Unit1_LeeJ

//Unit 1. Linear Motiontoc//

=Section 1: 1-D Kinematics=

Lesson 1: Describing Motion with Words & Lesson 2: Describing Motion with Diagrams
1. What are words that describe motions? 2. What is mechanics? 3. What is Kinematics? 4. What is Scalars and Vectors?

__//**Class Notes:**//__


 * //Distance//**
 * how far you’ve traveled in total
 * Unit: m eter (m)
 * Symbols: d
 * Type of Quantity: Scalar


 * // Dispacement //**
 * net/change in position relative to some origin
 * take direction into account
 * Unit: meter (m)
 * symbols: d
 * Type of Quantity: Vector


 * // Speed //**
 * rate of change of position, how fast you move
 * Unit: m/s
 * Symbols: v
 * Type of Quantity: Scalar


 * // Velocity //**
 * includes direction
 * based on displacement
 * speed in a specific direction
 * Unit: m/s
 * Symbols: v
 * Type of Quantity: Vector

how fast speed/ velocity changes
 * // Acceleration //**
 * m/s 2
 * Symbols: a
 * Type of Quantity: Vector


 * Scalar:** only include quantity
 * Vector:** include quantity and direction

//1. At rest// //2. Constant Velocity// // 3. Increasing Velocity //
 * //4types of motion//**
 * no motion, not moving
 * no change in speed
 * covering same distance in same time
 * Vav = ∆d / t

//4. Decreasing Velocity//
 * starting slower and **steadily** getting larger
 * starting faster and **steadily** getting slower


 * Instantaneous**: have small distance of measuring.

__//**Summary**//__


 * **Mechanics:** the study of the motion of object
 * important to understand its meaning rather than memorizing
 * **Kinematics:** Science of describing the motion of objects using words, diagrams, numbers, graphs and equations
 * //2 Categories of mathematical//** // mathematical //


 * //quantities that are used to describe the motion of object//**
 * 1) **Scalar:** fully describe with numerical values
 * 2) **Vector:** fully describe with numerical values and direction.

//**Average vs instantaneous**//
 * average: the average of all instantaneous value
 * instantaneous: the value at given

//**5 quantities that describes the motion of object**//
 * 1) **Distance:** Scalar quantity that refers the total movement of object.
 * 2) **Displacement:** Vector quantity that refers change of position of object from original position.
 * 3) **Speed:** Scalar quantitiy that refers how fast the object moves.
 * 4) **Velocity:** Vector quantity that refers rate depend on displacement. must include direction
 * 5) **Acceleration:**Vector quantity that is determinded by rate of changing velocity.
 * // **Constant acceleration:** //when the rate of acceleration is constant
 * // Calculating average constant acceleration : // a // = //∆v / t
 * // Direction of the acceleration vector is depend on whether the object is becoming faster or object is becoming slower and whether object's velocity is + or - . //
 * // Rule of Thumb: when an object is slowing down, the direction of the object turn to its opposite direction //
 * //Calculating average constant speed://** Vav = ∆d(distance) / t


 * //Calculating average constant velocity://** Vav = ∆d(displacement) / t

physics should be described by word that related to physics with visual images in your mind.
 * //__Describing motion with diagram__//**

//**Ticker Tape Diagram**//
 * on the tape, it draws trail of dots per constant time.
 * the trail of dots represent the history of motion of an object
 * when the length of the space between continued2 dots is long, it means speed of an object is fast and when the length of the space between continued 2 dots is short, it means speed of an object is slow
 * when the space between continued 2 dots is constant, an object is moving at constant speed.
 * when the space between continued 2 dots is increasing of decreasing, the object is accelerating.[[image:untitled.JPG]]


 * //Vector Diagrams//**
 * vector diagram decribes vector quantities with vector arrow
 * It describes direction of an object and numerical quantity of the object
 * the length of vector arrow describes the numerical quantity of an object
 * ex) when the change in length of vector arrow is constant, the speed of an object is constant
 * ex2) when the change in length of vector arrow is increasing or decreasing, the speed is of an object is accelerating[[image:vector.JPG width="451" height="162"]]


 * //__Practice Problem!!__//**


 * lesson 1.b.1.** **a)** scalar **b)** vector **c)** vector **d)** scalar **e)** scalar **f)** scalar
 * lesson 1.c.1.** **distance:** 420m **displacement:** 140m, right
 * lesson 1.c.2.** **distance:** 95yd **displacement:** 55yd, left
 * lesson 1.c.3.** 0 **lesson 1.c.4. distance:** 500miles **displacement:** 0miles, right
 * lesson 1.d.1. average speed:** 140 m/min **average velocity:** 46.67 yd/min, right
 * lesson 1.d.2. average speed:** 9.5 yd/min **average velocity:** 5.5 yd/min, left
 * lesson 1.e.1. constant acceleration:**2 m/s 2
 * lesson 1.e.2. constant acceleration: -**2 m/s 2
 * lesson 2.a.1.** right to left, she slowed down the speed untill she stopped on the section that have lots of drops then she started to accelerate again.
 * lesson 2.a.2.** she was moving constantly until 7th drop of oil, however she started to accelerate left to right.
 * lesson 2.a.3.** she was moving constantly and started to slow down until she stopped and then she started to accelerate and move constantly again but slower than before.

__//**Lab: Constant speed**//__

// also need snapshot of data table //
 * Objection:** What does graph of constant speed look like?
 * Hypothesis:** The graph of constant speed would look like a linear line graph
 * Rationale:** When the speed is constant, position of an object and time is directly related.
 * Data: [[file:Constant Speed.xlsx]]**

**Conclusion:** As I expected, the graph of constant speed looked like a linear line graph because when the speed of an object is constant, the position of an object and time is directly related. In the data of this experiment, the slope of linear line graph represents the average speed of the ball because slope formula (y 2  – y 1 ) / (x 2  – x 1 ) is equal to ∆d / t in this lab which is the formula of the average speed of constant speed and graph shows 0.7976 slope in shallow line and 0.999 slope in steep line. In addition, R 2 <span style="background-color: transparent; color: #000000; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> value means how the linear equation fits well to the data. When R <span style="background-color: transparent; color: #000000; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super;">2 <span style="background-color: transparent; color: #000000; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">value is closer to 1, it means the graph fits more accurately to the data. In my data, the R<span style="background-color: transparent; color: #000000; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super;">2 value was 0.985 in steep line and 0.995 in shallow line, meaning the linear line fitted into the data scatter accurately. // good //

__//**Intersting Applet about acceleration**//__ // good description. include a screen shot of the applet inside of the file. //

[] This is an animation that you can control the acceleration of the car and could easily see how acceleration affects to a motion of an object. Also you can see the relationship between acceleration and velocity-time graph.

06/28/11 ==Lesson 3: Describing Motion with Position vs. Time Graphs & Lesson 4: Describing Motion with Velocity vs. Time Graphs & Lesson 5: Free Fall and the Acceleration of Gravity & Lesson 6: Describing Motion with Equations==

__//**Class Notes**//__
 * Motion Diagrams (Vector diagram)**
 * Qualitative representations
 * Relative sizes & directions of velocity & acceleration
 * Direction and speed of the object is represented by arrows
 * If the arrows are longer, it means faster speed
 * At rest, there is no motion diagram
 * At constant, there is no acceleration and the arrows have constant length.
 * At increasing, the lengths of the arrows areincreasing, velocity and acceleration points are in same direction.
 * At decreasing, the lengths of the arrows are decreasing, velocity and acceleration points are in opposite direction
 * Practice problem à in the note

//** Graphs **// __ At rest __
 * Ticker Tape diagrams**
 * Quantitative representations
 * Do not tell about direction.
 * At rest: x…………………..
 * At constant: x…x…x…x…x…x…x…x
 * At increasing: x…x…...x….…..x….……..x……….…..x
 * At decreasing: x…………x……….x……...x….…x
 * Should check where the starting position is because increasing and decreasing would occur confusion if there is not clear starting position.

__ Constant __ __ Increasing __ __ Decreasing __
 * Motion Diagram: v = 0, a = 0, diagram does not exist
 * d-t graph: a horizontal line
 * v-t graph: at 0 horizontal
 * Motion Diagram: Constant length of vector arrow, a = 0
 * d-t graph: linear with constant increase of d value(-value of d would change direction in opposite way)
 * v-t graph: a horizontal line
 * Motion Diagram: Vector arrow increase. a = same direction as v value
 * d-t graph: curved line with shallow start and steep end.
 * v-t graph: linear graph, a = slope, begins with small number and increase to bigger number
 * Motion Diagram: Vector arrow decrease. a = opposite direction of v value
 * d-t graph: curved line with steep start and shallow end.
 * v-t graph: linear graph, a = slope, begins with big number and increase to smaller number

__//**practice problems**//__ // You are welcome, even encouraged, to take a picture of your work and include it here. However, you must make sure it is large enough to be easily legible. This is definitely NOT. Remember, it is no big deal if your wiki is long, so don't worry about space issues. //

Questions // I like this format... are you finding it useful? //
 * //__Summary__//**
 * 1) What is slope represent in constant position-time graph?
 * 2) What is slope represent in increasing or decreasing velocity-time graph?
 * 3) What is free fall?


 * // Position vs time graph //**
 * relationship between position of an object and time.
 * Shapes of the graph represent different meaning.
 * Horizontal line: the object does not move
 * linear: constant velocity
 * Curved with shallow starting and steep end: increase in velocity
 * Curved with steep starting and shallow end: decrease in velocity
 * Slope of constant p-t graph represents the velocity of the object.
 * small slope represent small velocity, large slope represent large velocity
 * if velocity is negative, the object is moving left or opposite direction against when velocity is positive or moving right
 * position and time varies directly
 * Equation to get slope: rise / run. = (y2 – y1) / ( x2 – x1)[[image:pt_Graph.JPG]]


 * //Velocity vs time graph//**
 * relationship between velocity of an object and time
 * Shapes of the graph represent different meaning
 * Horizontal line at 0: the object is at rest
 * Horizontal line(not at 0): an object has a constant velocity.
 * linear: a velocity of an object is increasing when the value of the graph increase from small point to bigger point
 * linear: a velocity of an object is decreasing when the value of the graph decrease from big point to smaller point
 * slope of a linear graph represents acceleration
 * small slope represent small acceleration & large slpe represent large acceleration
 * Area between axis and the graph represents displacement

// good to include snapshots of graph shapes. I like that you were very selective in what you included. //

//**Free Fall**//
 * the state when the motion of an object is only effected by gravity
 * DO NOT encounter air resistance
 * acceleration of gravity: 9.8 m/s/s = g
 * Ticker tape of dot diagram can record it
 * downward acceleration
 * In position-time graph: curved, starts at high position with shallow line(small velocity) and ends at 0 or low position with steep line(large velocity).
 * In velocity-time graph: linear, velocity increase from 0 velocity to negative direction, decrease from positive velocity, slope is -9.8// a picture of this would be most helpful. //
 * constant acceleration
 * Vf = g * t
 * d = 0.5 * g * t2
 * rate of free fall acceleration won't effected by the mass of an object.

//**Answer for questions:**// __1. What is slope represent in constant position-time graph?__ à The slope in constant position-time graph represents the velocity of an object. __2. What is slope represent in increasing or decreasing velocity-time graph?__
 * //Kinematic equation//**
 * equations that describe the motion and relations of an object.
 * use many quantities
 * vav = ∆d/t and a = ∆v/t can change to variaty forms to solve problems that are related to velocity and acceleration
 * Use given to figure out what kind of equation you should use
 * Usually used to find unknown value by using given value
 * Sometimes, by using graphs, you can determine the given values and find out unknown values.

à ﻿The slope in increasing of decreasing velocity-time graph represents the acceleration of an object.

__3. What is free fall?__ à ﻿Free fall is the state when a motion of an object is only affected by gravity.
 * __//Lab: Free Fall //__**


 * __//﻿﻿//__// Object: //** What is acceleration due to gravity.
 * // Hypothesis: //** Acceleration due to gravity would be 9.81 m/s/s

//**Procedure**// // Use a freeform narrative style for procedure. See sample lab report for an example. //
 * 1.** Prepare a spark tape that is long enough to reach from ceiling to floor.
 * 2.** Hold spark timer on to the ceiling.
 * 3.** Put a spark tape into the spark timer.
 * 4.** Tape a 200g weight on to the spark tape.
 * 5.** Let the weight fall to the floor.
 * 6.** With a meter stick, measure the displacement of dots until you reach the 30th dot and record it on the data table
 * 7.** With the collected data, graph a scatter graph in Excel and draw trendline with the graph's equation and R² value.
 * 8. ** By using the equation, determine acceleration of gravity.

//**Data**// // need data table shown. Something is very wrong with your graph... the equation makes no sense. //



//**Analysis**// In the graph, x-axis represented time in second and y-axis represented displacement of dots on the spark tape. The graph showed curved graph with increasing displacement value. By using the graph’s equation, **A** value represented the acceleration of gravity, **B** value represented initial velocity and **t** represent time when the equation of the graph is d = 0.5At2+Bt. As a result my acceleration of gravity was 7 rather than 9.81, class' average value of acceleration of gravity. During the experiment, my percent difference with class mates was 22.91 percent. My result had lot difference with other’s data because the dots on my spark tape were not straight and unclear starting position.

__//**Interesting applet about Free Fall**//__ // good one! thanks //

[] This animation shows how the free fall works with gravity and compares the 2 balls. It shows red ball with 0 velocity and bule ball with velocity that you set would arrive at ground in same time.

=__//**Section 2: Newton's Law**//__=

Lesson1: Newton's First Law of Motion & Lesson 2: Force and Its Representation
__//**Class Notes**//__ **//__Newton’s Law of Motion__//**
 * Newton’s 1st law**
 * Also called law of inertia
 * When an object is at rest, an object will stay at rest. When an object is in motion, an object will stay in motion at constant speed in a straight line. Unless forced to do otherwise.
 * At rest à Static equilibrium, forces are balanced. v = 0, a = 0
 * In motion à Dynamic Equilibrium, forces are balanced. v ≠ 0, a = 0
 * Related to Galileo’s incline experiment.


 * Mechanical Forces**
 * Push or pull
 * Unit: N(newton)
 * External to the system (object)
 * Contact ( 1 exception)
 * CANNOT be transferred or carried
 * There are 4 mechanical forces
 * //Weight://
 * Unit: w or Fg
 * Always pull of earth on mass.
 * Points straight down.
 * Calculation: w = m(in kg) * g(9.8m/s/s)
 * //Friction://
 * Unit: f or Ff
 * 2 surfaces rub together
 * Parallel to surfaces, opposite direction of motion.
 * f = μ * N
 * //Normal://
 * Unit: N of FN
 * Support force, whenever 2 surfaces touch
 * Perpendicular surface and through system.
 * //Tension ://
 * Unit: T or FT
 * Rope or chain
 * Cannot push, only pull
 * Runs along the rope away from object

//**Free body diagram (FBD)**//
 * Very self-centered
 * Representation of all forces acting ON a system
 * All forces are shown with linear arrows and are labeled with symbols

__//**Summary**//__ Issac Newton stated 3 laws to explain motion of an object


 * //Newton's First Law of Motion: Law of Inertia//**
 * An object at rest favors to stay at rest
 * An object in motion favors to stay in motion with constant speed and same direction
 * UNLESS irregular force interrupts the state of the motion.
 * Inertia:tendency to resist the change in motion
 * Galileo Galilei first thought the concept of inertia by using his imaginary experiment.
 * Force not needed
 * The strength of inertia, which represent strength to resist against the change in motion, directly varies with mass.[[image:no_friction.JPG width="407" height="419"]]
 * //Balanced and Unbalanced Force//**
 * When forces have same magnitude with opposite direction, the forces are balanced and at equilibrium.
 * If an object is at equilibrium, it will not accelerate
 * Unbalanced force is a force that doesn't have other set of force that has an opposite direction and same magnitude to cancel out and balance.
 * Unbalacned force only: there is only single force.


 * //Force//**
 * push or pull
 * occurs from interactions of other objects
 * vector quantity
 * 2 categories:
 * **//contact force//**: resulted when 2 objects that occurs interactions are contacting each other.
 * // tension: // Forces transmitting through ropes or chains.( F ten)
 * // normal force: // Supporting force ( F ﻿norm)
 * // air resistance: // air opposed the motion of an object( F air)
 * // friction force: // Occur between contacted surfaces. resist force against motions. ( F frict)
 * // spring: // Occured by compress or stretch ( F spring)
 * // applied force: // Force that is applied to an object.( F app)
 * **//force caused by action at distance//:** Forces that occur without physical contacts and able to cause interaction of objects.
 * gravitional: weight, attraction from massive object. downward direction( F g )
 * other examples: electrical, magnetic
 * Unit is N(Newton)
 * 1N = 1kg * (m/s/s)
 * ** Most of the information is on notes and the explanation of each forces are only breif explanation
 * mass and weight are different.(mass represents the amount of an object how ever, weight represents gravitional forces on an object.)
 * Sliding vs Static friction
 * Sliding friction occurs on the surface of an object when an object slides.
 * Sliding Ffrict = μ • Fnorm
 * μ: coefficient of sliding friction between two surfaces
 * Static friction occurs on the surface of objects when they are at rest
 * Ffrict-static ≤ μfrict-static• Fnorm

//**Lab: Newton's 2nd law**// a) Net force & Acceleration of an object? b) Mass of object & its acceleration?
 * //__Free Body Diagram(FBD)__//**
 * Digrams that shows values and directions of all forces that exist in the object
 * Special type of Vector diagram
 * size of arrows represent magnitude of the force.
 * with magnitude on the diagram, you can get net force
 * Objective:** What is the relationship between
 * Hypothesis:** a) directly proportional. Because when force increases, acceleration also increases as much as force increased. b) Inversely proportional. Because when mass is greater, acceleration decrease.

// missing data table again. //
 * Data:**

In the experiment, we can determine that force and acceleration are directly related but mass and acceleration are inversely related. By using the data and relationships, we can figure out that acceleration is force/mass, which Newton's Second Law stated. Therefore in y = 0.5454x + 0.0313, the equation of relationship of force and acceleration, 0. 5454 is a mass of the system. Its actual mass was 0.530kg and made 3% of percent error. Additionally, in y = 0.2285x^-1.227, the equation of relationship between mass and acceleration, 0.2285 represents force becuase a = (F/m) and is equal to a = (0.2285 / x^1.227). Also the actual force was 0.294N and made 22% of percent error. The reason for errors is mostly because of friction.
 * Analysis**

[]
 * //__ Interesting applet about Acceleration of Gravity __//**
 * //__﻿__//**
 * //__﻿__//** Shows an effection of the acceleration of gravity

Lesson 3: Newton's Second Law of Motion
__//**Class Notes**//__
 * //__Newton’s Second Law__//**
 * ∑F = ma
 * a = ∑F / m
 * ∑F is net force, what is causing the mass to acceleration
 * m is system mass what is being accelerated
 * //__Friction__//**
 * Coefficient of friction
 * number that represents how t2o surfaces interact when you tried to slide
 * It has no unit and has really small number.
 * Symbol: µ = f/Nsurface

// **__Summary__** //
 * Newton's Second Law **
 * Deals with behavior of forces that are not balanced
 * Net force: acting upon an object and its mass
 * mass and acceleration is inversely related
 * acceleration is directly related to net force
 * ∑F = ma
 * a = ∑F / m
 * 1 Newton = 1kg * m/s2
 * Gravitational Force(weight): w = m * g
 * Frictional Force: f = µ / N
 * Ration of force and mass: F / m, sometimes called gravitational field strength


 * Double Trouble**
 * Also called "Two Body problems"
 * Physics problem that deals with the situation involving two objects
 * Usually requir system analysis to determine acceleration of the system
 * Individual object analysis: seperate 2 objects and analyse each.

The table shows that friction is exist on every surface and different type of surfaces have different value of coefficient of friction. // describe trends shown, as discussed in class //
 * //__Activity: Coefficient of Friction__//**
 * **// Location //** || **// Coefficient of Friction Trial 1 //** || **// Coefficient of Friction Trial2 //** || **// Coefficient of Friction Trial 3 //** || **// Average Coefficient of Friction //** ||
 * // Gym floor // || 0.28 || 0.279 || 0.3 || 0.286 ||
 * // Concrete // || 0.49 || 0.49 || 0.48 || 0.486 ||
 * // Floor tile // || 0.283 || 0.275 || 0.275 || 0.278 ||
 * // Tabletop // || 0.199 || 0.213 || 0.202 || 0.205 ||
 * // Carpet // || 0.463 || 0.417 || 0.39 || 0.42 ||
 * // paving stone // || 0.35 || 0.36 || 0.36 || 0.358 ||

// must show one sample calculation for µ //

When a third grader was asked to cite Newton's first law, she said, "Bodies in motion remain in motion, and bodies at rest stay in bed unless their mothers call them to get up." []
 * //__Interesting Joke about Newton's First Law__//**



Lesson 4: Newton's Third Law of Motion
__//**Class Notes**//__ Air Resistance Third Law Apparent weight
 * Occurs because of collection of air particles
 * Greater surface collects more air particles therefore more air resistance occurs
 * With faster speed, the ability to move air particles away is not enough to push all particles away
 * Every action has an equal but opposite reaction.
 * All forces come in pairs that equal in size, pointing in opposite directions, acting on 2 separatesystems.
 * It means if you touch something with force, the object will touch you with equal force.
 * If there is more than one supporting, the force of you is divided into those supports
 * Ex) bridge. When there is 2 supports, and 1000N person is standing on the middle of the bridge,each support would have 500N each.
 * Not actual change of weight but just feels like weight is changing
 * Ex) when elevator is starting to move, you feel more weight and when elevator stops, you feelless weight.


 * //__Summary__//**
 * Air resistance**
 * When velocity increases, more air resistance occurs
 * When an object has larger surface, more air resistance occurs
 * Due to collection of air particle while an object is moving.


 * Newton's Third Law**
 * For every action, opposite force exists
 * Forces comes in a pair

//Question:// How much mass sould you hang to make the cart move 0.8 m in 2.1 second?
 * //__MiniLab: Drop and pull__//**

//Calculation//

//Data// //Analysis// During the calculation, our group figured out that 19.2grams are needed to move cart 0.8m in 2.1 seconds. In the experiment, the average that took time to move with 19g was 2.12 seconds. We made 1.26% of percent error because we were not able to put 0.2 grams more and also the initial velocity when the cart started to move was not 0.
 * **Trial 1** || **Trial2** || **Trial3** || **Average** ||
 * 2.12s || 2.16s || 2.10s || 2.12s ||

=﻿Section 3: Vectors: Motion and Forces in Two Dimensions=

Lesson 1: Vectors - Fundamentals and Operations

 * //__Summary__//**
 * Vector**
 * decription includes both numerical value and direction
 * Ex) acceleration, displacement, velocity
 * represented by Vector diagram or motion diagram
 * Vectors have direction of East, North, West, South, Northeast, Northwest, Southeast, Southwest
 * Vectors increases toward counter clock wise direction
 * Scale and length of vector describes magnitude of vector
 * Vector Addition**
 * Vectors can be added to determine its resultant = Net Force
 * Uses Pythagorean Theorem to determine magnitude of net force
 * Uses SOH-CHA-TOA to determine the direction of net force
 * Resultant**
 * Vector sum of 2 or more vectors
 * Vector Component**
 * Simply if an object has net force directs to NorthWest, it is combination of the force component directs to North and the force component directs to West.
 * Vector Resolution**
 * The process to determine the magnitude of components of vectors
 * Parallelogram Method:
 * first put parallelogram around the vector(diagnol) and then each side of parallelogram is the vector's x and y components
 * addition of both component should direct the direction of the vector
 * [[image:parallelogram.jpg]]
 * Trigonometric Method:
 * always use cos for x- component and sin for y-component.
 * sin(angle) = y-component / given force
 * cos(angle) = x-component / given force
 * [[image:Trigonometric.jpg]]
 * Component Addition**
 * Use Pythagorian Teorem to determine the vector by addition of component
 * Component Addition**
 * Use Pythagorian Teorem to determine the vector by addition of component


 * //__Practice Problem__//**
 * ex1) plain
 * [[image:plain.jpg]]
 * ex2) boat
 * [[image:boat.jpg]]

problems in class

Lesson2: Projectile Motion
Projectile
 * //__Class Notes__//**
 * Horizontal and vertical are independent
 * Only force that affects the projectile object is gravity
 * Can determine the falling time with trigonometry
 * When 2 objects are in same distance from ground, projectile object and falling object hit the ground at the same time.


 * //__Summary__//**


 * 1) What did you read that you already understood well from our class discussion? Describe at least 2 items fully
 * The definition of projectile is an object that only have gravitional forces upon it. Every object are affected by gravitional force. In gravitional invironmant, every objects will fall to the ground. Without gravity, an object would not fall down and just keep moving unless you stop it with unbalanced forces. With the same gravitional forces, an objects from same displacement from ground will fall at same time. Even though, there is a horizontal velocity on an object, if object fall from same displacement from ground will fall at same time. For example, when you throw a ball from the top of the building, it will fall at same time with a ball,with same mass and weight, that was dropped on the same distance of the first ball.
 * When you use numerical values of projectile motion, to determine the value that you want to know with given values, you have to use trigonomety such as SOHCAHTOA, average velocity equation, which is v = d / t, and acceleration equation, a = Δv / t. As what we learned in earlier units,components, we can apply and combine the equations and ways to determine and solve the problem that involves the projectile motion. There are mostly three types of questions about the projectile motion with horizontal velocity. First, an object that was shotted from specific displacement usually gives the magnitude of distance or make you to determine with other given values. Also it always shot an object horizontaly. For second type of question, the projectile movement always start from ground such as shooting canon. For this type of questions, you just have to remember that the displacement of y axis will always be 0m and there is angles to use to determine asked value with sohcahtoa. Lastly, the third type of the question is combined question that involves both non-horizontally launching and start from scrtain displacement. In this type of questions, you have to use both ways of solving previous types and combined it to get the value that question is asking.
 * 1) What did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * There was no misconceptions or confusion
 * 1) What did you read that you still don’t understand? Please word these in the form of a question.
 * I understood concepts of the lesson.
 * 1) What did you read that was not gone over during class today?
 * All of the readings were review for the previous calss.


 * //__Lab: Projectile Motion__//**
 * //__Methods__//**
 * Part A**
 * Find vi using projectile motion
 * Find vi using photogate
 * vaverage = d(distance between gates(between laser points), 1.6 cm) / t(time in photogate)
 * compare the 2 vi values using %difference
 * Part B**
 * Calculate the place that the ball will fall and put the cub on the position
 * Check that your calculation is correct by the experiment

Calculated(without photogate) with Photogate
 * Data A**
 * Data B**
 * Calculation**
 * 1) Calculated value for time in Data table A without Photogate**
 * dy=vi * t+ (1/2) * a t^2
 * Plug in: .764 = 0 * t +( ½)(9.8)(t^2)
 * Answer: Square root of .764/.49 or .395 Seconds


 * 2) Calculation of initial velocity in Data table A without Photogate**
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">dx <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">= vit + (1/2)* at^2
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Plug in (For first result): .410 = vi*.395 +( ½)(0)(.395)^2
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Answer: vi = .410/.395 or 1.038 m/s
 * 3) Calculation of initial velocity in Data table A with Photogate**
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">dx <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">= vit + (1/2)* at^2
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Plug in: .016 = vi*.0151 + (½)(0)(.0151)^2
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">vi.016/.0151 or 1.060 m/s
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">4) Calculation to determine the distance where the ball will fall **
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">dx= vit + (½)at2
 * <span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Plug in: dx = .395*1.01m

In the experiment, we measured the height of the table that we used then used the calculation1 above to determine the time that takes to ball fall down. The calculation resulted 0.395 seconds. Then by using calculation 2 above to determine the initail velocity of the ball for each trial and averaged them. As a result, we got 1.010 m/s of average velocity. After these process of calculation, we used photo gate to determine the time that takes the ball to pass starts to pass the 2 laser points of each gate, which is nearly 1.6cm. By using calculation 3, we were able to determine the initial velocity that is calculated with photo gate for each trial and averaged them, 1.107 m/s. The percent difference was 9.15% and the reason of difference was that it was hard to measure the position of the ball when it hit the foil. For part B, by using calculated value and calculation 4, we determined where the ball will fall and placed cub. As a result, we calculated that 40cm from the ramp would be the place where the ball will tough the ground therefore we placed the cup and the challenge was successful.
 * Analysis**

[] In this applet, you can control the degree of gun and position of the gun to see what projectile motion is and helps to get concepts.
 * //__1Interesting Applet about Projectile Motion__//**

Lesson 3: Forces in Two Dimensions
**//__May the Force be Calculated__//** Most of problems about forces in two dimensions involve trigonometry. By determining components of the forces, you can decide the numerical value and direction of the force. All topics in this lesson was just review and practice for previous classes. For the questions that deals with forces of objects, you only have to simply determine the x, y components that we already learned, and use trigonometry(sohcahtoa) and Newton's second law, which represents acceleration is directly proportional to net force and inversely proportional to mass, to determine the direction of the unknown value for the force(pic 1). Sometimes, there is a problem that says about equilibirum. The definition of equilibrium is balanced forces. In equilibrium state, an object is at rest. For example, when 2 strings with same angle and same length with different direction holds an object steadily and the state is in equilibrium, each string has same forces,tension, and addition of the tensions will be same as weight force(see pic.2). Some questions do not include trigonometry skills(pic3); however then you only have to use newton's second law, which is simpler than other questions.
 * //__Summary__//**

Pic.1

Pic 2 Pic 3




 * //__LAB: Relationship of Acceleration and Angle of Incline__//**
 * Object:** What is the relationship between acceleration of an object and angle of the incline?
 * Hypothesis:** The acceleration of an object and angle of the incline are directly related, because when an angle of the incline increases, the slope of the incline will also increases and therefore the cart will get faster speed and acceleration.


 * Data**
 * Calculation**
 * 1.** to determine angle of incline. inverse sine( opposite / hypotenuse).
 * 2.** to determine acceleration. kinemetic equation. vi = 0; vf = 2(103 / average time); a = (vf - vi) / t

In the experiment, we measured the time of the cart untill it reaches to the end of the incline with stopwatch. We ignored the friction and the experiment represented the situation when the car goes down the hill. My hypothesis was correct that angles of inclines are directly proportional to acceleration. For example, when an angle was 1.43 degree, an acceleration of the cart was 0.157m/s/s and when the angle increased to 3.1 degree, the acceleration of the cart also increased to 0.422 m/s/s. Theoretically, acceleration should be same as g * sin(angle). Therefore in the graph, the equation should have the slope of 9.8 which is g. However, in our equation of the graph, the slope was 10.448. The possible source of error is only human error and because the measuring person is only react when the other person says "start". For the solution, one person can do both measuring and letting the cart go.
 * Analysis**

=﻿Section4: Circular Motion and Satellite Motion=

Lesson 3: Universal Gravitation
Newton’s Law of Universal Gravitation
 * //__Class Notes__//**
 * Mass of earth: 5.98 x 1024kg
 * Gravitational force is directly proportional to the product of the mass of object
 * Gravitational force is inversely proportional to the distance between the objects
 * Distance à the distance between center of an object to the center of the other object
 * G = universal gravitational constant = 6.67 x 10-11 Nm2/ kg2
 * Equation: G * m1 * m2 / d2
 * Earth’s radius: 6.38 x 106


 * Kepler’s Three law**


 * First law: Law of Ellipses
 * Planets move in elliptical orbits around sun with the sun at one focus.
 * Earth’s orbit has eccentricity of 0.09


 * Second law: Law of equal area
 * In any given time period, a planet carve out equal areas in its orbit around the sun.
 * Closer to sun, faster planet is moving
 * Third law: Law of Harmonies
 * Period= time it takes to move around the sun completely.
 * T(period)2 / R(distance from planet to sun)3 is constant for all planet

**//__They are attrating you!__//** The earth is rapidly spining along the sun, however, we can steadily stay on the earth due to gravitational forces. It is the force of attraction from massive object. Then shouldn't we attracted by some other massive object such as air plain? No, because the earth is way too massive than all the other massive object on the earth. This also proves the gravitational forces are directly related to the mass and the reason why the moon is moving around the earth. But the strange thing is why does moon moves around the earth even though there are more massive planets. This represents that the gravitational forces are square inversely related with distance between objects. This facts are stated in Newton's Law of Universla Gravitation. The equation to represent this relationship is f = (m 1 * m 2 ) / d 2 .However, this equation doesn't actually determine the force of gravitation. Later by discovering errors with actual value, Cavendish discovered G, Universal Gravitation Constant, is <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">6.67 x 10-11 Nm2/ kg2 ﻿ and stated the equation: Fgrav = <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">( G * m1 * m2) / d2 ﻿. With this equation, you can also determine the g value of variouse places such as top of the mountain.
 * //__Summary__//**

Lesson 1: Motion Characteristics for Circular Motion & Lesson2: Applications of Circular Motion __//**Class notes**//__ Circular motion
 * Two dimensional dynamic
 * Changing velocity could means either changing speed(size of the motion) or changing direction
 * Uniform Circular Motion(UCM): constant speed but changing direction
 * F = ma
 * No kinematics equation
 * ac = v2 / R(radius)
 * ac : centripetal(center seeking) acceleration
 * Force towards center and acceleration also towards center
 * Centripetal force is the force that makes object move circle
 * Radial axis: axis that is changing and points to the center
 * Positive to center of circle


 * //__Summary__//**

Questions
 * 1) What is the characteristics for circular motion?
 * 2) What is centripetal force?
 * 3) What is uniform circular motion?
 * 4) What is mathematical equation of acceleration of circular motion?
 * 5) How can we solve problems that involves circular motion?

Uniform circular motion
 * Constanct speed circular motion
 * Average speed = circumference / period = 2*<span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">π*radius(R) / period(T)
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Average speed and radius is directly proportional
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Direction is keep changing, tangent line represent it.
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Acceleration means changing velocity, therefore even though UCM has constant speed, it is accelerating because it keep changes direction of an object.
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Circular motion that has constant speed accelerate toward the center.
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">average acceleration = change in velocity / period

<span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">tangent direction acceleration of circular motion

<span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Centripetal force
 * Force that seeking center
 * For an object that is moving circular, there is net force toward center
 * Caused by inertia of an object
 * It only changes direction of an object
 * Without centripetal force, circular motion doesn't exist
 * IMPORTANT: there is no outer force but the reason you feel the pull in circular motion is due to inertia of an object
 * [[image:iner.jpg]]showing that centripetal force is caused by inertia

Mathematics of Circular motion <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Applications of Circular Motion <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">
 * average speed = distance / time = (2 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">π * R) / T(period)
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Acceleration = v 2 ﻿/ R
 * By combining these mathamtical equation with F = ma, which is formula that was stated in Newton's Second law, you will get a formula like picture below.
 * [[image:equation_fma.jpg]]
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">It uses equation of Newton's second law, and equations that we talked about in previous topic.
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">The concept is not really complex, it is easy enough if you know the equation and what should you put.
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; line-height: 115%;">Sample Question

> In problems that explains about roller coaster, there is three environment: loops, small deeps and hills, banked turns.
 * [[image:sample_ques1_diagram.jpg]]
 * These problems also have same way to solve. You just simply use equations that we talked about.
 * Only thing that might cause a confusion is, when you are in a situation of hill, you should think about the circle that has part of hills
 * [[image:orllercoaster.jpg]][[image:circle_hills.jpg]]
 * The problems that involves Athletics, you also have to use the equations u learned in previous and trigonometry with FBD.

Answers for questions
 * What is the characteristics for circular motion?
 * The characteristics for circular motion is that the direct of veloicity is represented by tangent of the circle and direction keep changes in circular motion.
 * The major cause is inertia of the object
 * What is centripetal force?
 * It is the force that seeks toward center
 * What is uniform circular motion?
 * UCM is circular motion with constant speed
 * What is mathematical equation of acceleration of circular motion?
 * acceleration of circular motion = (v^2) / R
 * How can we solve problems that involves circular motion?
 * We can solve the problems that invoves circular motion by combining trigonometry, newton's second law equation and acceleration equation of circular motion.

__//**LAB: Min/ Max Velocity**//__ Part A: Find max tension of string at static equilibrium Part B: Find minimum velocity at top of loop Part C: Find maximum velocity at bottom of loop

In the experiment, we could get times, tension, circumference and revolutions to calculate theorical velocity and experimental velocity. As you see in calculation and data table, the experimental velocity of maximum velocity at bottom is 15m/s and 2.213m/s for minimum velocity at top. Also we calculated that theoretical(actual) velocity of maximum at bottom is 21.46 m/s and 4.5 m/s for minimum velocity at top. My percent error of minimum velocity was 103.3% and 30% for maximum velocity. The reason that there was large error was that we are human and we are not technically able to make tension 0 or spin the object with 21.46m/s speed constantly.
 * DATA**
 * Calculation**
 * Analysis**

__//**LAB: Conical Pendulum**//__ During the lab, the period decreased when the radius of a conical increased. The data shows that the period is slightly decreasing when radius is increasing. We calculated the theoretical periods by using newton's second law equation, trigonometry and acceleration of constant circular motion equation. For each of the each radius, 10cm, 20cm, 40cm, 60cm, and 100cm, theoretical value we got were 3.259s, 3.27s, 3.24s, 3.218s, and 3.142s relatively. By comparing with actual average time, which represent experimental periods, there were 2%, 0.6%, 0.9%, 2%, 0.5% for each of the percent error. The possible source of error occurs when the person who let the ball go cannot match actual radius of the conical pendulum and also human's reaction time and observation skills do not allow exact theoretical value of the experiment.
 * Object:** what happens to the period when you increase the radius of a conical pendulum?
 * Hypothesis:** The period will decrease when the radius of a conical pendulum increase.
 * Data**
 * Calculation**
 * Analysis**


 * //__Interesting applet about Pendulum__//**

[] This appelt shows what pendulum is and the forces of the pendulum. It also gives

the breif explanation and formula. The best thing about this applet is that it compared the mass of pendulum as Tarzan to help understanding.