AY Honors/Physics/Answer Key/es
1
1a
La física es una rama de la ciencia que se ocupa de la materia, la energía, el movimiento, la carga y la fuerza.
La física comienza con la observación. Se puede observar el mundo que rodea con nuestros 5 sentidos, o se puede utilizar una serie de herramientas tales como la balanza, la regla de un metro o una regla, el reloj o cronómetro para proporcionar una medición más precisa. Galileo usó su pulso en cuando sus experimentos, pero un cronómetro habría mejorado la precisión de sus mediciones. Los físicos también utilizan herramientas más complicadas mientras miran eventos más complicados, como la colisión de partículas subatómicas en un acelerador atómico. La herramienta más importante de la física es la matemática. Puede pensar en la matemática como el lenguaje de la física.
1b
La masa es la cantidad de materia relacionada con el peso por medio de la segunda ley del movimiento de Newton.
[math]\displaystyle{ Force=mass \cdot Acceleration }[/math].
We can only know if an object has mass if we try accelerate it.
[math]\displaystyle{ Mass = \frac{Force}{Acceleration} }[/math]
If we measured the mass of an object with an ordinary bathroom scale on Earth, on the Moon, and on Mars, we would find that it weighed most on Earth and least on the moon. In each case, the mass did not change, but the weight did. This is because the gravitational force of each planet is different, but the spring in the scale has not changed. For this reason, we use a balance to determine the mass of an object.
With a balance, as the force of gravity changes, it is pulling equally on both sides of the balance. We are now truly measuring the mass of the object, not its weight. Think of a teeter totter on the moon. If your friend is heavier than you, you will still be lighter on the moon, but if you and your friend are balanced on Earth, you will still be balanced on the moon teeter totter.
Weight is equivalent to the Force in Newton's second law of motion. You would truly feel lighter on the moon, but you have lost no mass, you have simply moved to a different gravity field or inertial framework.
1c
Work is a measure of energy. If we push a heavy load, then the work that we do is how hard we push the load times how far we push the load.
- [math]\displaystyle{ Work=Force \cdot distance }[/math]
1d
Force is an influence on an object that causes the object to change its motion - either its speed or the direction in which it moves.
1e
Power is the amount of energy expended per unit of time. If you can do lots of work quickly, then you are using more power.
- [math]\displaystyle{ Power= \frac{(Work\ done)}{(time\ it\ took\ to\ do\ the\ work)} }[/math]
1f
Potential energy is the energy of an object based on its position relative to other objects. For example if I lift a ball above the ground a given distance, then the ball has the potential to fall the distance that I've raised it. The potential energy of a ball can be measured by measuring how high you raise the ball against the force of gravity on the mass of the ball.
Potential energy of the ball is given by the relationship:
- [math]\displaystyle{ E = m \cdot g \cdot h }[/math]
Where
- E = energy
- m = Mass of the ball
- g = Acceleration due to gravity (9.8 m/sec/sec on Earth)
- h = height we raise the ball
We also see potential energy as the stored energy of a battery. The energy of a battery is stored chemically. It becomes kinetic energy in the form of heat and light when we turn on the switch of our flashlight.
1g
Kinetic energy is the amount of energy that an object has based on its motion relative to other objects. Kinetic energy in its simplest form is related to the speed of an object in relation to the observer. Kinetic energy in its most complex form can be heat.
The kinetic energy of a moving ball can be measured by knowing two things about the object
- 1) The mass of the object. (Determined using a balance.)
- 2) The velocity of the object (Time how long it takes to travel a given distance) [math]\displaystyle{ velocity=\frac{distance}{time} }[/math]
- [math]\displaystyle{ \ Kinetic\ energy = \frac{1}{2} \times (Mass\ of\ object) \times (Velocity\ of\ object)^2 }[/math]
- We write this as [math]\displaystyle{ E_k=\frac{1}{2} m v^2 }[/math]
1h
Weight is the force that gravity exerts upon a body. According to Newton's second Law of motion:
- [math]\displaystyle{ The\ weight = (mass\ of\ object) \times (local\ acceleration\ of\ gravity) }[/math]
Weight is commonly mistaken for mass, but weight could be significantly more on a planet with a larger gravity, or could be significantly less on a planet with a lower gravity. Mass on the other hand is the same in both circumstances.
1i
Matter is anything that has mass. There are four states of matter: solid, liquid, gas, and plasma. Physicists tend to divide the universe up in two general categories
- Energy
- Matter
Einstein showed these to be related ([math]\displaystyle{ E=mc^2 }[/math]).
1j
Inertia is a property of matter that works against an external force. According to Newton's first law of motion, a body at rest tends to stay at rest unless acted on by an outside force. An object in motion tends to stay in motion unless acted on by a force.
1k
Friction is the rubbing of the surface of one object against the surface of another.
At the atomic level you can think of bumpy surface like sand paper rubbing against another surface. When the two surfaces are at rest, the high spots of one surface fit into the valleys of the other surface and it takes quite a bit of force to move one over the other. Once they are moving, the two surfaces bounce from peak to peak like a skier only hitting the tops of the moguls. We observe that it takes more energy to start pushing an object than to keep it moving once moving.
We call these two frictional forces
- 1) Static Friction
- 2) Kinetic Friction
The energy that we lose to friction is turned into heat. Rub the palms of your hands back and forth across each other. Your hands will start to get warm, in fact this is a good way to warm your hands when it is chilly. This heat can cause problems in the fan of your computer, or the cylinders of a car, so bearings, oil and grease are used to help reduce the heat and damage that can be caused by friction.
1l
A wave is a forward moving disturbance traveling without moving forward the particles of the medium through which it moves.
In a guitar string for example, the string will vibrate up and down, but the particles that form the string do not move horizontally along the string. Likewise, if you throw a pebble into the water, the water goes up and down and the wave spreads out from the splash point, but there is not a flow of liquid along the surface of the water.
1m
The center of gravity is the point from which all the gravitational forces within an object appear to come. This point is the same as the center of mass in a uniform gravitational field.
1n
An exponential notation is a mathematical notation that makes it easier to work with very large numbers or with very small numbers. In physics it is very common to have very large numbers such as the number of atoms in a drop of water, or the number of stars in a galaxy. It is also quite possible to have very small numbers such Planck's constant (0.0000000000000000000000000000000006626068 m2kg/s).
We write numbers in scientific notation by getting rid of the zero space holders.
- In large numbers
| [math]\displaystyle{ 1\times10^9 }[/math] | [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 1,000,000,000 }[/math] |
| [math]\displaystyle{ 6.02\times10^{23} }[/math] | [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 602,000,000,000,000,000,000,000 }[/math] |
| [math]\displaystyle{ 2.9979\times10^8 }[/math] | [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 299,790,000 }[/math] |
- For small numbers the exponent is negative
| [math]\displaystyle{ 0.00001 }[/math] | [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 1\times10^{-5} }[/math] |
| [math]\displaystyle{ 0.000000015 }[/math] | [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 1.5\times10^{-8} }[/math] |
| Planck's constant | [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 0.0000000000000000000000000000000006626068 m^2kg/s }[/math] |
| [math]\displaystyle{ = }[/math] | [math]\displaystyle{ 6.626068\times10^{-34} m^2kg/s }[/math] |
The exponent tells us how many places we need to move the decimal point. We move it to the right for positive exponents and we move it to the left for negative exponents.
Exponential notation is used on many calculators and programming languages. The ×10 is replaced by the letter E, so we would write 31E6 instead of 31×106.
1o
Absolute zero is a theoretical minimum temperature at which all motion of an atom ceases.
This minimum temperature is:
- 0 Kelvin = -273.15° Celsius = –459.67° Fahrenheit
The coldest temperature ever was measured by a MIT team in 2003. The temperature was 450 picoKelvin. This is 450x[math]\displaystyle{ 10^{-12} }[/math] Kelvin or 450 trillionths of a degree from absolute zero.
1p
A fulcrum is the support on which a lever turns in moving a body.
By changing the distance between the load and the fulcrum, we can increase or decrease the mechanical advantage of the machine known as a lever.
The Center support of a teeter totter is the fulcrum of the teeter totter.
2
All science starts with observations. A biologist might observe a bird and describe its colors or actions. A chemist might note a pungent aroma. A physicist might observe an object falling. Each of these events would be an observation. We use our senses, or use machines that can increase the power of our senses.
The observation causes us to ask basic questions about the event. These questions can form the basis of a hypothesis. A hypothesis is a scientist's guess about what might explain the observations. A hypothesis is most useful if it suggests an experiment that can be done to either prove or disprove the ideas we have as to the way things work.
We do an experiment to test the hypothesis, this leads to more observations and we start the process all over again.
We can summarize this by:
When an idea has been tested many times it is called a theory, and if it is tested so thoroughly that we are sure that it accurately describes the phenomenon, it might be called a Law.
The scientific method can be applied to any field of study, and tends to be self corrective. Errors cannot stand long - when others do the experiment they will either get the same results or different results. If they get different results, then more observation, hypotheses, and experiments are needed.
The scientific method can be applied to any field of study, including Bible Study. We are not talking about applying science to the Bible, although that can be quite useful. The science of archaeology adds more to our understanding of the world of the Bible with each new discovery.
We can also apply Physics to the Bible, for example the Bible does not say how tall the lamp stand was in the sanctuary, but it does tell us how much the lamp stand and it’s utensils weighed. Exodus 25:39 (One talent of gold would have a volume of about 2 liters). We can use our knowledge of science (density, tinsel strength, etc.) to make an estimate of its height.
The use of science adds details to the story, but does not enhance the spirituality of the Bible reading. The important thing for Christians is not knowing each and every statistic in the Bible, but knowing the God of the Bible (John 17:3). This requires knowledge of the character of God, but it also requires personal interaction with God (John 17:23). With this in mind, there are several useful ways to use the scientific method to learn more about God and to enhance our relationship with him.
Observations
The scientific method of study starts with an observation, and in the spiritual world, there are two types of observations:
- 1) Text based observation
- We observe the text of the Bible and then, using this observation as a starting point, we start to ask questions and compare scripture to scripture to find answers.
- 2) Life based observations
- We observe events in our life or the lives of our family and friends. These observations lead us to ask questions. These questions, in turn, lead us to search for answers in the Bible. We then choose to act, either accepting the counsel of the Bible or rejecting it.
Hypothesis
When we ask questions, we start to formulate a hypothesis. A good hypothesis leads to predictions that can be shown to be true or false by use of an experiment.
As we use the Scientific method in Bible study, our observation leads us to create a hypothesis. This hypothesis helps create a framework that we use to study the Bible. For example the text: “I the LORD do not change…” in Malachi 3:6 might be used to create a hypothesis that “God is consistent”. We then look at the action of God to see if this is true. We will search the scripture comparing scripture to scripture to find further examples of God acting in a consistent manner.
This is the method used by the Christians of Berea:
“Now the Bereans were of more noble character than the Thessalonians, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true.”
We all have hypotheses that we have accepted as true. These hypotheses are based on our training, and experiences. All experiences that we have had in the past guide the hypotheses that we are making today. For example, if someone has had a difficult relationship with their father, they may have a different view of God the Father than someone who has had a wonderful relationship with their father.
It is impossible for us to open the Bible without having underlying hypotheses that we filter the Bible through. These hypotheses affect our understanding of the text. Recognizing our own biases can be difficult, but by looking honestly at our own underlying hypotheses, we can start to see the world more clearly.
Thomas Jefferson, the author of the Declaration of Independence, thought that Jesus was a good man, and we could learn from him morally. Jefferson did not believe the miraculous accounts of the Bible. He created what is commonly known as the "Jefferson Bible" by cutting these accounts from the books of Matthew, Mark, Luke, and John and arranging the remaining segments to form a story.
The story is in chronological order and contains most of the words of Jesus, but does not tell of the Angels announcing His birth, it does not talk of miracles, and there is no mention of the resurrection. Thomas Jefferson started with the hypothesis that all of these things were, in his words "nonsense".
Martin Luther, on the other hand, believed that the Bible and the complete Bible was true, including the miracles. Luther believed this so much that he wanted everyone to be able to read its words in their own language. He therefore translated the entire Bible into German.
Jefferson and Luther had a different hypothesis relating to the complete truth of the Bible. Their hypotheses lead them to totally different relationships with God. As you can see, the Hypothesis that we start our Bible study with is very important.
Experiment
As we apply the Scientific method to Bible study, we find that there are two types of experiments:
- 1) Application experiment
- You apply your hypothesis to real life situations.
- By actually putting the Bible text into practice, we can see if our hypothesis is valid. For example, If you read the text in Malachi 3:10
Bring the whole tithe into the storehouse, that there may be food in my house. Test me in this, says the LORD Almighty, and see if I will not throw open the floodgates of heaven and pour out so much blessing that you will not have room enough for it.
- Your hypothesis might be that God will bless you if you return your tithe. If you take action on these thoughts and do the experiment, you can find out if it is true.
- We might read in Proverbs 25:21-22
If your enemy is hungry, give him food to eat; if he is thirsty, give him water to drink. In doing this, you will heap burning coals on his head, and the LORD will reward you.
- Our hypothesis might then be "Our enemies are changed more quickly by being nice to them than by being mean to them."
- Our experiment then would be to try treating the class bully in a kind manner.
- 2) Bible Study or research experiment
- you take the approach of the Bereans and study the Bible to try to verify or nullify your hypothesis based on comparing scripture with scripture.
- We do not always have to do the experiment ourselves. The Bible can be viewed as a series of "spiritual" experiments. We see people who had faith and stood for right, we see people who failed repeatedly, but returned to God. We see others who have rejected God completely. Each of these stories is an experiment in spirituality. Life is not long enough to make all the mistakes on our own, therefore; a book such as the Bible can help us see how we should live in order to have a spiritually successful life. It also shows those who failed so we can know what behavior leads us away from God.
- When you find a spiritual principle in the Bible, you can find an experiment that was performed in the life of the patriarchs, kings, prophets, and apostles by comparing scripture with scripture.
- One of the distinct messages of the Seventh-day Adventist Church is that there is a "Controversy" between Jesus and Satan. (Job 1) We see from the scriptures that God is self-sacrificing love (John 3:16, 1 John 4:8), and Satan is defined by self-love (Isaiah 14:12-14). We can use this "Hypothesis framework" to study the scriptures. In each story of scripture, how can you see the forces of good struggling against the forces of evil? What does this teach you about God's love for his children and more specifically His love for you?
Once you have done the experiment or studied someone who has done the experiment, then you look at your hypothesis again. Do the results of your experiment support your hypothesis? If they do, your hypothesis could be valid, if not, change your hypothesis and begin the experiment and evaluation process again.
The framework of hypotheses forms our beliefs, and once we are more sure of our beliefs, we will start to take action. Our actions will be molded by our underlying hypotheses.
3
A controlled experiment is an experiment where you try to eliminate other factors that might affect the result. Let's look at one of the most famous Physics experiments and possibly one of the most important of all time. It will illustrate how we can deal with and control the variables. The experiment was done by an Italian Scientist by the name of Galileo Galilei.
For almost 2,000 years people believed the philosopher Aristotle who said that heavier objects fall faster than lighter objects. At the time of Galileo, there was no scientific method, and so people believed Aristotle based on his authority. Aristotle's idea was more than a hypothesis, in the minds of the people this was a law of physics.
Galileo asked questions about this law. It is obvious that a feather really does fall slower than a hammer, but he hypothesized that this is because air resistance prevents a feather from falling at full speed. Instead of thinking, as Aristotle did that moving objects tend to come to rest, he thought there might be something holding an object back "frictional forces" that slowed the object down.
Galileo probably did not drop objects from the Leaning Tower of Pisa, but he did experiments with an inclined plane or a ramp that he rolled objects down. This allowed him to slow down the falling action and thus minimize the "air friction". He was able to determine that objects are accelerating and that the mass does not affect the acceleration.
Galileo was able eliminate the "air friction" variable and this allowed him to "see" the underlying physics of falling bodies. He published his theories in his book entitled Discorsi e dimostrazioni matematiche, intorno à due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences) in 1638.
When designing an experiment you should try to figure out what variables might affect the experiment and then try to eliminate the variable. Sometimes the variables are not discovered until after the first or second experiment. Galileo's hypothesis was that air was affecting the falling objects.
As a demonstration drop a piece of paper and a book at the same time. Ask the students to hypothesize which will hit first, and then do the experiment. Was their hypothesis correct?
Now do the same experiment with the paper crumpled.
What happened?
Why?
This would be a good time to do the experiment of question 10 below.
4
Albert Einstein's Theory of Special Relativity was published on June 30, 1905. Most of the theory of special relativity has to do with the relation between moving objects and light that is passed between them.
Although light is a wave phenomenon, the Michelson Morley experiment of 1887 had shown that there is no medium needed for it to travel through space.
- E - is the symbol for energy.
- Energy is a unit of work in MKS system it is [math]\displaystyle{ Kg \cdot M^2/sec^2 }[/math] which is known as a Watt.
- In the CGS system it is a [math]\displaystyle{ g \cdot m^2/sec^2 }[/math] which is known as an erg. Energy can take the
- form of heat, and is measured in calories or Kilocalories when talking about heat. Calories are measured in
- a calorimeter by measuring the change in temperature of water by adding heat into the system. One calorie of
- heat raises one gram of water one degree centigrade. To show how mechanical energy or work is related to
- heat energy, paddles are turned in the calorimeter and the temperature change is measured.
- m- is the rest mass of a particle.
- This mass could be measured in kg or grams.
- c- is the speed of light.
- C stands for celeritas which is Latin for swiftness and is used to represent the speed of light.
- 299,792,458 Meters/second or 186,282.397Miles/second
- 2- The 2 on the right of the c represents the action known as squaring a number.
- We square a number by multiplying it by itself. In this equation we are squaring a very large number which yields a very very large number :[math]\displaystyle{ 299792458m/sec \cdot 299792458m/sec = 8.98755179\times10^{16}m/sec^2 }[/math]
What this equation indicates, is that mass and energy are interchangeable. Mass can become energy and energy can turn into mass. Before Einstein, there were two laws of physics
- Conservation of matter- This law stated that particles of matter are not created or destroyed
- Conservation of energy- This law stated that energy is not created or destroyed it just changes form
The [math]\displaystyle{ E=mc^2 }[/math] equation says that there is only one law:
- Conservation matter and energy- matter and energy are neither created or destroyed
It was not until 1938 that Lise Meitner and Otto Hahn were able to split a nucleus and see that energy was released. The energy released corresponded to the mass loss according to Einstein's equation.
It was shown that an atom with a large nucleus can break into two parts, emitting a gamma ray. If the mass of the two parts were added up some of the mass was missing. The gamma ray had no mass, only energy, but the energy was equivalent to the missing mass if we use Einstein's equation.
When we are talking about very energetic particles such as gamma rays, we often see the gamma ray becoming a pair of particles and then joining again to become a gamma ray.
A gamma ray with an energy of 1.022MEV (Million Electron Volts) can spontaneously form an electron anti-electron (Positron) pair. Each particle has mass that has the equivalent energy of .511MEV and one has a positive charge and one a negative charge. Because one is negatively charged and one is positively charged, they are likely to be attracted to each other and recombine and form a gamma ray again. The gamma ray has no charge or mass.
5
| System of Measure | Length | Mass | Time |
| English System | Foot | Slug | Seconds |
| SI System | Meter | Kilogram | Seconds |
| Metric (MKS) System | Meter | Kilogram | Seconds |
| Metric (CGS) System | centimeter | Gram | Seconds |
Most of the world uses the SI or Système International d'Unités for all measurements. It is only in the United States of America, Myanmar, Liberia, and a few other countries that the English system is used for most activities.
From a scientific point of view, it is very surprising that the English system is still in use in any technologically advanced country. Its use in the United States led to a catastrophic failure in the NASA Mars Orbiter mission of 1999. The $125 million Mars orbiter was lost because a Lockheed Martin engineering team used English units of measurement while the NASA team used the metric system for spacecraft navigation.
Many people think that pound is the English System's mass unit. It is actually the force unit. By continuing to convert from pounds to kilograms we further confuse the difference between force units and mass units.
6
A day is used to represent a year in two places in scripture:
After you have finished this, lie down again, this time on your right side, and bear the sin of the house of Judah. I have assigned you 40 days, a day for each year.
For forty years—one year for each of the forty days you explored the land—you will suffer for your sins and know what it is like to have me against you.
This is used in the prophecies of Daniel, especially Daniel 8:14
He said to me, "It will take 2,300 evenings and mornings; then the sanctuary will be reconsecrated."
Isaac Newton is known as one of the greatest physicists, but few remember that he devoted more time to the study of the Bible and alchemy than to the study of Physics, and in Observations upon the Prophecies of Daniel, and the Apocalypse of St. John he wrote:
- "The Sanctuary and Host were trampled under foot 2300 days; and in Daniel's Prophecies days are put for years: but the profanation of the Temple in the reign of Antiochus did not last so many natural days. These were to last till the time of the end, till the last end of the indignation against the Jews; and this indignation is not yet at an end. They were to last till the Sanctuary which had been cast down should be cleansed, and the Sanctuary is not yet cleansed."
7
- First law
- An object at rest will stay at rest and an object in motion will stay in motion unless acted on by a force.
- Experiment-You can do the experiment in question 8 of the physics honor to demonstrate inertia
- Second law
- The acceleration of a body is directly proportional to the force acting on it; This is written as [math]\displaystyle{ F=mA }[/math].
- Experiment- Use plastic spoons and marshmallows , nuts, apples or other objects to demonstrate how the same force (the bend of the spoon) accelerates the objects with different mass, different distances.
- How can you make sure that you get the same force each time?
- Does the objects mass affect the distance it travels?
- Does the mass affect the speed of the object?
- Experiment-Connect a fish scale to a small weight and see what measure you get if you pull the weight slowly or quickly
- Experiment- Use plastic spoons and marshmallows , nuts, apples or other objects to demonstrate how the same force (the bend of the spoon) accelerates the objects with different mass, different distances.
- Third law
- For every action or force there is an equal but opposite reaction.
- If I push on you, then you push on me with the same amount of force, but in the opposite direction
- Experiment-You can do the experiment in question 9 of the physics honor to demonstrate action--reaction principle.
8
- Theory-
- An object at rest will stay at rest and an object in motion will stay in motion unless acted on by a force.
- Materials-
- Table
- Table Cloth
- Books (various sizes)
- Method-
In this experiment, we will place a table cloth over a table, and then place the books on top of the table cloth.
- Questions-
- What happens if you try to pull the table cloth slowly?
- What happens if you try to pull the table cloth Quickly?
- What happens if the books are light?
- Does the type of table cloth matter? What if it is smooth like silk? or Rough like sand paper?
- What does this experiment tell us about Newton's First Law of motion?
- Is there another experiment that I can do to prove or disprove Newton's First Law of motion?
- Spiritual Application-
- We all resist change in our life. We become comfortable with the status quo. Sometimes a slow persistent push can overcome our inertia and get us headed in the right direction spiritually.
9
- Theory-
- For every action or force there is an equal but opposite reaction or force
- Imagine sitting in space (no friction to hold you in place) with a brick. If you throw the brick, the brick will go away from your original location, but you will also go away from your original location (Your speed will be slower than the brick because you are much heavier than the brick). A rocket does the same thing with the molecules of the exhaust. The molecules are very light, but are traveling very fast, and thus can accelerate the rocket to very high speeds.
- Material
- Balloons (this is your rocket)
- Drinking Straws
- Tape
- String
- paper
- scissors
- Method
- Provide as little guidance as possible. Let the spirit of learning guide.
- Competition between two or more groups can be prompted by seeing which team can get the balloon to fly to a specific target.
- Once a team figures out the way to guide the balloon, then you can have races between the various teams.
- Questions
- If you blow up a balloon, and then let it go without tying a knot in the opening, What happens?
- Does this agree with Newton's third law of motion?
- How can you make the balloon go where you want it to? (guide the balloon?)
- What provides the force?
- Spiritual Application
- When God acts, the universe reacts. We see this repeatedly in the creation story. God spoke and things appear. He says, "Let there be light" and there was light. "For every action there is a reaction"
10
- Theory
- The Earth attracts everything to itself. We represent the Newtonian attraction with a Big G which stands for Gravitation constant (in MKS units it has a value 6.67x[math]\displaystyle{ 10^{-11}m^3/(kgS^2) }[/math] and write the equation:
- [math]\displaystyle{ F = G \frac{m_1 m_2}{r^2} }[/math]
- The more mass an object has, the higher the Force exerted on it, this extra force exactly cancels out the inertia of the object, so we can see no matter how big or small an object is it will experience the same acceleration of gravity specified by little g. On the Earth we will let [math]\displaystyle{ m_1= }[/math]mass of earth and [math]\displaystyle{ m_2= }[/math]mass of object which we say is m: We can then set the Force of gravity = ma by Newton's 1st law of motion:
- [math]\displaystyle{ F = G \frac{m_e m}{r^2} = ma }[/math]
- Notice that we have m on both sides of the equation. So m is completely canceled out leaving us with
- [math]\displaystyle{ a = G \frac{m_e }{r^2} }[/math]
- G is constant, the Mass of earth [math]\displaystyle{ M_e }[/math] is constant, and near the surface of the earth, the distance from the center of the earth does not change much, so [math]\displaystyle{ r^2 }[/math] is almost a constant. This means that a is equal to a constant. We call this constant the acceleration of gravity near the surface of the Earth and represent it with the symbol g = 9.8M/[math]\displaystyle{ sec^2 }[/math].
- [math]\displaystyle{ x=\frac12gt^2 }[/math]
- Notice there is no mass indicated in the equation that specifies the acceleration of an object in a gravitational field.
- Materials
- Plastic beverage bottles
- water
- Method
- have the class drop plastic beverage bottles and judge which hits first. Have one half full of water and the other completely full of water. Make sure the lid is screwed on tightly.
- Questions
- Which one hit first?
- What would happen if the bottle was completely empty? Why?
- Spiritual Application
- In a Spiritual sense, we are all attracted by the Grace of God, big G, shown at the cross of Jesus. It does not matter how much Sin there is in our lives, the cross of Jesus attracts us equally and overcomes all the sin. In Christ, we are all sinless, no matter how bad we have been in the past.
- Galileo was able to step out on his faith that air frictions was holding back light objects such as a feather, and this is why Aristotle had said that heavier objects fall faster. He imagined a world that had no air friction, and thus was able to see the underlying physics. We must rely on faith as we look toward the heavenly kingdom and imagine a world without suffering, illness, and death.
11
- Theory-
- Simple machines are used to create a mechanical advantage. They do this by reducing the amount of force needed to accomplish a job. The list of machines usually includes the following machines
- Inclined plane- It takes less force to push a load up a slope than lift it straight up.
- Wheel and axle- The wheel is arguably the most important machine. It reduces the amount of frictional forces.
- Lever-Is composed of a fulcrum or pivot point and a long rigid bar or beam. The closer the object that we are lifting is to the fulcrum the easier (more mechanical advantage we have).
- Pulley-Is a wheel that is used with a rope to change the direction of a force. Multiple pulleys can be used together to create a block and tackle that will increase the mechanical advantage.
- Wedge-This machine is just two inclined planes, but is usually included because it is so useful.
- Screw-This is simply a circular inclined plane, but because it takes a rotational force and turns it into a linear force, it is almost always included in a list of simple machines.
- Simple machines are used to create a mechanical advantage. They do this by reducing the amount of force needed to accomplish a job. The list of machines usually includes the following machines
- The machine being studied here is a simple lever. The hammer handle is the lever arm, and the curve of the head forms the fulcrum. The claw of the hammer is also a wedge or inclined plane. Sometimes you use a hammer with a pry bar, nail puller or another hammer to wedge the claw under the nail head.
- The Lever uses the physics principle of torque or rotational force. Torque = force*distance.
- Materials-Hammer, nails, 2x4 at least 2 feet long, small block of wood
- Method- Drive a number of large nails (16 penny will work well) halfway into the 2x4 and have the class try pulling a nail. Then demonstrate how to position the block of wood to act as a fulcrum. Have the class repeat the experiment using the block of wood.
- Questions-
- Start with a description or demonstration of various machines as described in the theory section. Then ask the class "what kind of machine is a hammer"
- Where is the fulcrum on the hammer?
- Where is the fulcrum when using the block of wood?
- Which way was easier?
- What difference does it make how close the fulcrum is to the block of wood?
- What difference does it make where you grip the hammer? Is it easier near the head or at the end of the handle?
- Spiritual Application Example- If we let the fulcrum of the lever represent Jesus, then the closer we are to Jesus, the easier it is to lift us to a higher spiritual plane.
References
The people behind [math]\displaystyle{ E=mc^2 }[/math]
More explanation of [math]\displaystyle{ E=mc^2 }[/math]
Newton's Law of Motion
Galileo Falling Body Experiment
Galileo Falling Body Simulator
Lever
Could Archimedes move the Earth with a lever?
Simple Machines
Absolute Zero
Physical Constants
