Ch5_AronsonJ

=**toc Lesson 1**=

SPEED AND CIRCUMFERENCE: NOT-SO-DISTANT COUSINS!

Thanks to a fascinating lesson at the online Physics Classroom, I learned that average speed is directly related to circumference. Speed is equal to distance over time, which is equal to circumference over time, and circumference is equal to 2 times pi times radius. Therefore, speed is equal to 2 times pi times radius, all over time. The formula for this groundbreaking discovery is given below: Speed=2 πr/t In addition, I learned that any circular motion has a constant speed, but not necessarily a constant velocity, because velocity requires a change in position.

INTO THE BELLY OF THE CIRCLE: ACCELERATION OCCURS INWARDS IN CIRCLES

Again, the Physics Classroom has uncovered shocking details. First, acceleration is equal to final velocity minus initial velocity, all over time. The formula for this shocking revelation is given below: A=(vf-vt)/t Also, objects in circular motion with constant velocity accelerate towards the center of the circle. Without this inward force, circular motion would be impossible.

SEPARATION ANXIETY: OBJECTS IN CIRCULAR MOTION SEEK CENTER

As if the first two lessons were insufficient, the Physics Classroom is at it again. In their latest edition, they introduced centripetal force (when an object moves in a circle), and revealed that objects in circular motion tend to seek the center of their circles. The force with which they seek the center is called “centripetal force.” Centripetal force changes an object’s direction without changing its speed. Finally, we recapped that work is equal to force times displacement times cosine theta. The formula for this earth-shattering idea is given below: Work=(F)(Δd)(cos Θ )

WHO NEEDS OUTWARD FORCE ANYWAY? The Physics Classroom has continued to shock the world. The most recent lesson taught me that there is also a centrifugal force, which points outward away from the center. However, centrifugal force is often behind a physics misconception, which is that if there is circular and outward motion, then there is also outward force. This ill-conceived rumor is false, and is caused by confusion with Newton’s Law of Inertia. For example, when a car is turning in a circle.

EQUATIONS EQUAL LIFESAVERS

=** Lesson 2 **=


 * 1) What (specifically) did you read that you understand well? Describe at least 2 items fully.
 * 2) I understood two things, in particular, very well. First, I knew that friction is the centripetal force of a car driving in horizontal circular motion. Also, in that situation, friction would be the only force acting on the object, so it would be equal to the net horizontal force. Second, I knew how to draw the free-body diagram, with normal force acting upwards, weight force downwards and friction force inwards.
 * 3) I also understood that a sharper turn requires a smaller radius, and a wider turn requires a larger radius.
 * 4) What (specifically) did you read that made you feel little confused/unclear/shaky, but further reading helped to clarify? Describe the misconception(s) you were having as well as your new understanding.
 * 5) In my first reading, I thought that I read that net force is equal to mass //plus// velocity-squared divided by radius. Thankfully, this reading helped to clarify that issue for me, putting the equation into a context that I can understand. I now know that net force is equal to mass //times// velocity-squared divided by radius.
 * 6) What (specifically) did you read that you don’t understand? Please word these in the form of questions.
 * 7) Because in a clothoid loop you change speed, direction and radius, is there an equation or set of equations to solve for the centripetal force?
 * 8) How do you solve for centripetal force at different points in a loop?
 * 9) What (specifically) did you read that you thought was pretty interesting, that you didn't know before, or can easily apply to your every day life?
 * 10) I was very interested to read about contact force, which I experience every day. When I make a running turn in the hallway, or on the tennis court, or on another sports field, I resolve my body into components of force by leaning into the turn. Doing this balances the downward force of gravity and meets the centripetal force requirement of my circular motion, as the upward component balances the downward force of gravity, and the horizontal component pushes towards the center of the circle.

=**Lesson 3**=

KEPLER COMMOTION: LAWS THAT CHANGED THE LAWS

According to a source at the Physics Classroom named Johannes Kepler (descendant of his 1600s German astronomer namesake), three laws govern planetary motion: Furthermore, Isaac Newton used Kepler’s laws to suggest universal gravitation, which will be discussed in greater detail.
 * 1) Law of Ellipses=planets orbit the sun in the shape of an elliptical, with the center of the sun at one focus
 * 2) Eccentricity=difference of an ellipse from a perfect circle (e=0 is a perfect circle)
 * 3) Law of Equal Areas=an imaginary line from the center of the sun to the center of the planet will sweep out equal areas in equal time
 * 4) Law of Harmonies=the ratio of the squares of the periods of any two planets equals the ratio of the cubes of their average distances from the sun

UNIVERSAL MOTION: YOU BET IT'S REAL!

The Physics Classroom reports that, according to Isaac Newton, the force of gravity between earth and any object is directly proportional to the mass of the earth and to the mass of the object, but inversely proportional to the square of the distance that separates the centers of the earth and the object. In other words, more massive objects will attract each other with a greater gravitational force, but more separation distance will result in weaker gravitational forces. This is outlined by the following equation: “G” is the universal gravitation constant, and it will be discussed in greater detail.

“G” IS FOR GRAVITATIONAL PULL, THAT'S GOOD ENOUGH FOR ME!

A startling report from the Physics Classroom reveals that Lord Henry Cavendish used a torsion balance experiment to determine the value of universal gravitation. After an experiment using a light rod, and modern improvements, the value of “G” has been found to be 6.67 x 10^-11. Because “G” is a small numeric value, objects with greater masses will have greater (and more noticeable) gravitational force.

REMEMBER "g"?

Complicating what we have already learned about “g,” the Physics Classroom has reported that the German scientist named von Jolly discovered the value of acceleration due to gravity. “g” is also defined by the following equation:

In lay man’s terms, the value of “g” is directly proportional to the mass of the planet, but inversely proportional to the radius of the planet. We know that the value of “g” is 9.8.

=**The Clockwork Universe**=

THREE'S A PARTY: THEORIES OF PLANETARY MOTION

With credit to The Clockwork Universe, this reporter has learned about the three basic views of planetary motion in history. First was that of the ancient Greeks (Aristotle), which remained through the rule of the Catholic church in the 1500s: the geocentric model, which placed the Earth at the center of the universe. Next was that of Copernicus: the heliocentric model, which suggested that the planets moved in concentric circles around the sun. Finally came that of Kepler, which has today been proven correct: the sun-based universe in which planets orbit the sun in elliptical motion. Time is scientific discoveries’ best ally.

GEOMETRY AND ALGEBRA: A MATCH MADE IN HEAVEN

Crediting the same organization as above, I just ascertained that Kepler’s geometric ideas were supported by new discoveries in mathematics. René Descartes realized that geometric lines and shapes could be solved algebraically using a coordinate plane. Wow! This groundbreaking science, which is crucial to modern understanding of mathematics, is called “coordinate geometry,” or the representation of geometrical shapes using equations. Try taking math class without learning that!

NEWTON: A PI-ONEER OF QUANTITATIVE SCIENCE

Though Newton was today we call an "introvert," he was also a thinker. Not talking provided him with much time to ponder! Before Newton, people knew, but they did not know why. With Newton came new discoveries, leading one scientist to describe Newton as the “one man in the world’s history to be the interpreter of [universal] laws.” Of course, we know what laws those are: inertia, net force and system forces. These laws have helped scientists to apply numbers to theories, and to prove the science in the world around us.

APPLE TO NEWTON’S HEAD: THE GRAVITY OF THE SITUATION

Building on his three laws of motion, Newton proposed a universal law of gravity and mathematically proved Kepler’s theory of elliptical orbit. In fact, Newtonian physics even proved slight abberations of the planets from their elliptical orbits! Newton’s studies paved the way for mechanics, or the study of force and motion. Newton determined that the universe was predictable, a theory known as “determinism.” Groundbreaking!

= **Lesson 4** =

THREE’S A PARTY 2: KEPLER’S LAWS IN DETAIL

In a previous editorial, I gave an overview of Johannes Kepler’s three laws of planetary motion: the Laws of Ellipses, of Equal Areas and of Harmonies. The first law is that planets revolve around the sun in elliptical motion, with the center of the sun at one focus. The second law is that an imaginary line from the center of the sun to that of the planet would result in segments of equal area at each time interval. The third law states that the ratio of the square of a planet’s period to the cube of its distance from the sun is equal to that of all other planets in elliptical orbit. Kepler used these three statements to contextualize the data of Tycho Brahe, his mentor.

THE CIRCLE OF LIFE: SATELLITES NEED IT, TOO

We all know that satellites are up there, but how do they move? Both natural satellites (for example, the planets and moons) and man-made satellites (for example, defense and communications satellites) are projectiles: the only force acting upon them is gravity. As a result, satellites are governed by the laws of circular motion, but for ellipses instead of circles; that is, they experience inward forces, accelerations and tangential velocities. These centripetal forces keep a satellite in orbit. (Conversely, the tangential forces prevent the satellite from falling into the Earth.)

Fun fact: the Earth curves 5 meters for every 8000 meters along its horizontal; therefore, a projectile launched at 8000 m/s can orbit the Earth in circular motion!

IT’S A NUMBERS GAME: THE MATH BEHIND THE SCIENCE

According to the Physics Classroom, the period, speed and acceleration of a satellite are not dependent on the mass of the satellite, but on the radius of orbit and the mass of the central body that the satellite is orbiting. This is similar to projectiles on Earth: when you ignore air resistance, the mass of the projectile has no effect upon the acceleration or speed.

HAVE YOU LOST WEIGHT?: WEIGHTLESSNESS IN ORBIT

According to the Physics Classroom, the key to understanding this feeling of so-called “weightlessness” is first understanding the two types of forces: contact and non-contact forces. Contact forces result from physical touching between two objects, such as the normal force of a chair on your body, and non-contact forces result from action-at-a-distance forces. Weightlessness occurs when all contact forces are removed, and non-contact forces are the only ones acting on an object. When astronauts feel weightless, it is because there are no external contact forces pushing or pulling on their bodies; there is only the non-contact force of gravity.

FUN FACT: Scales do not measure your weight; they measure the upward force applied to your body!

EXTRATERRESTRIAL ENERGY: ENERGY IN SATELLITE ORBIT

The Physics Classroom added onto what we have learned about circular and elliptical motion. Satellites in circular motion experience no component of force in the same direction of motion, and they maintain a constant radius of orbit and a constant speed at a constant height above the Earth; satellites in elliptical motion experience a component of force in the same and opposite directions as the object’s motion, and they speed up as their distances from the Earth increase. Next, the work-energy theorem is described by the following equation:

** KE **** i **** + PE **** i **** + W **** ext **** = KE **** f **** + PE **** f **

Gravity is known as an internal (or conservative) force. Gravity slows down a satellite as it moves away from the Earth, but speeds it up as it moves towards the Earth.