Ch5_Doomank

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=Homework 12/13/11= a)
 * Lesson 1, Method 5**
 * //Uniform Circular Motion//
 * Uniform Circular Motionis the motion of an object in a circle with a constant or uniform speed. The distance of one complete cycle around the perimeter of a circle is known as the circumference. Average speed is simply circumference (2*pi*r) divided by time (t). Velocity vectors of uniform circular motion are **tangential**. The direction of the velocity vector at any instant is in the direction of a tangent line drawn to the circle at the object's location

b)
 * //An Accelerating Object is Changing Its Velocity//
 * An object moving in a circle at constant speed is indeed accelerating because the direction of the velocity vector is changing. Acceleration can be calculated as (v f -v i ) / (t). Objects moving in circles at a constant speed accelerate towards the center of the circle.

c)
 * //Centripetal Force Requirement//
 * The direction of the net force is in the same direction as the acceleration, so for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. The word //centripetal//means center seeking.The presence of an unbalanced force is required for objects to move in circles. The centripetal force for uniform circular motion alters the direction of the object without altering its speed.

d)
 * //Centrifugal and Centripetal: Two Different Things//
 * The common misconception, believed by many physics students, is the notion that objects in circular motion are experiencing an outward force. The sensation of being thrown outward, that many people are familiar with, is attributable to the idea of inertia, rather than the idea of force. It was due to your tendency to travel in a straight line while the car seat was making its turn. In fact, you were not thrown rightward at all; you moved in a perfectly straight line.

e)
 * //Mathematics of Circular Motion//
 * Acceleration can be found using the equation (v 2 ) / (R). V=velocity and R= Radius. The other equation that can be used is (4*pi 2 *R) / (T 2 ). R= radius and T= period. These equations for acceleration can be plugged into the net force equation (F=ma) for 'a'. Then they can be solved as one would usually solve an equation.

=Homework 12/22/11=
 * Lesson 2, Any Method**


 * Section A**
 * It is the friction force that supplies the centripetal force requirement for the car to move in a horizontal circle. Without friction, the car would turn its wheels but would not move in a circle (as is the case on an icy surface)
 * To solve a problem do the following
 * From the verbal description of the physical situation, construct a free-body diagram. Represent each force by a vector arrow and label the forces according to type.
 * Identify the given and the unknown information
 * If any of the individual forces are directed at angles to the horizontal and vertical, then use vector principals to resolve such forces into horizontal and vertical components.
 * Determine the magnitude of any known forces and label on the free-body diagram.
 * Use circular motion equations to determine any unknown information.
 * Use the remaining information to solve for the requested information
 * Section B**
 * Roller coaster loops assume a tear-dropped shape that is geometrically referred to as a clothoid. A clothoid is a section of a spiral in which the radius is constantly changing
 * There is a continuous change in the direction of the rider as she moves through the clothoid loop
 * The rider experiences the greatest speeds at the bottom of the loop - both upon entering and leaving the loop - and the lowest speeds at the top of the loop
 * For a rider moving through a circular loop with a constant speed, the acceleration can be described as being centripetal or towards the center of the circle
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l2b4.gif width="242" height="182" align="left"]]


 * Section C**
 * The most common example of the physics of circular motion in sports involves the turn
 * When a person makes a turn on a horizontal surface, the person often //leans into the turn//.
 * By leaning, the surface pushes upward at an angle //to the vertical//-->there is both a horizontal and a vertical component resulting from contact with the surface below.
 * This **contact force** supplies two roles - it balances the downward force of gravity and meets the centripetal force requirement for an object in uniform circular motion

=Homework 01/04/12=
 * Lesson 3, Any Method**


 * Section A**
 * As we rise upwards after our jump, the force of gravity slows us down.
 * As we fall back to Earth after reaching the peak of our motion, the force of gravity speeds us up


 * Section B**
 * 1600's, German mathematician and astronomer Johannes Kepler mathematically analyzed known astronomical data in order to develop three laws to describe the motion of planets about the sun
 * The paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)
 * 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. (The Law of Equal Areas)
 * 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. (The Law of Harmonies)
 * To Kepler, the planets were somehow "magnetically" driven by the sun to orbit in their elliptical trajectories. There was however no interaction between the planets themselves.
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l3b5.gif width="363" height="124" align="left"]]


 * Section C**
 * **ALL** objects attract each other with a force of gravitational attraction. Gravity is universal

> **G = 6.673 x 10-11 N m2/kg2**
 * Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force
 * The constant of proportionality (G) in the above equation is known as the **universal gravitation constant** . The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. The value of G is found to be


 * Section D**
 * Cavendish's apparatus for experimentally determining the value of G involved a light, rigid rod about 2-feet long.
 * Two small lead spheres were attached to the ends of the rod and the rod was suspended by a thin wire.
 * When the rod becomes twisted, the torsion of the wire begins to exert a torsional force that is proportional to the angle of rotation of the rod.
 * The more twist of the wire, the more the system pushes //backwards// to restore itself towards the original position.
 * Cavendish had calibrated his instrument to determine the relationship between the angle of rotation and the amount of torsional force
 * Cavendish then brought two large lead spheres near the smaller spheres attached to the rod.
 * Since all masses attract, the large spheres exerted a gravitational force upon the smaller spheres and twisted the rod a measurable amount.
 * Once the torsional force balanced the gravitational force, the rod and spheres came to rest and Cavendish was able to determine the gravitational force of attraction between the masses.
 * By measuring m1, m2, d and Fgrav, the value of G could be determined.
 * Cavendish's measurements resulted in an experimentally determined value of 6.75 x 10-11 N m2/kg2.
 * Today, the currently accepted value is 6.67259 x 10-11 N m2/kg2


 * Section E**
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l3e1.gif width="152" height="47" align="left"]]


 * Acceleration of gravity is dependent upon the mass of the earth (approx. 5.98x1024 kg) and the distance ( **d** ) that an object is from the center of the earth
 * The variation in g with distance follows an [|inverse square law] where g is inversely proportional to the distance from earth's center.
 * This inverse square relationship means that as the distance is doubled, the value of g decreases by a factor of 4

a)
Kepler was able to summarize the carefully collected data of his mentor (Tycho Brahe) with three statements which described the motion of planets in a sun-centered solar system. Kepler's three laws of planetary motion can be described as follows: Kepler's Three Laws are the Law of Ellipses, The Law of Equal Areas, and The Law of Harmonies.
 * The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)
 * 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. (The Law of Equal Areas)
 * 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. (The Law of Harmonies)

b)
Satellites are projectiles that orbit around a central massive body instead of falling into it. Satellites, projectiles that orbit around planets and other large bodies, are acted upon by gravity. Problem solving with satellites is similar to that of circular motion.
 * They are acted upon by the force of gravity - a universal force that acts over even large distances between any two masses.
 * Newton's Laws of Motion affect satellites.
 * For this reason, the mathematics of these satellites emerges from an application of Newton's universal law of gravitation to the mathematics of circular motion.

c)
>> || Screen_shot_2012-01-05_at_2.17.01_PM.png || >> || Screen_shot_2012-01-05_at_2.17.27_PM.png ||
 * How can you calculate the net force of satellites?
 * You use Newton's Second Law equation, F=ma. m is the mass of the satellite, and the distance between the center of the planet and the satellite is R. Then, you use the formula Fnet = ( Msat • v2 ) / R. This is derived from F = ma.
 * How can you determine out the gravity of satellites?
 * You use Newton's law of gravitation equation, which is Fg=(G*M1*M2)/R^2.
 * How can you calculate the velocity of satellites?
 * || [[image:jitskyhonorsphysics/Screen_shot_2012-01-05_at_2.17.01_PM.png caption="Screen_shot_2012-01-05_at_2.17.01_PM.png"]] ||
 * How can you calculate the acceleration due to gravity of satellites?
 * || [[image:jitskyhonorsphysics/Screen_shot_2012-01-05_at_2.17.27_PM.png caption="Screen_shot_2012-01-05_at_2.17.27_PM.png"]] ||

>> || Screen_shot_2012-01-05_at_2.18.02_PM.png || -also helps verify Kepler's Law of Harmonies.
 * How do you calculate the period of satellites?
 * || [[image:jitskyhonorsphysics/Screen_shot_2012-01-05_at_2.18.02_PM.png caption="Screen_shot_2012-01-05_at_2.18.02_PM.png"]] ||

d)

 * What is weightlessness?
 * It is a sensation you feel when you are in freefall. You feel like you are weightless, even though you still have a weight. It is caused by the sensation of having nothing pushing or pulling you.
 * Contact and non-contact force: What's the difference?
 * A contact force are when two surfaces have to touch for a force. An example is normal force. Gravity is a non-contact force, since it two objects don't have to touch for there to be gravity. For example, the moon and Earth exert gravity on one another, but don't touch.
 * When we measure our weights with a scale, why is it different in outer space?
 * Scales measure the normal force (the upward force on our body) at the point of contact with the scale. This force changes if there is an acceleration, but your weight remains the same. If there is an upwards acceleration, the scale would display a higher number for weight. If there is a downwards acceleration, the scale would display a lower number for weight.
 * Where else do you feel weightless?
 * Some examples would be a free falling elevator and a free falling amusement park ride.
 * Why do you feel weightless in outer space?
 * Astronauts have no external forces acting on them, just like in freefall.
 * Though the gravity from the planets affect the astronaut, there are no contact forces, so astronauts feel weightless.

e)

 * What is the work-energy theorem?
 * It says that the initial amount of the total mechanical energy, TMEi, of a system, plus the external forces,(Wext), on that system is equal to the total mechanical energy, TMEf, of the system. This mechanical energy can be in the form of potential energy or kinetic energy.
 * The equation for this theorem is KEi + PEi + Wext = KEf + PEf
 * What is the Wext term for satellites?
 * Since this term represents the amount of work being down by external forces, it is only gravity for satellites.
 * Also, since gravity is not an external force, but an internal (conservative) force, the Wextterm is zero.
 * This means the equation can be simplified into KEi + PEi = KEf + PEf
 * What are some characteristics of the energy analysis of elliptical orbits of satellites?
 * TME is constant
 * Wext is zero
 * The satellite moves fastest near Earth and slows down farther away from Earth
 * Kinetic energy changes
 * When it is going faster, the satellite's distance from the Earth decreases. Therefor, there is a gain of kinetic energy and a loss of potential energy
 * Mechanical energy is conserved
 * Total mechanical energy of the satellite remains constant
 * What are some characteristics of the energy analysis of circular orbits of satellites?
 * Speed is constant
 * Height above Earth is constant
 * Kinetic energy is constant
 * Potential energy is constant
 * If KE and PE are constant, TME is also constant.
 * What is a work-energy bar chart?
 * It is a way of representing the quantity and type of energy possessed by an object using a vertical bar.
 * The length of the bar shows how much energy is present. a longer bar representing a greater amount of energy.
 * In a work-energy bar chart, a bar is constructed for each form of energy.
 * A work-energy bar chart is presented below for a satellite in uniform circular motion about the earth.