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Homework

Circular and Satellite Motion Lesson 1 (12/13)

Speed and Velocity: same value, way different meanings.
1. Similar to the concepts used in kinematics, speed and velocity have the same scalar value but differs with magnitude (in that velocity has magnitude, speed does not). This concept can also be applied to circular motion, where for example it can be at uniform circular motion (a car going constant speed at 10mph). Average speed is calculated by distance/time ==> so technically circumference(2piR)/time, since this is a circle. Average velocity, however, must include direction, and unlike speed, is always changing. This direction is found by the tangent line to the circle, where the force is moving towards the center of the circle. Although direction is always changing, the line of direction will remain tangential to the circle.
Acceleration: is it the same in circles as in straight lines?
1. Acceleration equal to the change in velocity ( vf-vi) over the total amount of time passed. Since velocity is a vector, we are looking for the resultant. The direction of acceleration is in the direction of the resultant. If an object is moving at uniform circular motion, acceleration will be towards the center of the circle. A device that is often used to measure acceleration is called the accelerometer. It consists of an object suspended in a fluid (most likely water) and determines if the object has much inertia.
Centipede? No, Centripetal!
1. The Centripetal Force Requirement states that for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. The unbalanced force required by Newton's first law of motion (inertia) is necessary to keep an object moving in circular motion. The centripetal force of an object can alter the direction without altering speed. This is done by displacement, or the formula of work=force*displacement*cosineTheta. The centripetal force is directed perpendicular to the tangential velocity, meaning that the force can alter the direction of the object's velocity without altering speed. In conclusion, the centripetal force requirement is an inward net force, where centripetal, essentially means direction.
What's the difference between centrifugal and centripetal?! I always get confused.
1. Centrifugal, unlike centripetal, means AWAY from the center of the circle. This is a common misconception by people, as they sometimes think that a force is moving OUTWARDS from a circle. THIS IS NOT TRUE! DO NOT believe it! Always remember that CENTRIPETAL refers to the real motion of a circe, not centrifugal.
Equations! Equations! Read all about em!
1. Now that were in the circle world, the typical equations slightly differ. Average speed= 2piR/time, while acceleration= 4pi(sq)R/time, force= m/a. Essentially, the equations have the same concepts, but because we're not in a world full of radians and radii, the formulas change!

Circular and Satellite Motion Lesson 2a-c

How does Newton's Second Law pertain to circular motion?
1. When it comes to circular motion, the equations differ slightly.
2. However, it is very similar to kinematics and linear motion.
3. a=m(sq)/R
4. It is of the utmost importance to create FBD when solving these equations.
How do amusement parks use physics?
1. Loops, small dips and hills, and banking. Physicist have to calculate max speeds and minimum speeds, as well as accelerations for different rides such as roller coasters, log flumes, and ferris wheels. The most common ride we will look at is the roller coaster.
2. The clothoid loop experiences a change in direction. It is a series of overlapping and adjoining circular sections. The radius of these circular section decrease as it approaches the top of the loop.
  1. At the bottom of the loop, the track pushes upwards upon the car with a normal force. However, at the top of the loop the normal force is directed downwards; since the track (the supplier of the normal force) is above the car, it pushes downwards upon the car.
3. From rollercoasters, we can find minimum and maximum speeds based on the theory that humans can only withstand 4gs. So, all designers need to keep this in mind.
What about athletics?
1. Circular motion is involved in so many athletic sports: ice skating,baseball, track and field.
2. Circular motion is defined by the inward acceleration and caused by an inward net force.
3. Although it does not appear to be so, you can link circular motion (somehow) to every sport.
  1. the most common circular motion is the "turn"
  2. some may only be a quarter of a turn and some may be a full turn
4. Contact force has two roles:
  1. balancing the downward force of gravity
  2. meets the centripetal force requirement for uniform circular motion
  3. it normally has two components
  4. example: figure skater pushing on the ice, skier making a turn

I chose to talk about circular motion in everyday life with Jessica during school today.

Circular and Satellite Motion Lesson 3 (1/3)

How is there more to gravity?
1. Gravity is a force similar to many others, however it is ALWAYS present.
2. When an object is being thrown up into the air, gravity acts as a force to slow it down, causing it decrease acceleration and ultimately its speed. However when an object is in free fall, gravity acts as an accelerating force, increasing speed (9.8 m/s/s) and acceleration along the fall.
Who is Kepler and what are his three laws of planetary motion? How did Newton come into play?
1. Johannes Kepler was a German mathematician and an astronomer. His teacher Tycho Brahe helped him gather information about planetary motion around the sun.
  1. he couldn't really determine why there was this attraction, but he knew it existed.
2. Law of Ellipses
  1. The paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus.
3. Law of Equal areas
  1. An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time
4. Law of Harmonies
  1. The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.
5. Newton discovered the notion of UNIVERSAL GRAVITATION. This relates the cause for heavenly motion to the cause of earthly motion. He found the link by the INVERSE SQUARE LAW.
  1. the inverse square law states that relationship between the force of gravity between the earth and any other object and the distance that seperates the two centers can be described as: Fg ~ 1/d2.
  2. an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity.
What are Newton's Laws of Universal Gravitation?
1. Fg ~ m1*m2/d2
  1. m1= mass of object 1; m2= mass of object 2; d= distance between the two centers
2. as the mass of either object increases, the force of gravitational attraction between them also increasesG can also be used in this equation as a constant in the numerator. G= 6.67 * 10-11 nm2/kg2
  1. if the mass of one of the objects is doubled, then the force of gravity between them is doubled
How does the value of G come into play?
1. The value of G is 6.67 * 10-11 nm2/kg2
  1. For our sake, Fg~ G*m1*m2/d2
2. Lord Henry Cavendish discovered the value of G by using a torsion balance, which experimentally determined the relationship between angle of rotation and torsional force.
  1. the force of g is such a small number when in relation to small masses. However, if the mass is large, the attraction will be greater.
What is the value of g?
1. g= G*Mearth/d2
2. g= 2.45 m/s2
3. this same equation used to find the value of g on earth can be applied to other planets with the following subsituted information:
  1. g= G* Mplanet/Rplanet2

I discussed the difference of weight on different planets (because of gravity) at the dinner table with my mom.

The Clockwork Universe 1-4 (1/5)

Who were the "fathers" of discovering the Universe
1. Nicolaus Copernicus
  1. heliocentric view in which the Earth revolved around the sun
  2. Galileo supported him although he was denounced
2. Johannes Kepler
  1. modified Copernicus' model
    1. said that the planets moved in ellipses, rather than a circular motion around the sun
  2. Astronomia Nova (New Astronomy) was his book that showed his observational results
Was mathematics involved?
1. Yes, Renes Descartes, a very important mathematician of the time (16th century) discovered mathematical equations.
  1. these equations linked algebra and geometry on the coordinate system
How did Isaac Newton expand upon these ideas and how did he apply them to physics?
1. Newton, with his knowledge of physics, was able to connect mathematics along with astronomy, at the right place and at the right time.
2. Newton had three key points
  1. deviation from steady motion
    1. when an object speeds up, slows down, or veers off from direction
  2. looked for a cause
    1. for example, slowing down may be caused by braking
  3. law of universal gravitation
    1. no matter what two objects it is, every object follows the same pattern
What was Newton's ultimate law for gravity that still use today?
1. Newton combined his generation laws of motion with gravity to mathematically demonstrate the elliptical orbit of a planet around the sun.
2. Additionally, his physics were able to predict that gravitation attractions between heavenly bodies would cause the bodies to somewhat go off track of their elliptical motion around the sun.
3. Pierre Simon Laplace branched off of his discovery with the study of mechanics. He discovered through determinism that certain things were bound to happen.

I spoke with Erica, an AP physics student, about the clockwork universe and how it works.

Circular and Satellite Motion Lesson 4 a-c (1/6)

What are Kepler's Three Laws?
1. The Law of Ellipses
  1. the path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus
2. Law of Equal Areas
  1. an imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time
3. Law of Harmonies
  1. the ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun
What are circular motion principles for satellites?
1. a satellite is any object that is orbiting the earth, sun or other massive body and it can be natural or man made. They move in an orbit around
2. satellites act in a similar motion to projectiles, as gravity is the only force affecting it
3. the motion of satellites can be described by acceleration and velocity
  1. these are constantly changing
4. however, satellites too move in an elliptical motion, with the central body being at one focus
How does mathematics factor into gravitational pull?
1. We start with this equation Fg= (G*m1*m2)/d2
2. Velocity= sqrt((G*mcentral)/R)
3. Acceleration= (G*Mcentral)/R2
4. T2/R3 = 4π2/G*Mcentral

I made flash cards to remember these equations.

Circular and Satellite Motion Lesson 4d-e (1/9)

How does weightlessness have to do with orbit?
1. Weightlessness is a sensation experience by a person when there are no external objects touching one's body or exerting a push on it. These "sensations" exist when all contact forces are removed.
2. Technically, you are momentarily in free fall, where the only force is gravity.
3. The force of gravity supplies the centripetal force to allow the inward acceleration of circular motion (orbit)
What is the relationship between energy in satellites?
1. The motion of satellites can be either circular or elliptical. They move at constant speed and remain at the same height.
2. Throughout the trajectory, the force of gravity acts in a direction perpendicular to the direction that the satellite is moving, ALWAYS.
  1. there is no acceleration in the tangential direction, so the satellite remains in circular motion at a constant speed
3. The work-energy theorem states that initial amount of total mechanical energy of a system plus the work done by external forces on a system is equal to the final amount of total mechanical energy on the system.

Ch5_CantorA

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