Ch_5_tonuzire

Remzi Tonuzi  Ch apt er 5 toc

= Homework: =

Lesson 1
Method 5 (for all)

A) An object that is moving in uniform circular motion is moving around the outside with a constants speed, but not a with a constant velocity. The velocity is changing because although velocity relies on speed, it relies on direction as well (magnitude and direction). This is because velocity is a vector. Velocity is always tangent to the circle, and the tangent line points in a new direction constantly.

B) A huge misconception is that objects that are traveling in a circular motion with constant speed do not have acceleration. This is false because acceleration is change in velocity. Velocity is both speed and direction, and although the speed is constant the direction isn’t. Every position of the circle contains a change in velocity. You can take two of the positions and find their accelerations by using vector addition.

C) Centripetal acceleration is needed for an object that is in uniform circular motion! An object that is in uniform circular motion will experience a net force that points in towards the center of the circle. An object needs this force or it will not be able to change its direction. The reason the force can change the direction is because it is perpendicular to the tangential velocity. This causes the object to change direction but not speed.

D) Never use the F-word! Centrifugal forces are described as the opposite of centripetal force, therefore, they are pointing outward and away from the center of the circle. This force is considered a huge misconception because the feeling of being thrown outward from a rollercoaster or car gives people the feeling that there is a force pushing them outward. This is not a centrifugal force, but rather an object’s inertia keeping it moving in the same direction and doing what it has been doing before the car or coaster changed direction.  E)

By finding force, speed, and acceleration, we can solve problems pertaining to circular motion. The equations that will do so are: acceleration = v^2/R, Fnet=(m)(a), Average Speed = distance/time = 2πR/T.



Lesson 2
A)

In order to solve problems, we draw Free Body Diagrams and then create equations based off of the diagram using F=ma. Circular motion changes acceleration to V^2/R to correspond with the circular forces. To find other forces, you can solve for them by using forces on different axes

B)

Rollercoasters contain three types of circular motion: loops, small dips and hills, and banked turns.There is less normal force at the top of the loop because of your weight and at the bottom, there is more normal force. The same goes for dips and hills; there is less normal force at the top than at the bottom of the dip. These all deal with centripetal force.





C)

Whenever someone in any sport (track and field, soccer, football, etc.) makes a turn, it deals with circular motion. An example would be an ice skater that makes a turn while moving on the ice. He has to change the angle of his legs towards the center in order to execute the turn.





** Lesson 3 **
A) Gravity causes things in the air to fall down back to the ground. Gravity is more than just a word, or the value of 9.8m/s/s. Gravity isn’t just something associated with falling situation.

B) Kepler developed three laws after his analysis of data: The Law of Ellipses - 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 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 , and The 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 . Newton deduced that the course these planets traveled would be similar to a cannonball being shot with a velocity great enough to orbit the Earth. He came to the realization that this applied to objects in the Heavens, like the moon. He figured out that the force of gravity was inversely proportional to the square of the distance between the objects.

C) The Universality of Gravity exists between planets, heavenly bodies, and between objects everywhere, and Newton's law of universal gravitation states that every object’s attract each other with a force of gravitation (including people). Those forces aren’t significant though because they are small, unless the mass is greater. Both mass and distance affect gravitational force. Gravity is directly proportional to the product of two masses of two objects and Henry Cavendish discovered the universal gravitational constant; G = 6.673 x 10-11 N m2/kg2.



D) Once Newton figured out that Fgrav=m1*m2/d^2, Cavendish found the value of the universal gravitational constant by using a Torsion balance. He measured the relationship between the angle of rotation and the amount of torsional force. Afterward, he placed two big metal spheres by the smaller ones until the torsional forces balanced the gravitational forces. Cavendish measured m1, m2, d, and Fgrav and found the value of G, 6.75 x 10^-11 N m^2/kg^2, similar to todays G value of g.67259 x 10^-11 N m^2/kg^2.

E) 9.8 m/s/s has been the commonly used value for the acceleration of gravity; but, this is the acceleration due to gravity at sea level. If an object is closer or further to the Earth, the value of acceleration due to gravity changes. This has been proved using Fgrav= (G*M)/d2. The larger the distance, the smaller value for g is, and because the larger the planet is, the value of g is also larger. The acceleration value g for other planets can be found using the following formula:



** The Clockwork Universe **
1)

In 1543, Copernicus theorized that the solar system moved in a heliocentric pattern, meaning that the Earth orbited the sun in a circular pattern. Kepler improved this and discovered that the planets moved in elliptical movements around the sun instead of the perfectly circular orbit that Copernicus had thought. Although he wasn’t entirely sure, he said the Sun had an influence on the orbit pattern.

2)

Descartes made a new math discovery; he discovered that geometry problems could be recast into algebra problems by using the coordinate plane and putting lines and shapes on it. This new type of math was called coordinate geometry - geometrical shapes are represented by equations and geometrical truths are established by putting equations together and rearranging them. This new type of math allowed advancements in mathematics and sciences.

3)

Newton was able to create a fundamental structure that would help many other people understand the laws of the universe. Newton did this by using a using a single set of laws. Some key points were: 1- He looked at the deviation from motion, 2 - He looked for forces that could cause deviation, and 3 – Using quantitative link between force and deviation from steady motion, he developed his Law of Universal Gravitation.

4) Newton’s one law for gravity can be applied to every piece of matter in the universe. This finding developed mechanics, a study of force an motion. It considered the universe predictable and that it could be predicted with as much accuracy as desired. Determinism (Newtonian mechanics) is the idea that the universe has been set, its future motion is completely predictable and that it resembles clockwork. There was a lot of disagreement with this idea because of religion.

** Lesson 4 **
A) Kepler made three laws for planetary motion: The Law of Ellipses, The Law of Equal Areas (simply put that a planet moves its fastest when it is closest to the sun and slowest when it is furthest from the sun), The Law of Harmonies (basically compares the orbital period and the average radius of one planet’s to another’s). It also stresses that for every planet in the solar system, Radius^3/Time^2 is constant.

B) Satellites are objects that orbit a larger or more massive object, and can be of nature, like the Moon orbiting the Earth, or a man made object like a satellite. Satellites are projectiles and are only affected by gravity; but, if they are launched a speed great enough, they will remain at the same distance from the surface because the rate that they will fall equals the rate that the object curves around the surface. The velocity vector is tangential to the orbit, so the acceleration and force vectors point inward, toward the center of the object that is being orbited.

C) Force of gravity between two objects can be calculated by using their masses, the constant G, and the distance between their centers in the formula  Acceleration can be obtained from this equation:  Velocity can be derived from the acceleration derivation:
 * Fgrav = ( G • Msat • MCentral ) / R2. **
 * v **** 2 **** = (G • M **** Central **** ) / R **

D)

Contact forces are forces that need contact between objects, while action-at-a-distance forces (such as gravity) affect objects at distance, without needing contact. Weightlessness occurs when there is no normal force, or contact. A scale reading only measures the contact/normal force. It balances with gravity, letting you to find your weight, but if you’re in a moving elevator, the amount of contact force to balance weight may be different, therefore showing different weights. An astronaut is weightless because there is no normal force, but gravity is still acting on them.

E) The inward force and the tangential velocity are perpendicular to each other when a satellite orbits at a constant radius and speed, which means both variables can’t affect each other. But, in elliptical orbits, the two vectors aren’t perpendicular to each other, so some force can end up slowing it down or speeding it up during its orbit. Also, the work-energy theorem mentions that the initial amount of total mechanical energy (TMEi) of a system and the work done by external forces (Wext) on that system together equal the final amount of total mechanical energy (TMEf) of the system.

** KEi + PEi + Wext = KEf + PEf **

“The Wext term in this equation is representative of the amount of work done by [|external forces]. For satellites, the only force is gravity. Since gravity is considered an [|internal (conservative) force], the Wext term is zero. The equation can then be simplified to the following form.” (physicsclassroom.com)
 * KEi + PEi = KEf + PEf **