Ch5_TalasH

=Lesson 1: Motion Characteristics for Circular Motion = a, b, c, d, e Method 5

**A**

__Traveling in Circles With the Same Radius__ Uniform circular motion is the motion of an object in a circle with a constant or uniform speed. An object in this motion will travel the same distance in each second of time and the perimeter of the circle in which an object travels on is called the perimeter. This is very similar to the average speed equation, average speed = circumference (2 π r) / time, where t is the period, the time it takes to make one cycle around the circle.Velocity changes in uniform circular motion the object is constantly changing directions when moving in a circle, which is best described a tangential because thedirection of the vector is in the direction of a tangent line drawn to the circle at the object's location.

**B**

__Acceleration Does Not Have to Do With Speed?__ There is acceleration in an object at uniform circular motion because even the magnitude of velocity is not changing, the direction is. The acceleration is in the same direction as the velocity change; directed towards the center of the circle because objects moving in circles at a constant speed accelerate towards the center of the circle. Accelerometers are used to measure accelerations by placing 2 of them on a rotating platform and when spun, on can clearly see the direction of lean of the corks (direction of acceleration). This is because the cork's mass and inertia is much less hand will have a greater acceleration pointing towards the center.

**C**

__Newton's Second Law Follows Centripetal Force__ The centripetal force requirement states that there must be an inward force (pushing or pulling) acting upon an object in order to cause its inward acceleration. Newtons first law states that it not a force that is making an object move inward or outward, but it's reaction to the acceleration that it is experiencing. When a car is making a sharp turn, the passenger is experiencing the tendency of his/her body to continue in its path tangent to the circular path along which the car is turning; he/she has a false feeling of being pushed in a direction that is opposite to the acceleration. The magnitude of the velocity can not be changed because work, a force acting upon an object to cause a displacement (Work = Force * displacement * cosine (Theta)), is 0 joules.

**D**

__The F Word is Not the Same as Centripetal__ <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Centrifugal means away from the center or outward. However, in circular motion there is an inward force even though the object or person may feel like they are experiencing an outward force. If an object is moving in a straight path and a whiteboard is moving in a circular motion under it, it will continue it's straight path unless an outward forces, such as a block, allows it to also move in a circular path.

<span style="font-family: Arial,Helvetica,sans-serif;">**E**

<span style="font-family: Arial,Helvetica,sans-serif;">__Mathematics in Circular Motion__ <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">To find acceleration, one can use the equations a = v^2 / R or 4 π^2R / T^2. The net force is always greater than the outward force. To find the net force, one must use these equations: F = ma, F = m * 4π^2R / T^2. Also, F = m * v^2 / R is used which shows that the net force required for an object to move in a circle is directly proportional to the square of the speed of the object if the mass and radius are constant.

=<span style="font-family: Arial,Helvetica,sans-serif;">Lesson 2: Circular Motion and Satellite Motion =

<span style="font-family: Arial,Helvetica,sans-serif;">**A**

<span style="font-family: Arial,Helvetica,sans-serif;">** Newton's Second Law - Revisited ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Consider a car moving in a horizontal circle on a level surface. The diagram below depicts the car on the left side of the circle. <span style="font-family: Arial,Helvetica,sans-serif;">toc



<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Applying the concept of a centripetal force requirement, we know that the net force acting upon the object is directed inwards. Since the car is positioned on the left side of the circle, the net force is directed rightward. 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).





<span style="font-family: Arial,Helvetica,sans-serif;">m = 945 kg <span style="font-family: Arial,Helvetica,sans-serif;">v = 10 m/s <span style="font-family: Arial,Helvetica,sans-serif;">R = 25 m <span style="font-family: Arial,Helvetica,sans-serif;">Force of friction = ? <span style="font-family: Arial,Helvetica,sans-serif;">μ = ?

<span style="font-family: Arial,Helvetica,sans-serif;">Since Fgrav = Fnorm= 9261 N. Only the friction force remains unknown. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">The force of friction is the net force since it’s the only one horizontal force. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Fnet = m * v2 / R

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">After substation we find that the force of friction is ** 3780 N **.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Now we can find μ.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Ffrict = μ * Fnorm

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">3780 = μ * 9261

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">μ = 0.408

<span style="font-family: Arial,Helvetica,sans-serif;">**B**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Roller Coasters and Amusement Park Physics**



<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">A clothoid is a section of a spiral in which the radius is constantly changing. The radius at the bottom of a clothoid loop is much larger than the radius at the top of the clothoid loop. A mere inspection of a clothoid reveals that the amount of curvature at the bottom of the loop is less than the amount of curvature at the top of the loop.



<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Acceleration changes due to both a change in speed and a change in direction. A rightward moving rider gradually becomes an upward moving rider. A rider also changes speed. As the rider begins to ascend (climb upward) the loop, she begins to slow down. Also an increase in height results in a decrease in kinetic energy and speed. So the rider experiences the greatest speeds at the bottom of the loop and the lowest speeds at the top of the loop.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">In the case of a rider moving through a noncircular loop at non-constant speed, the acceleration of the rider has two components. There is a component that is directed towards the center of the circle and attributes itself to the direction change. This tangential component would be directed opposite the direction of the car's motion as its speed decreases (on the ascent towards the top) and in the same direction as the car's motion as its speed increases (on the descent from the top).

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;"> The normal force must be sufficiently large to overcome Fgrav and supply some excess force to result in a net inward force.

<span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 18px; text-align: center;">**Suggested Method of Solving Circular Motion Problems** > Use the remaining information to solve for the requested information.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Construct a free-body diagram.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Identify the given and the unknown information.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">If any of the individual forces are directed at angles, use horizontal and vertical components.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Determine the magnitude of any known forces.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Use circular motion equations to determine any unknown information.
 * 1) If the problem requests the value of an individual force, then use the kinematic information (R, T and v) to determine the acceleration and the Fnet; then use the free-body diagram to solve for the individual force value.
 * 2) If the problem requests the value of the speed or radius, then use the values of the individual forces to determine the net force and acceleration; then use the acceleration to determine the value of the speed or radius.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Normal force provides a sensation or feeling of weightlessness or weightiness. When at the top of the loop, a rider will feel partially weightless if the normal forces become less than the person's weight. And at the bottom of the loop, a rider will feel very "weighty" due to the increased normal forces. It is important to realize that the force of gravity and the weight of your body are not changing. Only the magnitude of the supporting normal force is changing!

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">The magnitude of the normal forces along these various regions is dependent upon how sharply the track is curved along that region (the radius of the circle) and the speed of the car. These two variables affect the acceleration according to the equation

<span style="font-family: Arial,Helvetica,sans-serif;">**C** <span style="font-family: Arial,Helvetica,sans-serif;">Athletics <span style="font-family: Arial,Helvetica,sans-serif;">The most common example of the physics of circular motion in sports involves the turn. It could be a softball player running the bases and making a turn around second base. You can be sure that turning a corner involves circular motion principles. Not all turns involve a complete circle, but any turn can be approximated as being a part of a larger circle or a part of several circles of varying size. A sharp turn can be considered part of a small circle. A more gradual turn is part of a larger circle.



<span style="font-family: Arial,Helvetica,sans-serif;">There must be some object supplying an inward force or inward component of force. 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//. As such, 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. The horizontal component of the contact force pushes the person towards the center of the circle. This contact force is depicted in the diagram below for a speed skater making a turn on ice.



<span style="font-family: Arial,Helvetica,sans-serif;">The force is a vector combination of a normal force and a friction force. As the skater leans into the turn, she pushes downward and //outward// upon the ice. The high pressure and temperature of the blade upon the ice creates a shallow //groove// in which the blade momentarily rests. The blade pushes outward upon the vertical wall of this groove and downward upon the floor of this groove. There is a //reaction force// of the ice pushing upward and inward upon the skate.

<span style="font-family: Arial,Helvetica,sans-serif;">If this blade-ice action does not occur, the skater could still lean and still try to push outward upon the ice. However, the blade would not get a //grip// upon the ice and the skater would be at risk of not making the turn. As a result, the ice skater's skates would move out from under her, she would fall to the ice, and she would travel in a straight-line inertial path. Without an inward force, the skater cannot travel through the turn.



=<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Lesson 2 The Clockwise Universe Parts 1 - 4 = <span style="font-family: Arial,Helvetica,sans-serif;">**Method 3: P-Q-R-S-T**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">What was the heliocentric view and who believed in it?

<span style="color: #404040; font-family: Arial,Helvetica,sans-serif;">The idea that the earth moved around the sun; this idea was also called the copernicon theory since copernicus launched this idea.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">How did Kepler modify the Copernican theory?

<span style="font-family: Arial,Helvetica,sans-serif;">Kepler agreed that the planets move around the sun, but their orbital paths were ellipses, not circles.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Who came up with the law of universal gravitation and what is it?

<span style="font-family: Arial,Helvetica,sans-serif;">Finally Newton produced a quantitative link between force and deviation from steady motion and, at least in the case of gravity, quantified the force by proposing his famous law of universal gravitation.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">What are mechanics?

<span style="font-family: Arial,Helvetica,sans-serif;">The study of force and motion

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">What is determinism?

<span style="font-family: Arial,Helvetica,sans-serif;">The thesis that states that for everything that happens there are conditions that predict the motions.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">What is the doctrine of free will?

<span style="font-family: Arial,Helvetica,sans-serif;">It asserts the idea that human beings are free to determine their own actions.

=<span style="font-family: Arial,Helvetica,sans-serif;">Lesson 4: <span style="background-color: #ffffff; font-family: Arial,Helvetica,sans-serif;">Circular Motion and Satellite Motion =


 * <span style="font-family: Arial,Helvetica,sans-serif;">A **

What is Kelpers Law of Ellipsis?

The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus.

What is Kepler's Law of Equal Areas?

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.

What is Kepler's Law of Harmonies?

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.


 * <span style="font-family: Arial,Helvetica,sans-serif;">B **

What is a satellite?

Any object that is orbiting the earth, sun or other massive body.

What are examples of natural and man made satellites?

The moon, the planets and comets are examples of natural satellites. Satellites launched from earth for purposes of communication, scientific research, weather forecasting, intelligence, etc are man made.

Why is a satellite a projectile?

This is because a satellite is an object upon which the only force is gravity

How does a satellite fall?

Because the earth curves, it falls around the earth instead of into it; it never reaches the earth.

Where is the acceleration, net force, and velocity of a satelitte directed?

The velocity would be directed tangent to the circle at every point along its path. The acceleration (caused by the net force) and the net force would be directed towards the center of the circle. However, in an ellipse they are directed towards the focus of the ellipse. Since sometimes the velocity and the inward force are sometimes opposite and sometimes the same, elliptical motion is unlike uniform circular motion (velocity slows down and speeds up).


 * <span style="font-family: Arial,Helvetica,sans-serif;">C **

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">What is the mathematical equation to calculate the net force of satellites?

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Fnet = ( Msat • v2 ) / R

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Equation for calculating the gravitational force?

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Fgrav = ( G • Msat • MCentral ) / R2

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Calculating velocity?

<span style="font-family: Arial,Helvetica,sans-serif;">Set the above expressions for centripetal force and gravitational force can be set equal to each other. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">(Msat • v2) / R = (G • Msat • MCentral ) / R2

<span style="font-family: Arial,Helvetica,sans-serif;">Now Simplify

Calculating acceleration?

We can get the equation for acceleration through the value of g.



How (mathematically) are the period and radius related? What do you realize?

We can derive this equation from the previous velocity equation:



This proves Kepler's Law of Harmonies that says the ratio of the period squared is equal to the ratio of the radius cubed. We realize that the mass of the satellite does not matter, but the mass of the central body does.


 * <span style="font-family: Arial,Helvetica,sans-serif;">D **

Why do people have feelings of weightlessness (like on a roller coaster)?

If there is no normal force acting upon a person's body, he or she will not have any sensation of his or her weight. Without the contact force (the normal force), there is no way of feeling the non-contact force (the force of gravity).

What is the difference between "weight" and "weightlessness"?

"Weightlessness" is a feeling or sensation that occurs in a state of free fall because there are no contact forces acting on the object and just gravity, however, the object's "weight" still exists.

What does a scale really measure?

The upward force of the scale upon the person equals the downward pull of gravity (also known as weight). And so the scale is really measuring the external force which is the same as the person's weight (when at a state of equilibrium).

Why do astronauts feel weigthless in space?

Astronauts simply feel weightless because there is no external contact force pushing or pulling upon their body. They are in a state of free fall. Many think it is because there is no gravity in space, however, this is wrong there is an inward gravitational pull in earth's orbit which is the centripetal force that makes objects orbit.


 * <span style="font-family: Arial,Helvetica,sans-serif;">E **

How does velocity change in an elipse?

It increases as it moves closer to the earth and decreases as it moves further from the earth.

What is the work energy theorem?

KEi + PEi + Wext = KEf + PEf

Wext = amount of work done by external forces. (for satellites this is zero)

What is the energy analysis of circular and elliptical orbits?

In a circular orbit, kinetic energy is dependent upon the speed of an object, and so it will be constant throughout the satellite's motion. And since potential energy is dependent upon the height of an object, it will also be constant. So if the KE and the PE remain constant, this means that the TME remains constant.

In an elliptical orbit, the satellite slows down and speeds up which means since the speed is changing, the kinetic energy is changing. Also, when the satellite is moving closer to the earth, it gains potential energy, but when it moves farther away, it loses potential energy because the speed is changing. When there is a loss of potential energy, there is a gain in kinetic energy. However, throughout the entire elliptical trajectory, the total mechanical energy of the satellite remains constant.