Ch5_Knapelr

toc Hw - lesson 1: a-e 12/13/11

The kinematics concepts are relevant when trying to find speed and velocity of a circle as well as what we have done in the past. Just like before the equation for average speed is a v = d/t which d for a circle would be equal to circumference = 2 πr. Therefore, the final equation for the average speed of a circle would be avg v = 2 πr / t. How velocity of circles differ from what we learned before is that the magnitude of the object moving changes constantly as it moves.
 * USING KINEMATICS CONCEPTS FOR CIRCLES!**

Many people think that since when moving in a circular motion you are moving constant speed so there is no acceleration, this is wrong! An acceleration object is an object with a changing velocity and as we now see the velocity's magnitude is changing so the acceleration is changing as well. The formula for average acceleration is avg a = (V f - V i )/t.
 * MISCONCEPTIONS**

The centripetal force is needed for an object to move in a circular motion, meaning that there is a net force acting towards the center. This concept also is applied with inertia in mind, an object at rest will stay at rest unless acted upon by an outside force. People or other objects inside the car or object would continue in straight, while the car or object moves inward. There is a push or pull on the object towards the center which is needed for a centripetal force. Centripetal describes the direction of the force. work = force*displacement*cosine(theta).
 * WHAT YOU NEED!!**

Forces, for circular motion, are directed inward, not outward even though people think otherwise. Centrifugal is the outward feeling when moving in a circular motion. It is critical not to get an outward feeling and an outward force confused as they do not mean the same thing. The outward feeling is due to your body wanting to go straight while the car is turning.
 * INWARD, NOT OUTWARD!**

Speed, acceleration, and force can be measure and calculated with different equations. The equation for average speed is avg v = 2 πr / t. The equation for acceleration is avg accel = 4π 2 r / t 2. The equation for net force is F net = m * (4π 2 r / t 2 )
 * MATH MATH AND MORE MATH**

Hw lesson 2
12/22/11 Method 3 We are able to use the equations for the second law and relate them to circular motion. We can use the equation Fnet =m*a by using the centripetal forces instead of using the x or y axis.
 * How can Newton's second law be associated with circular motion?**

The force that pointed to the center of the circle is the centripetal force that enables the object to move in circular motion.
 * What is the centripetal force in horizontal motion?**

Centripetal acceleration most likely occurs on roller coaster clothloid loops. Since this is not a circular loop the radius is constantly changing. The radius at the bottom of the loop is larger than the radius at the top of the loop. Acceleration is due to both change in speed and direction.
 * The physics of roller coaster Clothoid loops?**

There is both a normal force and weight acting upon the cart. At the top of the loop both of the forces are pointing toward the center of the circle. At the bottom of the loop the normal force points toward the center of the circle while weight points downward.
 * What are the forces in a clothoid loop?**

Step 1: create a free body diagram Step 2: Identify the quantities Step 3:identify any unknown forces to plug into the equation fnet=m*g Step 4: If not given, then solve for the acceleration by using the speed and radius Step 5: Determine the normal force.
 * How to construct a clothoid loop problem?**

Race cars, Ice skating, baseball running, etc.
 * What sports use circular motion?**

If a person who is skating is moving in circular motion at an angle then you must use components to solve the problem. you would break up the normal force, since the only forces would be normal and weight and weight always points downward.
 * Circular motion with angle:**

Hw lesson 3
1/4/12

Many people just know the name as the thing that holds objects from floating on earth, but in reality its much more than that. Gravity is a force that pull everything towards the center of the earth.
 * Why is gravity so important?**

Gravitational force pulls objects toward the center of the earth and also if you jump up you are moving against he force of gravity. There is acceleration of gravity which is acceleration when the only force acting upon the object is gravity. Its numerical value is 9.8 m/s/s for all objects no matter what their mass is.
 * Gravitational force vs. Acceleration of gravity**

He thought that the planets were magnetically driven by the sun.
 * What are Kepler's three laws of planetary motion?**
 * 1) The paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus. **(Law of Ellipse)**
 * 2) 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. **(Law of equal areas)**
 * 3) The ratio of square of periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. **(Law of Harmonies)**

Gravity forces things not to move in the path that they would in the absence of gravity. Ex: no gravity: a cannon ball shot would travel in a straight line forever with gravity: a cannon ball shot would eventually fall down to the earth's surface.
 * Newton and universal gravitation**

It accelerates towards the earth at a rate of ,00272 m/s^2
 * The moon**

The gravitational attraction between any object and early is inversely proportional to the distance separating the earth's center from the objects center. The force of gravity acting between earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object. It is also inversely proportional to the square of the distance that separates the centers of the earth and the object.
 * What affects the magnitude of a gravitational force?**

All objects attract each other with a force of gravitational attraction and gravity is universal. Gravitational attraction is dependent upon the masses of both objects and inversely proportional to the square of the distance between the two objects.
 * What is Newton's law of universal gravitation?**

Fgrav = (G*m 1 +m 2 )/ d 2
 * Equation**

Hw lesson 2 parts 1-4
copernicus had a theory, a heliocentric view, that the earth rotated around the sun. This lead to many confrontations between the Catholic church and people that followed copernicus, Galileo was one of these people.
 * What were scientist views before Newton?**


 * What are the three views of planetary motion?**
 * 1) The earth was the center of the universe, this was believed by the ancient greeks and the Catholic church.
 * 2) Copernicus's theory in which the planets move around the sun
 * 3) The Keplerian theory that the planets move in an elliptical orbit about the sun which is at one focus.

He modified copernicus's theory about the planets revolving around the sun. He found that the paths of the planets were elliptical rather than circular. He thought that this was because of some magnetic influence form the sun.
 * What did Kepler do?**

He was able to figure out the coordinate plane. This grid could be "laid" across all over space to help figure things about space and the planets out. This gird and "geometric mapping" helped scientists use math to figure things out about the planets.
 * How did Decartes help discover things about the universe?**


 * What are the three points about Newton?**
 * 1) He did not focus as much on motion as he did on the deviation of motion
 * 2) Whenever there was a deviation of motion Newton looked for a reason to why this happen --> he describe this a being a force. Ex - Applying the breaks makes your car slow down.
 * 3) He found a quantitative link between force and deviation from steady motion which then lead him to his universal law of gravity.

Mechanics is the study of force and motion, this is also know as determinism. This law explained why every planet would move around the sun in an elliptical orbit. This allowed for people to see that religion and science overlapped and that people had free will and could do what they want.
 * What is the significance of Newton's ONE law for gravity?**

Hw lesson 4(a-c)
Kepler’s first law explains how planets orbit the sun in an elliptical path. An ellipse is a curve in which the sum of the distances from every point on that curve to two other points is constant. These two other points are also known as foci. When the there is only one foci that means it is a circle, therefore the close together the foci are then the more circular the ellipse is. The sun is located at one of these foci. Keplers second law describe the speed that any planet can move while it is orbiting around the sun. This speed is constantly changing, it moves fastest when closest to the sun. But, the planet would carve out the same area in the same amount of time. Keplers third law compares the orbital period and the radius of orbit of a planet to those of other planets. This law makes a comparison between all of the planets. The ratio of squares of the periods to the cube of their average distances from the sun is the same for every planet. T 2 /R 3

A satellite is any object that is orbiting the earth, sun or other massive body. There are natural satellites, the moon, planets, and comets, and man-made satellites, for communication and research. A satellite is an object upon which the only force is gravity. Newton was the first to theorize that a projectile launched with sufficient speed would actually orbit the earth. So what launch speed does a satellite need in order to orbit the earth? For every 8000 meters measured along the horizon of the earth, the earth's surface curves downward by approximately 5 meters. The velocity of a satellite would be directed tangent to the circle and the acceleration would be the directed towards the center of the circle (direction of acceleration changes). Gravity supplies the centripetal force. Satellites may orbit paths known as ellipses. The central body in this case is located at one of the foci. The velocity and acceleration are pointed towards the focus of the ellipse.

If the satellite is moving in circular motion the equation is ** F ** ** net **** = ( M **** sat **** • v **** 2 **** ) / R ** If the net force is the result of the gravitational force than the equation is ** F ** ** grav **** = ( G • M **** sat **** • M **** Central **** ) / R **** 2 **
 * (M **** sat **** • v **** 2 **** ) / R = (G • M **** sat **** • M **** Central **** ) / R **** 2 **

The acceleration of a satellite in circular motion about some other mass can use this equationWhere ** G ** is 6.673 x 10 -11 N•m 2 /kg 2, ** M ** ** central ** is the mass of the central body about which the satellite orbits, and ** R ** is the average radius of orbit for the satellite. Where ** T ** is the period of the satellite, ** R ** is the average radius of orbit for the satellite, and ** G ** is 6.673 x 10 -11 N•m 2 /kg 2.

Hw lesson 4(d-e)
The idea of being “weightless” can be felt in space and on top of a rollercoaster. Contact forces are when two objects in contact. Action-at-a-distance forces are gravity acting upon an object. You feel weightless when there are no external objects touching one’s body and all forces are removed. In a state of free fall you feel weightless. A scale measure the upward force applied to your body. Astronauts are weightless because there is no external contact force pushing or pulling upon their body. The only force acting on them is gravity. Their tangential velocity allows them to remain in orbital motion.

The orbits of satellites about a central massive body can be described as either circular or elliptical. There is no acceleration in the tangential direction and the satellite remains in circular motion at a constant speed. The work-energy theorem states that the initial amount of total mechanical energy of the system + the work that was done by external forces on that system is = to the final amount of total mechanical energy of the system. There is an equation for this formally known as: ** KE **** i **** + PE **** i **** + W **** ext **** = KE **** f **** + PE **** f ** The w represents the amount of work done by external forces. A satellite stays the same distance able the surface of the earth and thus the speed is constant and therefore kinetic energy is constant. One way to represent the amount and type of energy can be shown by a work-energy bar chart. Length of the bar represents the amount of energy that is present.