unit1_ChanL

toc __ **Lesson 1: Summary of Describing Motion with Words** __ **:**
 * Mechanics** is the study of objects in motion and focuses on explanations and descriptions of the motion of the objects.
 * Kinematics** is the method of describing motion using graphs, words diagrams,etc.
 * go for concepts not memorization.

__Lesson 2: Distance/ Displacement:__

 * name || definition || units || symbol || type of quantity ||
 * **Distance** || total movement**,** how far you have traveled in total. || meters || d || scalar ||
 * **Displacement** || net movement,tied to a direction**,** relative to origin. || meters || d || vector ||
 * **Speed** || rate of change of position, how fast the object is moving. || meters/second || v || scalar ||
 * **Velocity** || speed that includes direction,based on displacement || meters/second || v (->) || vector ||
 * **Acceleration** || how fast your speed or velocity changes. || meters/second^2 || a || vector ||
 * **Time** ||  || seconds || t ||   ||
 * Vector**- includes both quanity and direction
 * Scalar**- needs only quantity **NOT** direction


 * __4 Types of Motion__**
 * **at rest** -> mo motion at all
 * **constant** **velocity**-> no change in speed, (no acceleration) covering same distance in same time. Vav= d/t instantaneous(relative average)
 * **increasing** **velocity** -> starting slower and steadily getting larger/faster
 * **decreasing** **velocity** -> starting faster and steadily slowing.

__**Lab: Constant Speed**__ Objective: What does a graph of constant speed look like? Hypothesis: a graph of speed would be a constant line with a direct relationship between time and distance. Rational //e//
 * as time(x-axis) goes up the distance(y-axis) will also increase at a constant value.

Data & observations: TOP is shallow Bottom is steep = //FIXED*// =


 * Analysis: the graph makes a linear function that shows a direct relationship between time and distance. the slope shows that the constant speed results in a constant increase of distance over time. the R^2 value shows that the graph will have a 99.2 percent chance of being linear and my hypothesis was correct. the graph shows that the shallow slope balls moved at .797 meters per second and the steep slope balls traveled at .999 meters per second.**
 * //A few formatting issues: all sentences begin with capital letters! While you can be less formal on the wiki, you still need to use decent grammar and spelling, especially on the labs. Also, superscripts and subscripts can be made by clicking on the 4th button from the left on the edit toolbar and selecting "Vertical Spacing".// **

__HW:__
 * __Lesson1__: In physics, descriptions are very important as are the words used to make these descriptions. Vectors and scalars are two concepts that i had a firm understanding of both in class and during my readings. scalars involve only magnitude or number, and vectors are both magnitude and direction.**
 * Before reading i was unclear about my understanding of acceleration and velocity. from my readings i discovered that the definition of velocity was very simple; it is the speed with a specific direction or the displacement over time. acceleration is also a simple concept, measuring rate of change in velocity over a specific time. the meters traveled divided by time squared gives you acceleration. **
 * //this is incorrect!// **


 * "Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration."**
 * after reading everything over i have a good understanding over the concepts but i am still a little unsure of acceleration when given a positive or negative distinction. this we did not yet fully cover in class. //Are you okay with this now?// **


 * __Lesson 2:__ describing motion with position vs time graphs**
 * i understand all of the graph information and types of motion. i can interrupt //interpret?// the graph based on the slope and correlation of the line. the slope of the position time graph is velocity. most of what i read was straight forward but it took time to adjust to all of the directions that are connected with the values. //Here would be appropriate to state what these actually are. You are being a little vague in this summary, you need to incorporate specifics or else this will serve no purpose.// **


 * in class we did not go over the shapes of the graph and how the negative and positive velocities affect the graph.**
 * //Same comment, be specific about this: state the general shapes and how the negative and positive velocities affect the graph. Remember, this will serve as your notes in addition to helping you to review/study the material.// **


 * Joke:**
 * []**
 * //good one for first law, but not about graphing...// **

__Motion diagrams:**__ Convention - agreement amongst a group
 * qualitative representations
 * relative sizes and directions of velocity and acceleration
 * at rest (v=0, a=0),
 * constant --> --> --> (a=0) v+
 * increasing . -> ---> > (a--->) velocity and accel point in the same direction v+, a+
 * decreasing ---> -> ---> . (a<---) v+, a-

__**MD Practice**__:
 * 1) --->--->-->->---> (up) -A <---, v+
 * 2) ---> ---> ---> A=0 -v
 * 3) --> -> ---> -> +a > +v
 * 4) -> ---> --> ---> . down -v, +a

__**ticker tape diagram:**__
 * 1) constant .....x....x....x....x....x
 * 2) increasing .x.x..x...x....x......x..........x
 * 3) decreasing .x..........x........x.....x...x..x.

__**FreeFall Lab**__:
//very good results! Your measuring must have been extremely precise. I'm impressed! (Note: you don't need a legend if there is only one line on your graph.//
 * objective**: what is the acceleration due to gravity?
 * hypothesis**:the acceleration due to mass should be 9.81 m/s^2
 * procedure**: in this lab we gathered our materials, the electric reactive tape, the mass and the spark tape. we hung the spark timer from the ceiling and fed the spark tape through it. we then tied a mass to the tape, started the timer and dropped the mass from the ceiling with the tape feeding through. i then took the tape and counted and measured the displacement of the points on the tape. i graphed the data on excel.
 * Data Table**:
 * number of marks || seconds || displacement in cm || displacement in meters ||
 * 0 || 0 ||  || 0 ||
 * 1 || 0.016667 || 0.43 || 0.0043 ||
 * 2 || 0.033333 || 1.04 || 0.0104 ||
 * 3 || 0.05 || 2.06 || 0.0206 ||
 * 4 || 0.066667 || 3.28 || 0.0328 ||
 * 5 || 0.083333 || 4.65 || 0.0465 ||
 * 6 || 0.1 || 6.41 || 0.0641 ||
 * 7 || 0.116667 || 8.39 || 0.0839 ||
 * 8 || 0.133333 || 10.61 || 0.1061 ||
 * 9 || 0.15 || 13.23 || 0.1323 ||
 * 10 || 0.166667 || 16.01 || 0.1601 ||
 * 11 || 0.183333 || 18.98 || 0.1898 ||
 * 12 || 0.2 || 22.31 || 0.2231 ||
 * 13 || 0.216667 || 25.85 || 0.2585 ||
 * 14 || 0.233333 || 29.74 || 0.2974 ||
 * 15 || 0.25 || 33.88 || 0.3388 ||
 * 16 || 0.266667 || 38.34 || 0.3834 ||
 * 17 || 0.283333 || 42.99 || 0.4299 ||
 * 18 || 0.3 || 47.82 || 0.4782 ||
 * 19 || 0.316667 || 53.03 || 0.5303 ||
 * 20 || 0.333333 || 58.49 || 0.5849 ||
 * 21 || 0.35 || 64.15 || 0.6415 ||
 * 22 || 0.366667 || 70.28 || 0.7028 ||
 * 23 || 0.383333 || 76.45 || 0.7645 ||
 * 24 || 0.4 || 82.68 || 0.8268 ||
 * 25 || 0.416667 || 89.59 || 0.8959 ||
 * 26 || 0.433333 || 96.61 || 0.9661 ||
 * 27 || 0.45 || 103.81 || 1.0381 ||
 * 28 || 0.466667 || 111.52 || 1.1152 ||
 * 29 || 0.483333 ||  ||   ||
 * 30 || 0.5 ||  ||   ||
 * 31 || 0.516667 || 135.81 || 1.3581 ||
 * 32 || 0.533333 || 144.51 || 1.4451 ||
 * 33 || 0.55 || 153.48 || 1.5348 ||
 * 34 || 0.566667 || 162.48 || 1.6248 ||
 * 35 || 0.583333 || 172.09 || 1.7209 ||
 * 36 || 0.6 || 181.76 || 1.8176 ||
 * 36 || 0.6 || 181.76 || 1.8176 ||

Analysis: d=At^2+Bt, d=1/2a t^2 + ViT the formula for the graph uses A as one half of the acceleration and B as the initial velocity. the proper value for the expected acceleration is 9.81 m/s^2, in my experiment i got a velocity of 9.558. this makes my percent error 2.56%. my percent difference for the two class averages are 5.26% for the acceleration and 63% difference for the initial velocity. based on these results my initial velocity was too high and i began my graph marginally off. although my initial velocity was slightly off my acceleration was very close to the expected and my r^2 value equaled to 1 which is the perfect value. R^2 =1 showed that the graph will always form a polynomial graph. the difference in the accelerations was most likely due to the friction between the timer and the tape which slowed the mass.+

__**Lesson 2 a and b**__: It is important to be able to visualize your interpretations of physics. a common way to visualize physics is diagrams like the ticker time analysis. the ticker timer is a machine which places ticks in regular intervals on a piece of tape that is fed through it. the difference between the tick marks shows a difference of speed. the further apart the marks the faster the tape was moving, changing distance showes changing velocity and there fore changing acceleration. __**C**__: Vector diagrams use arrows to show speed, acceleration and direction. the size of the arrows demonstrate speed with the large arrows being the fastest. the direction of the arrows shows the direction of the velocity. changing arrow sizes show increasing or decreasing motion as same size lines show constant motion. __**Lesson 4 a**__: A Velocity-Time graph can also represent all types of motion. an object moving at a constant speed makes a horizontal line because the velocity remains constant as time passes. an object that is accelerating in a positive direction forms a linear positive line that starts around the origin and extends to the top right. the graph will be positive if it is above the x-axis and negative if it is below the x axis. an object can still have an increasing speed while being negative. __**B:**__ Acceleration forms the slope of the line in a v-t graph. if acceleration is 0 the slope is 0. if acceleration is 10 the slope is 10. the lines in the graph can have sudden changes in pattern to show acceleration after constant speed. __**C**__: acceleration is zero, then the velocity-time graph is a horizontal line - having a slope of zero. If the acceleration is positive, then the line is an upward sloping line - having a positive slope. If the acceleration is negative, then the velocity-time graph is a downward sloping line - having a negative slope. If the acceleration is great, then the line slopes up steeply - having a large slope. __**D**__: Slope is acceleration. rise over run to find slope. __**Lesson 5a**__: a free falling object is one that is affected only by the forces of gravity while falling. these objects do not encounter air resistance and accelerate at 9.8m/s/s. this related back to the ticker tape experiment, increases speed. __**B**__: g stands for the acceleration of gravity, 9.8 m/s/s. the affects of gravity are different on different planets and even different places on a planet. __**D**__: the formula for determining velocity of a free falling object is g*t=Vf. the distance can b found with the formula d= .5 (g)*t^2 __**E**__:a big misconception is that larger objects fall faster. this is not true unless there is an excessive amount of air Resistance which there can not be for something to be free falling. increasingforce tends to increase acceleration while increasing mass tends to decrease acceleration __**Lesson 6a**__:kinematic equations can be used to represent all types of motion. all of the equations include initial velocity and 3 of the 4 other terms, time, final velocity, distance and acceleration. __**B**__: there are multiple steps involved in answering a problem. each equation will leave out a variable and this will guide you to the equation. __**C**__: An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object.If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s.If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity ( vf ) after traveling to the peak would be assigned a value of 0 m/s.If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. __**D**__,E: //These summaries are very good: I think you truly filtered out the most important information. You may find it useful to include some of the diagrams of prictures from the site, or to sketch your own in Word or on paper and scan. Nice job! Do you need to finish these last 2 sections?//
 * __HW__:** Lessons 2,4,5,6
 * __E__**: the areas of a v-t graph can form 3 shapes, a rectangle, a triangle or a trapezoid. the area of the shape equals the displacement of the object. the area of a trapezoid is 1/2 b(h1+h2). not in class
 * __C__**:Graphs can represent free falling with a neg velocity. a position time graph will show a slow start to a steep dop from left to right. a v-t graph will be a linear negative line below the x axis.
 * 1) Construct an informative diagram of the physical situation.
 * 2) Identify and list the given information in variable form.
 * 3) Identify and list the unknown information in variable form.
 * 4) Identify and list the equation that will be used to determine unknown information from known information.
 * 5) Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information.
 * 6) Check your answer to insure that it is reasonable and mathematically correct.

http://www.livephysics.com/forums/viewtopic.php?t=480 //again, very cute, but not relevant to this topic!//

__**Newton's Laws**__:
__**1st law:**__ **inertia**: tendency to keep doing what you are already doing. at rest= static equilibrium, forces are balanced Galileo made many thought experiments one of which was that a ball dropped on a ramp will move until it reaches the same height as it was dropped at as long as there is no friction dynamic equilibrium, moving at constant speed in a straight line. .
 * an object in motion will stay in motion, at constant speed in a straight line
 * an object at rest will stay at rest
 * unless acted upon by some other force.


 * __Mechanical Forces__**:
 * push or pull
 * external to the system (object)
 * contact (1 exception)
 * cannon be transferred or carried

//oh! What happened to this table? It looks a bit confusing.//

> || Weight > m in kg > g=9.8 || > || Friction > || Normal = = > || Tension Unit for force is Newtons (N)
 * ** Type… ** || ** Symbol ** || ** Caused by…. ** || ** Always points…. ** ||
 * w, Fg || pull of earth on mass || points down, w=m*g
 * f, Ff || two surfaces rub together || parallel to surfaces, opposite the direction of motion, relative to the specific object. f= u*N(normal force) ||
 * N, Fn || "support force" whenever two surfaces touch. || perpendicular to the surface and through the system ||
 * T, FT || Only caused by rope or chain, only pulling force. || Always runs along the rope, away from the object. ||

__**Newton's second Law Lab**__:
Analysis: force is proportional to acceleration and acceleration is inversely proportional to mass. this means as the force increases the acceleration increases and ass the mass increases the acceleration decreases. acceleration = net force/mass. net force = mass*acceleration. y intercept = f/m but is held down by friction. in the equation for the first graph .5454 is the system mass and x is the acceleration. the system mass for the experiment was actually .530kg so the percent error is about 3%. For the second graph the equation for the line is a= .2285/x^1.227. in the equation x stands for the mass.,, the force for the weight hanging should be .03(9.8)=.294 N : so there is a 22% error to .2285. the major reason for experimental error in both graphs is friction and partially the effects of the pulley.
 * Objective**: what is the relationship between net force and acceleration of an object?
 * mass of an object and its acceleration.
 * Hypothesis**:increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. the graph for force and acceleration will be a linear direct relationship with acceleration increasing as force increases. the graph of mass vs acceleration will be a inverse relationship because as the mass increases the acceleration decreases.

//data and observations, as well as graphs, go before the analysis.//

//Units for force (on F vs. a graph) should be Newtons, not kg.//



__**FBD**__: Free body diagram

 * representation of all forces acting on the system
 * all forces are shown with linear arrows and are labeled with symbols.

__**Hw**__:Newtons law lesson 1a: Newtons first law is the law of inertia. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a separate force. All objects resist changes in their state of motion. B: Galileo made many thought experiments one of which was that a ball dropped on a ramp will move until it reaches the same height as it was dropped at as long as there is no friction. dynamic equilibrium, moving at constant speed in a straight line. newton studied this idea and came to the understanding that force is not what keeps objects forever in motion because it is the force of friction which brings the object to a stop. mass is related to inertia therefore the object with the least inertia also has the least mass. C: inertia can also be referred to as a tendency of an object to resist changes in velocity. D: balanced forces means that the forces an all directions equal each other out and result in no movement. if an object is under equal force from its weight and a surface(normal force) then it will not move unless there is a unbalanced force coming from one side that will move it. B: applied force is direct force on an object. gravitational force is g*m equal to weight. normal force is contact force which supports an object. friction is an opposite force that parallels an object in motion and slows it. air Resistance force is the force an object undergoes as it travel through air. tension force is force from a rope of chain and goes in the direction the rope is pulling. The spring force is the force exerted by a compressed or stretched spring upon any object that is attached to it. An object that compresses or stretches a spring is always acted upon by a force that restores the object to its rest or equilibrium position. weight of an object is the force of gravity acting upon that object. Mass is related to how much //stuff// is there and weight is related to the pull of the Earth. sliding friction results when an object slides across a surface. static friction results when the surfaces of two objects are at rest relative to one another and a force exists on one of the objects to set it into motion relative to the other object. C: Free-body diagrams are diagrams used to show the relative magnitude and direction of all force==\ting upon an object in a given situation. D: The existence of an unbalanced force for a given situation can be quickly realized by looking at the free-body diagram for that situation. net force is the sum of all the forces acting upon an object.
 * Lesson 2**a: a force is push or pull upon an object resulting from the object's //interaction// with another object. Whenever there is an //interaction// between two objects, there is a force upon each of the objects. When the //interaction// ceases, the two objects no longer experience the force. Forces __only__ exist as a result of an interaction. two types of forces, contact forces and forces from a distance. contact forces are from a direct interaction. forces from a distance are forces that are made without physical contact (gravitational pull) force is measured in Newtons (N). 1N = 1kg*m/s^2 . force is a vector unit and must be attached to a direction. it is common to represent forces using diagrams in which a force is represented by an arrow. size of arrow relates to magnitude of force. forces can balance each other.

[] //Do you understand what is funny about this?//

__**Net force**__: net force = system mass * acceleration. acceleration = net force (mass * g) / system mass (m1+m2). if mass=1000kg and T= 18000n than a = (T-W)/m. //this isn't the definition of net force, though.//

LAB: average mu for coefficient of friction. table: .205 floor tile: .278 gym floor: .286 pavers: .358 Carpet: .42 concrete: .486 //show your calculations!//

For this lab we dragged plastic carts with weights inside of them to measure the resistance caused by friction. we used an instrument to measure the friction force using this number we divided by the mass. //And was about the results?//

Hw: __**Lesson 3 Newtons second law of physics**__ a: the second law pertains to objects whose forces are not equal.this law states that acceleration is dependent of net force and mass.The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s. B&C&D: most of b is repetitive and i have already read n summarized. 3 equations you need to know: net force = m*a, gravitational force = m*a, and frictional force = u* normal force. the rest is problem solving.. E: things in free fall drop at 9.8m/s/s things fall at the same speed because larger objects have more inertia. net force/ mass= gravitational force. more problems for practice F: two step equations use two missing factors. the system mass is all the mass involved. the acceleration of the system is the same as that of the individual objects





__**Newton's third law**__:
every action has an equal but opposite reaction. all forces com in pairs, that equal in size, pointing in opp directions, acting on 2 separate systems. apparent weight is what one's weight seems to be while they are accelerating up or down.'

LAB:drop n pull challenge problem:
How much mass should you hang to make the cart move .8 meters in 1.3seconds. Delta distance = Vi*t+1/2a*t^2 .8=0+1/2a(1.3^2) .8= .845a a=.9467m/s/s m1*9.8/m1+.5=.9467 m1= .053gk after testing the experiment i got the times, 1.3, 1.28, 1.27 the average is 1.29. 1.3-1.29/1.3)*100= .76% error the precent error was most likely human error because the cart is not held at a initial velocity of 0. the cart cannot be held at the laser zone without starting the timer.

HW: vector
Third law A & B: a push or pull force on an object is the result of another object. contact interactions or interactions from a distance. action and reaction forces. forces are paired acting in opposite directions with equal strength. helps fish swim by letting them push the water and in doing do propel themselves. forces that push a ball left to a bat/ there are also forces that push right from the bat. Vectors a: vectors show direction and magnitude using degrees and compass directions. degree usually read counter-clockwise. length of arrow shows magnitude. B vector addition: two vectors can be added together to fond the resultant or the net force. the Pythagorean theorem cam also be used to find resultants for more complicated equations. v1^2 +v2^2 = R^2. trig is also used to find direction in degrees. C&D: misplacement of a+b+c=r. vectors have different directions that give them values and let them work with or against each other. each part of a 2 dimensional vector is called a component. - Resultant- the total displacement of two or more vectors - can be written as A+B+C=R but it means the addition of the total displacement, not the distance of each - you can find: resultant displacement resultant force resultant velocity - vector resolution- magnitude of a vector - parallelogram method- draw accurately to scale and measure
 * Resultants**
 * Vector Resolution**

- trigonometric method- uses trig to find other sides and angles if one side and one angle is known - Pythagorean approach is used for adding vectors at right angles: basically draw a line from the start point to the finish point - the resultant for this diagram is equivalent to: -but if at some point the vector backtracks then you have to subtract that from the triangle Joke for vectors, Q: What do you get if you cross an elephant with a mountain climber. A: You can't do that. A mountain climber is a scalar. Q: Why did the chicken cross the road? A: To make a normal vector. []
 * Component Addition**

Class work: diagonal vectors
vfx=vix+axt =9.4+0.09 =9.4m/s

vfy=vif+ayt =3.4+(-9.8)(.9) =-5.4m/s

10.8m/s @ 30 degrees below 0

=9.4m/s || 10sin20 =3.4m/s ||
 * || x || y ||
 * vi || 10cos20
 * a || 0 || -9.8m/s/s ||
 * t || .9s || .9s ||
 * vf || 9.4m/s || 5.4m/s ||

Lab: Ball and ramp lab \
Hypothesis: If there is no vertical initial velocity than the horizontal distance can be calculated using the formula for kinematics on specific axis.

Analysis: this lab proved that there was no horizontal motion initially in the lab. using the formula assuming that the initial velocity on the y is 0 i was able to predict the horizontal distance. my initial velocity on the x had a 10 percent difference from the measurement made by the photo gate timer. the photo gate reading was more accurate because the method my group used to find initial velocity was very inaccurate. there was a lot of room for human error and many of the measurements could have been off.

HW: Projectile motion
a:i understood the fact that A projectile is any object that once //projected// or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity. one thing i did not completely understand but now do is that a projectile is acted upon only by gravity and no other force. often when one thinks of a projectile they think of a moving rocket being propelled by another force. now i understand that motion does not need a force to be produced; only acceleration does. i also completely understand the fact that if there was no gravity than a forced object like a cannon would fire in a straight direction a go on forever. gravity only acts vertically, there was nothing i do not understand but we did not completely cover the consents that i have mentioned in my summary. B & C: i completely understand that the projectile undergoes horizontal and vertical motion and they are both independent of each other. the horizontal motion is constant and has a constant velocity. the vertical motion is accelerating at an increasing motion downward, with the acceleration of gravity (9.8). one thing that previously confused me was that the presence of gravity does not affect motion along the x axis. this means that the projectile has a constant velocity in one direction but is accelerating in another. to clarify:The projectile still moves the same horizontal distance in each second of travel as it did when the //gravity switch// was turned off. The force of gravity is a vertical force and does not affect horizontal motion; perpendicular components of motion are independent of each other. projectiles travel with a parabolic trajectory due to the fact that the downward force of gravity accelerates them downward from their otherwise straight-line, gravity-free trajectory. This downward force and acceleration results in a downward displacement from the position that the object would be if there were no gravity. vectors can also be given values to help the reader. The important concept depicted in the below vector diagram is that the horizontal velocity remains constant during the course of the trajectory and the vertical velocity changes by 9.8 m/s every second. These same two concepts could be depicted by a table illustrating how the x- and y-component of the velocity vary with time.

D: The horizontal displacement of a projectile is dependent upon the horizontal component of the initial velocity. As discussed in the previous part of this lesson, the horizontal displacement of a projectile can be determined using the equation x = vix • t A non-horizontally launched projectile with an initial vertical velocity of 39.2 m/s will reach its peak in 4 seconds. The process of rising to the peak is a vertical motion and is again dependent upon vertical motion parameters (the initial vertical velocity and the vertical acceleration). The height of the projectile at this peak position can be determined using the equation y = viy • t + 0.5 • g • t2 i understand the equations an how to find all variables in this section E &F: this sections is all problems and how to solve them which i completely understand. you must find and list all given variables for both x and y and then use kinematics equations to find the missing values.

LAB: cart and ramp
concept: what is the relationship between acceleration of an object and angle of incline. Hypothesis: If the angle of incline is larger than the acceleration of the cart will also be greater. this is most likely because of the force of weight acting on the object bring it downward. Materials: track, cart, meter stick, stopwatch. Analysis: in theory, based on the equation net force= max, gsin=a. this means that the relationship between the angle and acceleration is based on gravity. in the graph the slope of the line is equal to g (9.8). the greater the incline the more acceleration. my group results had a very high percent error of almost 72.5%. this is most likely due to human error in using the stopwatch and measuring the distances. the group that had the most accurate results had one member release the cart and start the timer at the same time, minimizing the timing errors. if the lab were redone i would use photo gate timers and try to make the measurements as precise as possible. the angle and the acceleration have a direct variation relationship.
 * length incline m || hight m || angle || time down incline 1 s || time 2 s || time 3 s || t average || distance (m) || a (m/s/s) || Sin θ ||
 * 1.22 || 0.043 || 2.01986 || 2.15 || 2.25 || 2.18 || 2.193333 || 1.03 || 0.428211121 || 0.035246 ||
 * 1.22 || 0.081 || 3.806864 || 1.53 || 1.63 || 1.56 || 1.573333 || 1.03 || 0.832196208 || 0.066393 ||
 * 1.22 || 0.069 || 3.242229 || 1.75 || 1.88 || 1.88 || 1.836667 || 1.03 || 0.610669925 || 0.056557 ||
 * 1.22 || 0.196 || 9.24496 || 0.9 || 1.03 || 0.97 || 0.966667 || 1.03 || 2.20451843 || 0.160656 ||
 * 1.22 || 0.282 || 13.36464 || 0.75 || 0.72 || 0.75 || 0.74 || 1.03 || 3.761869978 || 0.231148 ||
 * ||  ||   ||   ||   ||   ||   ||   || d=vit+.5at^2 ||   ||
 * ||  ||   ||   ||   ||   ||   ||   || 1.03=0*.74+.5a(.74^2) ||   ||
 * ||  ||   ||   ||   ||   ||   ||   || a=(1.03/.74^2)*2 ||   ||

HW:__**A Force Addition**__:
using a force board one could test a method of vector addition and add up the three forces pulling against the center. If a head to tale diagram is drawn then one would see that the three vectors make a triangle, ending at the starting point. This means there is no net force. However whenever there is movement there will be net force.

B **__Resolution of forces__**: Forces that are in a direction not on either the x or y axis can be broken down into two vectors, one along the x and the other along the y. Given the force value of the diagonal, and a degree value one can find the two components of the system. This involves trig functions and SOH CAH TOA. These equations are very important for sailing and flying when dealing with wind and currents. a boat would be off target if it expected to go in a straight line and must take into account the forced applied by the wind and water. C: __**Equilibrium**__: an object is said to be in equilibrium when all the forces that are acting on it are balanced. This means that there is 0 movement. Equilibrium can be reached using multiple methods; a painting held up by two diagonal strings matches the force of weight with their vertical components. this means that its forces going up and down are balanced. usually these strings will be symmetrical to each other and balance out the y component. Weight = 50N D **__Net Forces with diagonal force__**s: Net force equations can be solved by splitting all diagonal forces into their x and y components and inserting those values into their proper equations. Once in their proper equation the steps to completing the problems are the same. this is learned through practice using net force=ma and trig functions to determine the components. E: __**Off centered planes**__: in an equation where the plane is off centered one should simply tilt their x and y axis and treat all horizontal and vertical forces as if they were the diagonals. this will eliminate a majority of the problems and leave only one or two diagonals to deal with. the rest of the equations are solved just as the rest are. F: __**Two System diagrams**__: When there are two object connected by a pulley the system becomes more dificult to calculate.Problems involving two objects, connecting strings and pulleys are characterized by objects that are moving (or even accelerating) in different directions. They move or accelerate at the same rate but in different directions. As such, it becomes important in approaching such problems to select a different reference frame and axes system for each object. Universal Gravitation: a __**Gravity**__: The force that pull things towards earth's surface. Makes what goes up come down. acceleration of gravity is 9.8m/s^2. B: __**Gravitation**__: everything has its own gravitational pull. This is why planets orbit the sun, it has to do with the distance from the sun and the combined masses. Fgav ~ 1/d^2 (1= system mass product) C__**:Newtons Law**__: newton realized that the mass of the earth had a lot to do with it gravitation. distance is measured from the center of one planet to the center of the other object. Since gravitational force is inversely proportional to the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases D/E: __**Big G little g**__: Big G is a constant for gravity that is used to find Fgrav. it is the value for the pull of one object on another based on gravitation. G=6.75 x 10-11 N m2/kg2 d Little g is the acceleration of gravity that represents 9.8m/s/s. gravity has different values at different locations around the earth and above its surface.
 * 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
 * Q:** What is the physicist's definition of a vector space?
 * A:** A set //V// such that for any //x// in //V//, //x// has a little arrow drawn over it.

LAb: min/max velocity
Analysis: Based on the experiment and my calculations, the experimental and theoretical data was very different. for each part of the lab there was very high percent error of around 50%. This is most likely because of human errors in timing the revolutions and spinning the mass at a constant speed. Also the varying string lengths and different string resistances caused a large variation of data.
 * Mass (Kg) || Radius(m) || Revolutions || Distance (m) || Max Load(kg) || Time of period (s) || Minimum Velocity (m/s) || Average Velocity ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 6.34 || 3.667 || 3.608 ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 6.41 || 3.627 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 6.5 || 3.577 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 6.38 || 3.644 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 6.5 || 3.577 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 6.54 || 3.555 ||  ||
 * Mass (kg) || Radius(m) || Revolutions || Distance (m) || Max Load (kg) || Time of preiod (s) || Max Velocity (m/s) || Average Velocity ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.77 || 6.167 || 6.237 ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.72 || 6.249 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.64 || 6.387 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.81 || 6.102 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.7 || 6.283 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.73 || 6.233 ||  ||
 * 0.02 || 0.37 || 10 || 2.325 || 0.950 || 3.73 || 6.233 ||  ||

Lab: conical pendulum:
Objective: what happens to the period when you increase the radius of a conical pendulum? Hypothesis: if the pendulum is has a larger circumference than the speed will increase and the period will remain the same.

data: average period 10cm radius: 3.315s/ Actual Period: 3.259/ 2% error 20cm radius: 3.291s/ Actual Period: 3.27 / .6% error 40cm radius: 3.277s/ Actual Period: 3.24/ .9% error 60cm radius: 3.287s/ Actual Period: 3.218/ 2% error 100cm radius: 3.16s/ Actual Period: 3.142/ .5% error Length of string: 2.64m

Analysis: this lab tested the period and velocity of a ball moving in a pendulum. As the radius of the pendulum got larger, the speed also increased therefore decreasing the period. This experiments proves my hypothesis wrong because the radius and period have an inverse relationship. after completing the experiment the class noticed that there was only a small percent error of about 2% or less for each radius. The very slight margin of error was most likely due to timing errors and possible elliptical paths for the pendulum. Also the angle of the viewer could change the time they measured because they would not be able to see directly when and where the pendulum passed.

HW: __**Circular motion a n b**__:
What is uniform circular motion? the motion of an object in a circle with a constant or uniform speed. How do you find the average speed of an object in circular motion? to do this one must find the circumference and divide it by the time it takes the object to move around the circumference. an object with the largest radius must move at the fastest speed to keep up with objects of circular motion of a smaller radius. What direction is the velocity vector moving? As the object //rounds// the circle, the direction of the velocity vector is different than it was the instant before. the velocity vector is tangential to the circle. Is there acceleration in uniform circular motion? why? Yes there is because acceleration is linked to a change in velocity, which is a vector. Because the velocity changes direction as the object moves around the circle, there is acceleration. In what direction is the acceleration pointing? The acceleration points towards the midpoint of the circle. The acceleration of the object is dependent upon this velocity change and is in the same direction as this velocity change. The acceleration of the object is in the same direction as the velocity change vector __**Centripetal force D,C,E**__: What is centripetal force? when the net force points to the circles center point. Moving objects will tend to naturally travel in straight lines; an unbalanced force is only required to cause it to turn. Thus, the presence of an unbalanced force is required for objects to move in circles. What causes the need for unbalanced forces? the inertia of an object requires that an unbalanced force act upon an object or else it will continue in a straight line. Why is it that one will hit a car when it turns. this is because the person is still moving forward in a straight line and the car has not turned away from them. this gives the sensation of being pushed outward. What is the forbidden f word? It is centrifugal which means away from the center. what quantities must one know to do i circular motion problem? force, speed and acceleration. It the acceleration is directed inward which way is positive? the inward direction is considered positive.

__**Lesson 2ABC**__: What does newtons second law state? Acceleration is directly proportional to net force and inversely related to mass. What types of forces act on a car in circular motion? weight, friction and normal forces are all involved in this system. How does a rollar coaster manage the forces acting upon it? A roller coaster uses normal forces to its advantage and the normal forces push against the weight and outward force. the makers must limit the speed at certain points but mast also maintain a steady and fast speed to keep motion. whenever the ride curves the force points back to the center and keeps the ride in motion. in athletics an athlete can get more traction a speed by tilting and dis positioning the weight and normal forces. this provides more grip for faster turns and more control.- it balances the downward force of gravity and meets the centripetal force requirement for an object in uniform circular motion. The upward component of the contact force is sufficient to balance the downward force of gravity and the horizontal component of the contact force pushes the person towards the center of the circle.