as a mathematician. This is ironic because math is one of the only unbiased subjects in society. There is no segregation when dealing with numbers and symbols. Since Emmy lived in such a turbulent time, it is rather ironic that she would excel in such a stable field as mathematics where there is a right answer and a wrong answer.

Part 5 – How did she cope when men tried to sabotage her career at every opportunity? Although many men felt that Emmy Noether was not deserving of respect within the field of mathematics, she proved them wrong by releasing over 40 papers and numerous theorems. She also aligned herself with genius (e.g. Albert Einstein) and gained assistance from some of her male friends. Through hard work and determination she overcame the adversity of sexism and established herself as a remarkably noteworthy mathematician.

My information was obtained from http://en.wikipedia.org/wiki/Emmy_Noether. and

http://www.agnesscott.edu/lriddle/women/noether.htm

Journal Entry 5/9 Continued

The person in the photo is the man's son. Since the man looking at the photo has no brothers and sisters we know that he is talking about himself when he says "my father's son". The riddle can now be read as "that man's father is me". Therefore the man in the photo is his son.

Journal Entry 5/16

To test Gretchen's idea, we need to use the magnet that we have. Although we are unsure at this point if the fur and silk have made magnets of the rods, we do know that these rods have opposite charges. We know they have opposite charges because they attract on another. If we put the two rods near the magnetic poles, and one rod attracts the magnet and the other rod repels the magnet, we will know that the rods themselves have become magnetic. When the experiment is performed the magnet is attracted to both rods which means they do not have opposite magnetic charges and therefore are not magnets. Gretchen is wrong. The rods aren't magnetic.

Journal Entry 5/9 Continued

I don't understand why my answer is wrong. Why isn't the person in the picture the son? If the person looking at the photo has the same father as the person in the photo and said person (the viewer) has no brothers and sisters, it has to be that person. The viewer is the son. I'm really struggling here, because I can't see where I made a mistake.

Journal Entry 5/9 Continued

Having reread my explanation, I can see how that sentence threw you off. It is supposed to read, "If Dan and the man in the photo have the same father, "that man's father is my father", then the man in the photo is Dan himself!" I accidentally typed photo twice when I meant father the second time. I think this clarifies my answer, but if it doesn't let me know and I will try again.

Journal Entry 5/9

(Q) A man is looking at a photograph of someone. His friend asks who it is. The man replies, "Brothers and sisters, I have none. But that man’s father is my father’s son." Who was in the photograph?

(A) Let's say that the man looking at the photograph is named Dan. Dan has a father, named Tom. Dan's grandfather and Tom's father is named John. The riddle says that Dan is the one looking at the photo, so "my" represents Dan. By starting at the end of the riddle, we can figure it out. "My father's son" actually means "Dan's father's son" which means Dan, because he is his father's son. The riddle also says "that man's father". "That man" represents the person in the photo. If Dan and the man in the photo have the same photo, "that man's father is my father", then the man in the photo is Dan himself!

Journal Entry 5/1

(Q) Why does a tank have treads?
(A) A flat piece of rubber has a large area that touches the ground. The tank itself has a constant force, regardless of the terrain that it covers. When an object has a force and a large area, its pressure is not very large. The addition of treads to the rubber breaks up the area though. Even with the same force, but with a smaller area in contact with the ground, the pressure of the truck is increased. If the tank has a larger pressure, it is better equipped to go through a rugged landscape.

(Q) How do cleats work?
(A) Cleats are similar to treads on a tank. If you are wearing a basic sneaker, a large area of rubber is touching the ground. Your weight does not fluctuate while wearing the sneakers, so your force is constant. Therefore, with a force and a large area, the pressure will be small. Cleats help to increase an athletes pressure because they reduce the surface area of the shoe. The spikes on the bottom of the cleat have less area than a flat piece of rubber. When the force remains the same, but the area is reduced, the pressure increases. This is good because it helps athletes grip the ground while playing their sport, and it reduces the time they spend on the ground as a result of slipping and falling.

(Q) Why does a pin have a dull end and a sharp end?
(A) The purpose of a pin is to be used by a person to sew. It needs to have two pressures. Low pressure is necessary to enable the use/holding of the pin and high pressure is necessary to puncture the fabric. In terms of a pin, the dull end has a large area. The user's force on the pin does not fluctuate. With a force and a large area, there is a small pressure. The sharp end of the pin has a smaller area than the dull end. Because the force of the user on the pin has not changed, the pressure is increased with a smaller area. This is great because pins can be used to hang things up and they do not make people bleed, unless they push from the wrong end of course!

Journal Entry 4/25

Sorry this blog is so late...when I checked the website, no assignment was posted. Here's my work though:

(1) If you were to pour some orange juice into a glass, the glass is acting as a force of the juice. The glass does not shatter or fall in on itself, so clearly the force of the glass on the juice is counteracted by some other force. This means that the orange juice must have a force on the glass. For orange juice to have a force on something else, it must be made up of tiny particles that are in constant motion. This makes sense because I know that if I were to leave that glass outside, when I came back the juice would have evaporated from the glass. If the particles inside were not moving, how would that orange juice have evaporated? It wouldn't have. I am confident in my belief that the collisions of the particles within the juice, which are moving, act as a force against the glass and prevent the glass from falling in on itself.

(2) I know that gases are made of very small particles, in constant motion, with a lot of empty space between them. If I were to position 5 people at different spots on the floor, then spray, consecutively, two fragrances into the air, the person closest to the initial spray would smell the fragrances first and the person farthest away would smell it last. Every single person, regardless of their position, would smell the fragrances. This is because the empty spaces in the air take in the particles of fragrance. The fact that people in different locations all eventually smell the fragrance proves that gases are in constant motion. The fact that fragrances (plural) can be sprayed into the air proves that there is empty space in said air. If there were no spaces, then the fragrance wouldn't go into the air at all and no one would smell it.

(3) I know that liquids are also made of small moving particles because of evaporation. When a liquid is spread across a piece of paper, that spot gradually and slowly shrinks. The liquid particles do not go into the desk, they jump off the paper into the empty spaces in air. I also know that the empty space within a liquid is present, but less than that of air. If I was to combine two liquids, let's say 50 ml of blue liquid and 50 ml of green liquid, these two would form one liquid that was slightly less than 100 ml, like 96 ml. This proves that some particles of one liquid go into the empty spaces of the particles of the other liquid. The fact that the two colors mesh into one also proves that the particles are moving (hitting off of one another) and falling into empty spaces. There are less empty spaces than in gas though because there is only so much additions to the water that you can have, before there's too many.

(4) When you add heat to a system, the particles begin to move faster and they hit off of each other more frequently. For example, when you put a pot of water on the stove and then turn it on, you are adding heat to the system. Initially, the water is still. With time though, the water begins to boil. The molecules of water are hitting off of each other so much (with the addition of heat) that they begin to break through the surface. In contrast, when a substance is cooled, the particles begin to slow down. This is turn lowers the frequency of their collisions. If you take a glass of water and put it into the freezer, it will eventually turn to ice. This is because the cold is slowing down the particles to a point where when they collide with one another they begin to stick together, rather than bounding off. These connections reduce the area of the water and turn it into a solid, rather than a liquid.

Journal Entry 3/27

What type(s) of energy can be identified in the system in the initial state?

There is elastic potential energy in the system because the spring is being compressed.

What type(s) of energy can be identified in the system in its final state?

In the final state of this system, the car has gravitational potential energy (more so than in the before state).

Is there any work done on this system? How do you know?

No work was done on the system because there were no external forces influencing the objects.

How does the total energy of the system in the initial state compare to the total energy of the system in the final state?

The total energy of the system in the initial state equals the total energy in the final system. The elastic potential energy was converted into kinetic energy and gravitational potential energy. The gravitational potential energy is larger than the kinetic energy because the car is at the peak of the track. Therefore it is at the highest point away from the ground. The kinetic energy cause the car to move though, hence its presence in the final state.

Journal Entry 3/14

Can a light object have a large momentum? Give two examples and explain.
Can a heavy object have a small momentum? Give two examples and explain.

Momentum is directly related to both mass and velocity. The size of momentum is large or small in relation to its size and speed. If a light object is moving extremely fast, like a tiny chihuahua running at top speed, its momentum will be large in terms of its small size, but in the scheme of things it will not be that big. If the little dog weighed 0.5 pounds and was running at 5 mph (which is probably really fast for a chihuahua), it's momentum would still only be 2.5. That's not very large. If that same chihuahua was dropped out of a plan however (and fell at 125 miles per hour) it's momentum would be 62.5. Although this momentum is much larger than when the dog was running, it is still not that big. The same thing goes heavier objects. It is nearly impossible for them to have small momentums. When mass is so large, it doesn't matter how slow the object is moving, their momentum is still larger than fast moving light objects. If there was a cement truck (75,000 pounds) moving along the road at 1 mph, the truck would still have a momentum of 75,000. The only time when a heavy object could have a small momentum would be if it was at rest and had no momentum.

Can a small Mini Cooper and a large Cadillac ever have the same momentum? What would that look like? Explain.

A Mini Cooper and a large Cadillac could have the same momentum. A Mini Cooper weighs about 2,700 pounds and a large Cadillac weighs about 7,000 pounds. Lets say that the Cooper was speeding along the highway, going 90 mph. Under the overpass of the highway, a large Cadillac is driving along the residential road at 35 mph. Because moment is calculated by multiplying mass and velocity, both the Mini Cooper and the Cadillac have a momentum of 243,000. They are equal!

Journal Entry 3/07

As a freshman, my goal was to graduate from High School with a firm and resolute idea of what I would do with the rest of my life. Looking back on this idea as a senior, I realize that my goal was unrealistic. I don't think it's possible to plan your future. There is no way to predict what obstacles I will face or what triumphs I will enjoy. Although the High School did not fulfill my freshman objective, it went above and beyond that. Pequannock Township High School opened my eyes to the many wonderful components of this world. I have always tended to have a rather rigid perception of the world; success has always been equated with a high-profile job as a lawyer or a doctor. Through the teachers and students I have met though, I've come to realize that there is so much more to life than just monetary prowess and fame. Teachers should push their students to continually search for the "truth and beauty" you so often talk of. By exposing kids to a diverse body of knowledge, the High School will go a long way in changing students lives for the better. In response to the teachers actions, students need to remain open-minded at all times and be willing to embrace things outside of their comfort zone. I am fortunate to have encountered teachers who have changed my way of looking at things, and because I held on to these insights I am all the better for it.

Four years from now I hope to be preparing to graduate from a distinguished university (such as Cornell!!) and be setting my sights on either law school or other graduate work. As I truly enter the "real world" I hope that I find a job that will satisfy all of my desires. I am dedicated to making the world a better place, however cliché that may sound. It is important "to be the change you wish to see in the world", as Ghandi said, and I know that I want to live in a society with an improved set of values. We need to come together and disregard all our differences so that everyone can benefit from the wonders of this world. At this point in my life I'll probably be dreading payments on loans and wishing for millions of dollars, but I'll still be true to myself. I know that I will be a much more diversified person. Right now I live in the bubble that is Pequannock. After college, I will have met people from all over the world, and I know that their experiences and their beliefs will all serve as influences on me!

Ten years from now I see myself completed with my graduate studies and securing a position at a law firm or in some corporation. I will also be working a lot on networking. I want to stay in contact with the people I meet at college because I know that they will be crucial when I decide to enter into the political arena. Because I will not have been out of college for very long, I probably will not be in a serious leadership position at this point. I will however be dedicating myself to my profession, while again remaining true to myself. I feel that I have very strong convictions and I would not violate them for anything. My goal is to not get caught up in the drama that seems to be constantly corrupting the world. I know that I will be able to evaluate myself through other people. I will contact friends from high school and get together with them. If they feel that I have changed greatly, in a bad way, from our last encounter, I will know that I did not achieve my goal.

Twenty years from now I will be testing the waters of the political pool. It has always been/always will be my dream to become President of the United States. I know that I cannot graduate from college and head to Washington, intent on securing the position as Leader of the Free World. After I have established a stable foundation upon which to live, and have begun my family, I will take the time to do what I really want, serve the people. I see so many things that are wrong with society, and I know that I am not alone in my beliefs. I hope that by the time I am ready to become a representative of the people, their faith has been restored in our government. If it has not, then there will really need to be drastic changes, many of which will hopefully come with my assistance. As I evaluate my life twenty years from now, I know that I will continually ask myself whether the world is a better place because of me. If it is not, I will need to reevaluate my priorities, because I am determined to make this land that has fostered me, great for those around me and those to come. Looking back on high school, I think that I will remember all of the laughter that I experienced. I don't think a single day has gone by when I haven't been smiling. I have felt some of the purest happiness amidst the walls of Pequannock Township High School, thanks to both my friends and my teachers. If I am ever feeling down I know that I can look back on my high school years, and they will lift up my spirits.

If I were to send a message to myself, twenty years from now, I would say, don't forget the calm you found in high school. It's so easy to get caught up in the stresses of life and to blow things out of proportion. With every dilemma you face, take a deep breath and search for the best solution. If you have a problem, that problem remains whether you are screaming or whether you are staying calm and addressing it. Also, don't ever lose sight of the goals that you set for yourself years ago. The journey of your life may have taken you down a rather unexpected path, but you still have the potential for greatness!

Journal Entry 2/14

1) The three experiments mentioned have prompted the discovery that circular motion is the result of an unbalanced force in the direction of the center of an object.
--> Bowling Ball: When the ball is rolled in a straight line, an unbalanced force is necessary to change its path of motion. Rapid taps on the side of the ball cause it to move in a circle. This tap is a force toward the center of the object. The path of motion that ensues is circular.
--> Bucket: When the bucket is swung in a circle, the water does not come out. The rope is an unbalanced force pulling on the bucket. Because the rope is pulling towards the center, the bucket moves in a circle and the water stays inside.
--> Air puck: If the air puck is turned on it will glide in a straight line. When it is attached to a string anchored to the floor, however, it begins to move in a circle. The string is an unbalanced force on the puck. Because this net force is pulling towards the of the object, said object moves in a circle.

2) When a small ball is rolled inside a ring-shaped track, the same pattern is observable. The track acts as an unbalanced force on the ball, pushing inward on this object. This causes the ball to move in a circle. The notion that the track is an unbalanced force can be tested if a piece of the track is removed. When a piece of the track is removed, the unbalanced force is removed from that portion and the ball leaves the track in a straight line.

Journal Entry 2/1 Continued

Newton's Third Law: F a on b = - F b on a

1. You are seated on a bench. The earth exerts a force on you, and the bench exerts a force on you. Do these two forces represent a Newton’s Third Law force pair? Explain.

In this situation, both forces are being exerted on me, which means they violate Newton's Third Law and cannot be force pairs.

2. A pen sits on a desk. The desk exerts a force on the pen, and the pen exerts a force on the desk. Do these two forces represent a Newton’s Third Law force pair? Explain.

In this case, the pen is object A and the desk is object B. Both are exerting a opposite force on the other, making them a Newton's Third Law force pair.

3. You pull on a rope. The rope pulls on a wagon. Do these two forces represent a Newton’s Third Law force pair? Explain.

Although there are two forces being exerted here, they are being exerted on different objects. Object A (me) is pulling on object B (rope). Object B (rope) however is pulling on Object C (wagon). These forces do not support Newton's Third Law.

4. A book slides across a tabletop. The book exerts a downward force on the table, and the table exerts a frictional force on the book opposite the direction of its motion. Do these two forces represent a Newton’s Third Law force pair? Explain.

Although there are two forces here, the book's downward force on the table and the frictional force of the table on the book, they do not correlate because one is a vertical force and the other is a horizontal force.

In my original post, I continually remarked that an object could not be moving without an unbalanced force. This is a false statement. Through recent lessons I have to come to realize that an unbalanced force is only necessary for initial movement. Once an object is in motion, there does not need to be an unbalanced force. For example, after a bowling ball is rolled and it reaches a constant speed, there is no unbalanced force on it, but it is still moving.

Journal Entry 2/7

Describe in words how the magnitude of the frictional force that the table's surface exerts on the block varies in opposition tot he forces exerted by the spring pulling on the block.

As the force exerted by the spring increases, the amount of friction exerted on the object by the surface increases. once the force of the spring overcomes the force of the friction however, both forces lessen. When there is constant motion, there is constant friction. These support Newton's Third Law which says that the Force of object A on object B is equal and opposite to the Force of object B on object A.

Journal Entry 2/1

1. You are seated on a bench. The earth exerts a force on you, and the bench exerts a force on you. Do these two forces represent a Newton’s Third Law force pair? Explain.

The earth is exerting a downward force on me, trying to pull me down. The bench on the other hand is exerting an upward force on me, pushing me up. I am not moving which means that there is no unbalanced force on me. Because these forces are opposite and equal, they represent a Newton's Third Law force pair.

2. A pen sits on a desk. The desk exerts a force on the pen, and the pen exerts a force on the desk. Do these two forces represent a Newton’s Third Law force pair? Explain.

The desk is exerting an upward force on the pen, pushing it up. The pen is exerting a downward force on the desk, pushing it down. Again, nothing is moving so there is no unbalanced force in this scenario. Therefore the forces are opposite and equal and represent a Newton's Third force pair.

3. You pull on a rope. The rope pulls on a wagon. Do these two forces represent a Newton’s Third Law force pair? Explain.

If my pull on the rope is to the left, I am exerting a force to the left. Because of me, when the rope pulls on the wagon it will also be exerting a force to the left. Although the forces may be equal, they are not in opposite directions. They cannot be a force pair for Newton's Third Law.

4. A book slides across a tabletop. The book exerts a downward force on the table, and the table exerts a frictional force on the book opposite the direction of its motion. Do these two forces represent a Newton’s Third Law force pair? Explain.

Although there are two forces here, the book's downward force on the table and the frictional force of the table on the book, they do not correlate because one is a vertical force and the other is a horizontal force. Also, because the book is sliding across the tabletop, there is an unbalanced force. Therefore, this is not a force pair of Newton's Third Law.

Journal Entry 1/24

Why is there a debate about whether or not Pluto is a planet?

There is debate about whether or not Pluto is a planet because objects have been discovered beyond it that are much larger and also orbiting the sun. This orbit makes these objects a part of our solar system, and since there are many varied definitions for what a planet actually is, they may all be worthy of the title: "Planet".

How is Pluto similar to the inner planets? How is it different?

Pluto is similar to the inner planets in that it is circular (which means that there is a gravitational force pulling all matter towards the center) and that it orbits the sun. Its orbit is questionable though, because it is the only object that crosses orbits with another (Pluto's "planetary orbit" crosses paths with Neptune). Within the eight inner planets, there are inner and outer planets. The inner planets are: Mercury, Venus, Earth and Mars. The outer planets are: Jupiter, Saturn, Uranus, Neptune. All of the outer planets are larger than the inner ones. Pluto does not fit this mold, for it would be considered an outer planet, but is smaller than the other outers. It is also different in that it does not have the hydrogen and helium atmosphere of the other outer planets.

What is the name of the region in the outer solar system, beyond Pluto, which contains many recently-discovered large objects?

The region beyond Pluto is called the "Kuiper Belt". It contains many recently-discovered large objects.

What do you think of the controversy about whether or not Pluto is a planet? How should we decide who is correct?

In a way it is entertaining that there is such a controversy surrounding Pluto. I think that because this celestial body is so distant and so mysterious, it appeals to the public and there is some kind of instinctual need to protect it. As far as determining whether or not Pluto is a planet, I don't think it should be considered one. Objects that are much larger have been discovered and they have not been classified as planets. The sense of obligation to keep Pluto as a planet is just a product of the human tendency to reject change. Just because Pluto has been considered a planet for 60 years, that does not necessarily mean that it is one. A universal definition of a planet is necessary to decide whether or not Pluto qualifies as one. If this definition is created, the future of planetary science will be a lot more manageable.

Journal Entry 1/11

1. What is the difference between a "force" and a "net force"?

"Force" is the result on an interaction between objects. When a ball is resting on the ground there are two forces interacting with it. The Earth is a force on the ball, pulling in down. The ground is also a force on the object, pushing it up, preventing it from being drawn into the core of the Earth. There is also force on an object when that object is pushed, or pulled, or lifted up. The "net force" is another term for an unbalanced force. In the previous example, the force of the Earth on the ball was balanced by the force of the ground on the ball. If that same ball was rolling along the ground and then a meter stick was pressed against the side of the ball, that meter stick would represent an unbalanced force. In this scenario, the forces of the Earth and the ground are still balanced, but the meter stick is unbalanced.

2. How do you determine the direction of the net force"

The direction of the net force of an object can be determined by using the arrows in a force diagram or by using simple addition and subtraction. Let's say that there is a large block sitting on the sidewalk, and Jen and Dan both stand on opposite sides of the block. Dan pulls the block 50 units to the right and Jen moves the block 35 units to the left. If we were representing this situation with arrows, the forces of the earth on the block and the ground on the block would be balanced, so their vertical arrows would be the same length. Their horizontal arrows would not be the same length however. Because Dan is exerting a greater force on the box (50> 35), the arrow to the right would be longer than the arrow to the left. From the diagram, we would be able to see that the direction of the net force would be to the right. If we were to use basic arithmetic to represent the same situation, we would represent 50 units to the right as (+50) and 35 units to the left as (-35). We would then add these numbers together, to get (+25). Because our answer is positive, we know that Dan is exerting a greater force and therefore the direction of the net force is to the right.

3. What is the connection between the net force exerted on on object by other objects, and the motion of the object?

Often times, the net force represents the direction in which the object moves. In the last example, the box moved to the right because Dan was exerting a greater force than Jen. The net force was going towards the right, so the box was moving to the right. The idea that an object always moves in the direction of the unbalanced force, however, is false. In the first example, when a meter stick is pushed against a ball that is rolling along the ground, the meter stick represents the net force. If the ball was rolling right and the meter stick was pressed against it, the ball would not suddenly start to move left. The ball continues to move to the right. This proves that objects don't always move in the direction of the net force.

Journal Entry 1/4

(a) You do not need to know how big the plane is to calculate the time it takes to get from New York to Los Angeles. you are given the average speed which makes the length of the trip directly discernible. Because the speed is given the size is unnecessary.

(b) When parking the plane, its size is necessary however. the distance between the two gates is directly dependent on the size of the plane. if the size was not specifically given and an estimate was used to construct the gates, there would be a serious problem upon landing.

(c) The size of the plane is not necessary if we are told that the plane taxied along the runway for 100 m. Regardless of the size of the plane, it moved for 100 m. You would consider the change in its distance from the nose of the plane. It does not matter what length is behind the nose because once the distance the nose has gone has reached 100 m, the movement stops.

(d) When a plane moves left its size is necessary because the shift can be depicted with a right triangle. if the plane taxied for 100 m, then turned left, it is 32 m left of that 100 m mark. To find how much the passenger moved you would construct a right triangle with legs 100 and 32 and you would calculate the hypotenuse. The hypotenuse would equal the distance the passenger moved with respect to the ground.