Unit1_KoscielnyD

toc = Lesson 1 = = Lesson 2 =

Vocabulary
in to account || d || m || Vector || rather than your distance || v || m/s || Vector || units-
 * ||  || symbol || units || Type of Quantity ||
 * distance || how far you have traveled in total || d || m || Scalar ||
 * displacement || the change in position from some origin- takes direction
 * speed || rate of change of position- how fast you are moving || v || m/s || Scalar ||
 * velocity || speed including direction- based on your displacement
 * velocity || speed including direction- based on your displacement
 * acceleration || how fast your speed or velocity changes || a || m/s^2 || Vector ||
 * acceleration || how fast your speed or velocity changes || a || m/s^2 || Vector ||

Vector- Quantity that includes quantity and direction Scalar- a quantity that requires only quantity

4 Types of Motion
we take average rather than instantaneous
 * at rest || no motion ||  ||
 * constant velocity || no change in speed, same distance in same time || vav= D d/ D t ||
 * increasing velocity || starting slower and **steadily** speeding up ||  ||
 * decreasing velocity || starting faster and **steadily** slowing down ||  ||
 * decreasing velocity || starting faster and **steadily** slowing down ||  ||

Lab: Constant Speed
Objective: What does a graph of constant speed look like? (position-time graph) Hypothesis: a positive diagonal line Rationale: if it is constant it should be straight and position should increase with time at a constant rate Data & Observations:

//insert pics of data table and graphs. I only open this document if I need to check your formulas or help you with something.// Analysis: //watch spelling!//

The graph is as I predicted- it is linear and looks as I thought it would. Slope is equal to speed, so the slopes of the linear best fit lines are the speeds the balls were traveling at in m/s. The ball coming from the shallow incline was traveling at 0.7976 m/s while the ball coming from the steeper incline was traveling at 0.9992 m/s. r^2 is the accuracy of the best fit line- the closer to one the more accurate the data. If r2 is less than .95 then the data is probably inaccurate due to typo. If the data does not have typos but is less than .65, then it is probably needs a different type of best fit line. My r^2s were 0.9959 and 0.9853 so I know my data was very accurate. //The r 2 values are about precision, not accuracy.//

Homework
** Introduction to the Language of Kinematics ** Mechanics - the study of the motion of objects - focus on meaning of language, principles, laws used to explain motion of objects - try to understand, not memorize, and try to relate it to the physical world
 * Reading Summary: **

Kinematics - the science of the motion of objects - uses words, diagrams, numbers, graphs, and equations. - a branch of mechanics - describe (+ explain) the motion of objects - focus on the //language// of kinematics

- Scalars- quantities fully described by a magnitude/numerical value alone - Vectors- quantities fully described by a magnitude/numerical value AND a direction
 * Scalars and Vectors**

- Distance- Scalar- how much ground an object has covered - Displacement- how far out of place an object is- what is it's overall change in posotion EX. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.
 * Distance and Displacement**

distance of 12 meters displacement of 0 meters

- Speed- scalar- how fast an object is moving- does not keep track of direction - Velocity- vector- the rate at which an object changes positions- direction aware
 * Speed and Velocity**



- Instantaneous Speed- the speed at any given instance in time - Average speed- the average of all instantaneous speeds: distance/time

Ex. The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion

asted for 24 seconds. distance of 12 meters in 24 seconds: average speed of 0.50 m/s displacement is 0 meters: average velocity of 0 m/s.

Acceleration- vector- the rate at which an object changes its velocity Constant Acceleration- object changes its velocity by the same amount each second (BUT an object with a constant velocity is not accelerating) Calculating the Average Acceleration:
 * Acceleration**



acceleration units (velocity units divided by time units)include: m/s/s i/hr/s km/hr/s m/s2 //There is a way to do super and sub scripts: Click on Style Text (4th button from the left) and choose "Vertical position".//

The Direction of the Acceleration Vector direction of the acceleration vector depends on two things: - whether the object is speeding up or slowing down - whether the object is moving in the + or - direction - RULE OF THUMB: If an object is slowing down, then its acceleration is in the opposite direction of its motion I.E. - When an object is moving in the //positive// direction, and is speeding up, the acceleration is in the same direction as the velocity- posotive accelaration - When the object is moving in the //negative// direction, and is slowing down; the acceleration is in the opposite direction as the velocity- positive acceleration - When the object is moving in the //positive// direction, and is slowing down, the acceleration is in the opposite direction as the velocity- negative acceleration - When the object is moving in the //negative// direction, and is speeding up, the acceleration is in the same direction as the velocity- negative acceleration - in physics, "+" often means to the right or up and "-" often means to the left or down

- constant positive velocity results in a line of constant and positive slope when plotted as a position-time graph EX.
 * The Meaning of Shape for a p-t Graph**





- changing positive velocity however would not result in a linear graph EX.






 * The Importance of Slope**

- the slope of the line on a position-time graph gives information about the velocity of the object because w hatever characteristics the velocity has, the slope will exhibit the same
EX. Constant Velocity ||~ Fast, Rightward(+) Constant Velocity ||
 * ~ Slow, Rightward(+)
 * = [[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a7.gif width="143" height="107"]] ||= [[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a11.gif width="142" height="106"]] ||

Constant Velocity ||~ Fast, Leftward(-) Constant Velocity ||
 * ~ Slow, Leftward(-)
 * = [[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a8.gif width="140" height="106"]] ||= [[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a14.gif width="142" height="105"]] ||

Slow to Fast ||~ Leftward (-) Velocity Fast to Slow ||
 * ~ Negative (-) Velocity
 * = [[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a16.gif width="133" height="118"]] ||= [[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a17.GIF width="139" height="118"]] ||


 * The Meaning on Slope for a p-t Graph**

- slope of the line on the graph equals the velocity of the car - during the stop, the slope of the line is 0 m/s - the same as the velocity during this time interval


 * Determining the Slope on a p-t Graph**

Steps: - Pick two points on the line and determine their coordinates - Determine the difference in y-coordinates of these two points (rise) - Determine the difference in x-coordinates for these two points (run) - Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).


 * Cartoon: Troll Science- Perpetual Motion: **

= Lesson 3 =

Motion Diagrams
- qualitative representation - relative sizes + directions of velocity + accleration --->... at rest- v=0 a=0 constant- v=-> -> ->(+v) or, if faster, --> --> -->(+v), if in the other direction, <-- <-- <--(-v) -the size and directions of the arrows (vectors) matters a=0 increasing- v= -> --> --->(-v) a= --->(-v) - when you're increasing speed a goes in the same direction as v decreasing- v= ---> --> ->(+v) a=<-(-v) - when you're decreasing speed, velocity and speed point in opposite directions

+
 * up and to the right

-
 * down and to the left

EX. 1. a ball being thrown up in to the air until it reaches its highest point 2. a car driving down a hill at constant speed 3. a skier going down hill 4. a person landing on a trampoline, sinking until stopping

Free Fall Lab
Objective: What is acceleration due to gravity? Hypothesis: 9.80665 m/s2 Procedure: I threaded a piece of spark tape through a spark timer and attached a weight to the bottom with tape. I let it drop and then used a meter stick to measure the distances between the marks the timer left and the first mark it left. Data Table //make sure that there are units in your headings! And watch sig figs, limit to a specific number of them and be consistent throughout your lab.// Graph Analysis The equation for this graph is d=At^2+Bt. In our class, we had an average of 4.54 for our A; were there no experimental error and no friction caused by the spark tape going through the spark timer, this number would be 4.903; this is because A= 1/2 the value of gravitational acceleration. My A value was 4.636, giving me a 2% difference from the average; I was a little closer to the actual value than most of the class. . //What about the "B" coefficient? What did it mean?//
 * dot # || times || displacement ||
 * 1 || 0.016667 || 0 ||
 * 2 || 0.033333 || 0.0055 ||
 * 3 || 0.05 || 0.0135 ||
 * 4 || 0.066667 || 0.022 ||
 * 5 || 0.083333 || 0.0345 ||
 * 6 || 0.1 || 0.0455 ||
 * 7 || 0.116667 || 0.066 ||
 * 8 || 0.133333 || 0.084 ||
 * 9 || 0.15 || 0.103 ||
 * 10 || 0.166667 || 0.123 ||
 * 11 || 0.183333 ||  ||
 * 12 || 0.2 ||  ||
 * 13 || 0.216667 || 0.207 ||
 * 14 || 0.233333 || 0.2435 ||
 * 15 || 0.25 || 0.279 ||
 * 16 || 0.266667 || 0.32 ||
 * 17 || 0.283333 || 0.3645 ||
 * 18 || 0.3 || 0.4085 ||
 * 19 || 0.316667 || 0.457 ||
 * 20 || 0.333333 || 0.506 ||
 * 21 || 0.35 || 0.557 ||
 * 22 || 0.366667 || 0.6115 ||
 * 23 || 0.383333 || 0.6685 ||
 * 24 || 0.4 ||  ||
 * 25 || 0.416667 ||  ||
 * 26 || 0.433333 || 0.851 ||
 * 27 || 0.45 || 0.919 ||
 * 28 || 0.466667 ||  ||
 * 29 || 0.483333 || 1.063 ||
 * 30 || 0.5 || 1.1395 ||
 * 31 || 0.516667 || 1.2195 ||
 * 32 || 0.533333 ||  ||
 * 33 || 0.55 || 1.386 ||
 * 34 || 0.566667 ||  ||
 * 35 || 0.583333 || 1.564 ||
 * 36 || 0.6 || 1.656 ||
 * 37 || 0.616667 || 1.7515 ||
 * 38 || 0.633333 || 1.8485 ||

Homework
**Reading Summary:** - some tape is attached to an object (that moves) is threaded through the ticker - the ticker makes ticks at regular time intervals, thus showing how quickly the object moved at different points - if the dots are farther apart the object was moving more quickly, if they are closer to together they are moving less quickly I.E.
 * Ticker Tape Diagrams**

- diagrams that show the direction something is headed in and whether it is at a constant velocity, speeding up, or slowing down I.E.
 * Vector Diagrams**

--- - v-t Graph- velocity versus time graph - used to describe motion - constant velocity+: horizontal line with a y value equal to the velocity - increasing velocity+: diagonal line I.E. Zero Acceleration ||~ Positive Velocity Positive Acceleration || Slope= acceleration - when there is a negative (leftward or downwards) velocity, the location of the graph will reflect that I.E.
 * The Meaning of Shape for a v-t Graph**
 * ~ Positive Velocity
 * = [[image:http://www.physicsclassroom.com/Class/1DKin/U1L4a4.gif width="121" height="114"]] ||= [[image:http://www.physicsclassroom.com/Class/1DKin/U1L4a5.gif width="120" height="114"]] ||

- if a line crosses over the x-axis, the object has changed directions - speeding up means the velocity is increasing: thus if the Y coordinate is getting greater (or more negative if it is negative) then the object is speeding up, and vice versa I.E.



- even in more complex graphs, the slop always equals the acceleration EX
 * The Meaning of Slope for a v-t Graph**

From 0 s to 4 s: slope = 0 m/s/s From 4 s to 8 s: slope = 2 m/s/s

Examples of how to interpret a v-t graph
 * Relating the Shape to the Motion**



     - same as determining any other slope:
 * Determining Slope on a v-t Graph**

Steps: - Pick two points on the line and determine their coordinates - Determine the difference in y-coordinates of these two points (rise) - Determine the difference in x-coordinates for these two points (run) - Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

- to calculate the area of these graphs first break them in to shapes I.E.
 * Determining Area on a v-t Graph**
 * -** the area between the line and the axes represents the displacement
 * [[image:http://www.physicsclassroom.com/Class/1DKin/U1L4e1.gif width="166" height="129"]] || [[image:http://www.physicsclassroom.com/Class/1DKin/U1L4e7.gif width="163" height="126"]] || [[image:http://www.physicsclassroom.com/Class/1DKin/U1L4e8.gif width="164" height="127"]] ||

 - Then plug the values in to the equations for each shape Area Equations: - Rectangle: b*h - Triangle: .5b*h - Tapezoid: .5b*(h1+h2 - There are two methods of calculating the trapezoid- you can use the equation or break it in to a triangle and a rectangle --- - A free falling object is one that is being acted upon only by gravity (no air resistence - on earth, free falling objects have a downward acceleration rate of 9.8 m/s/s Acceleration = 9.8 m/s/s- symbol: g p-t graph will look like: v-t graph will look like - these graphs are negative because the acceleration is downwards
 * Introduction to Free Fall**
 * Acceleration of Gravity**
 * Representing Free Fall by Graphs**

- velocity of a free-falling object is changing by 9.8 m/s every second: velocity is dependent on how long it's been falling - to determine the velocity after t seconds use:
 * How Fast and How Far**

vf = g * t
- the distance of the object is dependent upon the time of fall - to determine the distance after t seconds use:

d = 0.5 * g * t2


- ALL objects fall at the same rate of acceleration i.e.-->
 * The Big Misconception**

- quantities associated with motion: displacement (also distance) velocity (final and initial) (also speed) time - equations that describe and represent the motion of objects:
 * Kinematic Equations**



process for problem solving: 1. make a diagram of the situation 2. find the variables given, the variable you're looking for, and the variable you won't use 3. find the equation based on the given information, the information you want to find, and the information that you won't use 4. subsitute given values for variables + solve algebraically 5. check answer- is it reasonable? is it mathematically correct?
 * Kinematic Equations and Problem Solving**

- A free falling object has an acceleration of -9.8 m/s/s: this is not always stated but it is always true - A dropped (not thrown) object has an initial velocity of 0 m/s - If an object is thrown up perfectly vertically, it will slow down as it goes up, at the peek of it's trajectory it will have a velocity of 0 m/s: the final velocity after traveling to its peek is 0 m/s - If an object is thrown up perfectly vertically,the velocity is equal to the magnitude and opposite in sign to the velocity when it comes back down
 * Kinematic Equations and Free Fall**

To find the displacement of an object you find the area of its graph EX.
 * Sample Problems and Solutions**
 * Kinematic Equations and Graphs**

Area = (10 s) * (5 m/s)
 * ~ Rectangle ||~ Triangle ||
 * = Area = base * height

Area = 50 m ||= Area = 0.5 * base * height Area = 0.5 * (5 s) * (10 m/s)

Area = 25 m || Triangle Area + Rectangle Area= displacement 50 m + 25 m = 75 m

- kinematic equations can only be applied to any motion were the acceleration is constant - when there are two separate constant accelerations, they must be calculated seperately

**Cartoon:Troll Physics- Free Falling**



= Lesson 5 =

Newton
1st law- law of inertia a. an object stay at rest b. an object will stay in motion (at constant speed in a straight line) c. unless forced to do otherwise

at rest= static equalibrium - v=0 - a=0 - forces are balanced

in constant motion= dynamic equalibrium - Galileo's incline experiment

Forces
- push or pull external to the system - there must be contact- cannot be transferred or carried - a force is only by direct contact and it cannot be saved - ALL FORCE measured in Newtons (N)
 * ** Type… ** || ** Symbol ** || ** Caused by…. ** || ** Always points…. ** ||  ||
 *  Weight || w, Fg || pull of the earth on mass ... || straight down || w=m*g ||
 *  Friction || f, Ff || 2 surfaces rub together || opposite the direction of motion || f= m*N ||
 *  Normal || N, FN || "support force"- whenever2 surfaces touch || perpendicular to the surface andthrough the system || - ||
 * Tension || T, FT || rope or chain ONLY- pull || runs along rope away from the object || - ||

Homework
**Reading Summaries:** - First Law of Motion: 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 an unbalanced force - one part of the law predicts the behavior of stationary objects while the other predicts the behavior of moving objects I.E. EX. If you run with a container filled with water it would tend to spill when the state of motion is changed, i.e. when... Other Examples:
 * Newton's First Law**
 * the container was at rest and you attempted to move it
 * the container was in motion and you attempted to stop it
 * the container was moving in one direction and you attempted to change its direction.
 * Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator.
 * The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.
 * A brick is painlessly broken over the hand of a physics teacher by slamming it with a hammer. (CAUTION: do not attempt this at home!)
 * To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted.
 * Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.
 * While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard.

- Inertia- the resistance an object has to a change in motion - moving objects eventually stop because of friction - Galileo did an experiment using balls and inclined planes- he found that after going down one incline the ball rose up the other incline to almost the same height as it started, he thought that friction was the force that prevented it from going to the same height I.E. - Force is not needed to keep an object in motion- force is needed to stop an object (for instance friction) and to combat opposing forces (for instance friction) - inertia varies with mass and is solely dependent on mass
 * Inertia and Mass**

Definitions of Inertia: - the resistance an object has to a change in motion - the resistance an object has to a change in velocity - the resistance an object has to acceleration
 * State of Motion**

Example of balanced force: - there are two forces of equal magnitude, on pushing up and one pushing
 * Balanced and Unbalanced Forces**

down- thus the forces are ballanced

Example of unbalanced force:

- there are two forces of equal magnitude, on pushing up and one pushing down- these forces are balanced - there is the force of the friction fighting the tendency of the object to remain in motion

**Cartoon:**

= Lesson 6 =

Newton's Second Law Lab
- Force is proportional to acceleration - Acceleration is inversely proportional to mass a=F/m F=m*a

Objective: what is the difference between... net force & acceleration on an object? mass of an object & its acceleration?

Hypothesis: The less massive the object, the faster it will accelerate (inverse), the more force you use, the faster it will accelerate (direct).

Data: //Units in headings, use subscripts and superscripts to make it easier to read. ACC doesn't mean anything... use proper abbreviations please. Whang*g is what???//
 * M-hang || M-cart || M-total || Whang*g || Acceleration m/s^2 || 2 || 3 || Avg ACC ||
 * 0.01 || 0.52 || 0.53 || 0.098 || 0.115 || 0.111 || 0.115 || 0.113667 ||
 * 0.015 || 0.515 || 0.53 || 0.147 || 0.22 || 0.218 || 0.214 || 0.217333 ||
 * 0.02 || 0.51 || 0.53 || 0.196 || 0.311 || 0.312 || 0.311 || 0.311333 ||
 * 0.025 || 0.505 || 0.53 || 0.245 || 0.398 || 0.393 || 0.398 || 0.396333 ||
 * 0.03 || 0.5 || 0.53 || 0.294 || 0.473 || 0.474 || 0.468 || 0.471667 ||


 * M-hang || M-cart || M-total || Whang*g || Acceleration m/s^2 || 2 || 3 || Avg ACC ||
 * 0.03 || 2.5 || 2.53 || 0.294 || 0.065 || 0.065 || 0.052 || 0.060667 ||
 * 0.03 || 2 || 2.03 || 0.294 || 0.113 || 0.117 || 0.104 || 0.111333 ||
 * 0.03 || 1.5 || 1.53 || 0.294 || 0.151 || 0.15 || 0.142 || 0.147667 ||
 * 0.03 || 1 || 1.03 || 0.294 || 0.222 || 0.217 || 0.222 || 0.220333 ||
 * 0.03 || 0.5 || 0.53 || 0.294 || 0.471 || 0.469 || 0.483 || 0.474333 ||

Graphs:

Analysis: Acceleration & Force The Y value for the best fit line should equal the total mass, 0.530, but it is off by ~3% at 0.545; this is probably due to friction. 0.0313 should be the friction divided by the mass. Acceleration & Mass the Y value, 0.2285x^-1.227, could also be read as a=0.2285/m^1.227, as the Y value equals acceleration and the negative power means that it is a fraction. As a= F/m, we know friction is 0.2285. //no, not friction! Net Force... which is the hanging mass.// Theory Derived The A-F graph is directly proportional, so a is proportional to f. Graph M-A is inversely proportional so //this discussion is very incomplete.//

Free Body Diagrams
-FBD - represent all forces acting on a system - all forces are shown and are represented with symbols

Homework
**Reading Summary:** - force is the push and pull of one object on another object - Two kinds of forces: Contact forces: - two objects are interacting - frictional forces - tensional forces - normal forces - air resistance forces - applied forces Action-at-a-Distance Forces: - forces that apply even when nothing is touching anything else - Gravitational Force - Electrical Force - Magnetic Force
 * The Meaning of Force**

- Force is measured in Newtons

- Force is vector- it has both magnitude and direction  < in this image force is balanced so the object remains at rest

 in this image the object will not remain in motion because friction, an unblanced force, is acting against it ->

- equation:
 * Types of Forces**
 * < **(and Symbol)** ||< Description of Force ||
 * < **Applied Force**Fapp ||< - a thing is pushed/pulled by another thing ||
 * < **Gravity Force****(also known as Weight)**Fgrav ||< - gravity pulling things down giving them weight

Fgrav = m * g where g = 9.8 N/kg (on Earth)and m = mass (in kg) || - pushes the objects away from each other || - static friction- friction when the things are at rest - depends on the nature of the two surfaces -equation for the maximum friction a thing can exert: Ffrict = µ • Fnorm || - most noticeable for things with big surface areas or that go at high speed || - pulls equally on the objects at each end || Mass vs Weight - Weight- force gravity exerts on an object - Mass- the amount of matter contained in an object
 * < **Normal Force**Fnorm ||< - the force two things apply to each other when they are at in contact
 * < **Friction Force**Ffrict ||< - sliding friction- the force exerted against an object in motion by another thing
 * < **Air Resistance Force**Fair ||< - special friction that is air-to-object rather than thing-to-object
 * < **Tension Force**Ftens ||< - force transmitted through taught rope
 * < **Spring Force**Fspring ||< - force of a streched or compressed spring on an attached object ||

- diagrams that show the magnitude and direction of ALL forces acting on an object - The size of the arrow sometimes reflects the magnitude - the arrow points in the direction the object is being pulled EX.--->
 * Drawing Free-Body Diagrams**

- an unbalanced force causes acceleration - an unbalanced force, as referred to in Newton's first law, is one that is not balanced by an opposing force EX. - vector diagrams can be used for finding how balanced the forces are EX. //I think that you should put this in your own words... like "add vectors that point in the same direction and subtract vectors that point in opposite directions" and provide one or two examples. You are not filtering the information enough. Same thing in the chart with types of forces... you are just copying his notes, not digesting it for yourself.//
 * Determining** **the Net Force**



= Lesson 7 =

Calculating Acceleration
- use the force equation or a velocity/distance/time equations, depending on what data is given

Homework
**Reading Summary:** - first law is for balanced forces - applies when forces are not balanced - acceleration is dependent on net force and mass - acceleration directly proportional to force and inversely so to mass - when forces are unbalanced there is always acceleration - Equations: a = Fnet / m Fnet = m * a - measure force with Newtons
 * Newton's Second Law**

- follow proven laws not false preconceptions - Use: Fnet = m * a Fgrav = m•g Ffrict = μ•Fnorm - Gravitational field strength- the thing that keeps all free-falling objects at the same acceletation: =Fnet/m =9.8 N/kg (on Earth) - Air resistance happens because a falling objects surface colides with air mollcules - two leading variables for AR: speed, area - two body problems: two things interacting with two variables to find - system analysis- you view the two things as one thing with combined mass - individual object analysis- either object used- this way you consider the force between the two objects **Cartoon:Troll Physics- Acceleration/Gravity:** = Lesson 8 =
 * The Big Misconception**
 * Finding Acceleration**
 * Finding Individual Forces**
 * Free Fall and Air Resistance**
 * Double Trouble**

Friction
Coefficient of Friction: - a number that represents how two surfaces interact when they try to slide across each other - ratio- no units - almost always between 0 and 1 = f/N

Friction Lab***
__Purpose__: to find different coefficients of friction around the school and see if they coincide with our ideas of friction

__Data:__


 * Location || Average mu ||
 * Gym Floor || 0.29 ||
 * Concrete || 0.49 ||
 * Floor Tile || 0.28 ||
 * Tabletop || <span style="font-family: 'Times New Roman',serif; font-size: 10pt;">0.21 ||
 * <span style="font-family: 'Times New Roman',serif; font-size: 10pt;">Carpet || <span style="font-family: 'Times New Roman',serif; font-size: 10pt;">0.42 ||
 * <span style="font-family: 'Times New Roman',serif; font-size: 10pt;">Paving Stones || <span style="font-family: 'Times New Roman',serif; font-size: 10pt;">0.36 ||
 * note: this was the only data you asked us to take down

__Calculations:__ __Analysis:__ Because our tools were so imprecise, it we cannot properly assume that more than one significant figure is accurate, but I have left two so the variety of the data can be seen. The largest sources of experimental error are the fact that we did not necessarily succeed in pulling our boxes at constant speed and that not all of us could necessarily read the scale very accurately while in motion. The amount of friction we calculated for each surface has in comparison to each other surface is fairly intuitive; the surfaces that feel smoothest to our touch (the table, the tile, the gym floor) are those with the least friction and the roughest feeling surfaces (concrete, the carpet, paving stones) have the most friction. This demonstrates how the "math stuff" has actual real-world meaning; we further our understanding of mu by demonstrating, rather than memorizing, how it,with normal force, shows the friction that will be between two objects.

Homework
**Cartoon: Troll Physics- Newton Turning Over in His Grave:**

= Lesson 9 =

Air Resistence
- particles of air build up underneath a falling object, and as the object moves faster, the molecules cannot move out of the way fast enough - Terminal velocity- when an object is no longer in free fall because air resistance has stopped accelerating

Air Resistance Lab
Calculations: Analysis: when designing my parachute I used tape to reinforce it,hoping the reinforcement would keep the parachute from closing. It was fairly successful in that, but the extra weight made my time shorter. People with the simplest parachutes did the best, as theirs seemed to drift down, even with the weight pulling the coffee filter mostly closed. Experimental error could have come from wind, but there wasn't much wind that day.Human error could have come from the timing, but the time was so long that it is unlikely that there was much experimental error.
 * Trial # || Fall Time (in seconds) ||
 * 1 || 1.97 ||
 * 2 || 2.50 ||
 * 3 || 1.62 ||

Homework
**Reading Summary:** - forces come in pairs- when force pushes one way another pushes in the opposite direction with equal strength Ex. Birds’ wings push air down, air pushes birds up; tires push pavement back, pavement pushes tires forward
 * Newton’s Third Law**

- Think of what is initiating the action and then what the reaction to that action is and you get the pair
 * Identifying Action and Reaction Force Pairs**

**Cartoon: Troll Physics- Flight Through Opposite Reaction:** = Lesson 10 =

Newton's Third Law
- Every action has an equal but opposite reaction - i.e. all forces come in pairs that are equal in size, pointing in opposite direction, acting on 2 separate systems

Newton's Third Law Lab
Question: How much mass should you hang to make the cart move 0.8 meters in 0.85 seconds? Calculations: Data: Error Calculation: I0.85-0.8682I/0.85= 0.021 2.1% error
 * Trial # || Time ||
 * 1 || 0.8897 ||
 * 2 || 0.8856 ||
 * 3 || 0.8293 ||
 * Ave || 0.8682 ||
 * Theo-Exp|/Theo= % Error

Experimental Error: A "picket fence" was added to the cart, adding about 20g and throwing our calculations off a little. Never the less, we had very little experimental error, leading me to believe that we did not have many other sources of error. Other sources of error could include holding the cart too far back (not starting at vi=0) and holding the cart to far forward (having the timer start before you let go of the cart). Human Error could have occurred if the person putting the weights back on the hanger after they had fallen off missed a weight; however we know this did not happen because of the consistency of the data.

Analysis: Even though are cart weight was off, the results for my group and the other groups were remarkably accurate, again demonstrating that the physics we study is not an abstract or theoretical, but has real world application.

Homework
**Reading Summary:** - Vector- describes magnitude and direction - When the direction of vectors is not straight north, south, east, or west, you use angles to fully describe it
 * Vectors and Direction**

- usually measured counterclockwise from east EX..

- for adding two opposite N, S, W, & E - Vector Sum- sum of two vectors - Pythagorean theorem can be used to find the displacement from two distances at right angls I.E. - add up the N-S and the W-E values and use Pythagorean Theorem or - head to tail method- draw a to-scale diagram and draw the line between the start and end points and find the length
 * Vector Addition**

- no matter how 3 angles are added they give the same resultant I.E. 20 m, 45 deg. + 25 m, 300 deg. + 15 m, 210 deg.SCALE: 1 cm = 5 m SCALE: 1 cm = 5 m


 * 15 m, 210 deg. + 25 m, 300 deg. + 20 m, 45 deg.****SCALE: 1 cm = 5 m**



- 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
 * Resultants**

- you can think of diagonal vectors as having 2 parts to make it simpler I.E. - 2 parts known as components
 * Vector Components**

- vector resolution- magnitude of a vector - parallelogram method- draw accurately to scale and measure I.E. - 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
 * Vector Resolution**
 * Component Addition**

- add the velocity of 2 forces to get the final velocity EX.
 * Relative Velocity and Riverboat Problems**

- two perpendicular forces cause something to move on a diagnal - can throw things off course and make them take longer because, for instance, they are displaced both down and to the right
 * Independence of Perpendicular Components of Motion**
 * - d = v * t**

**Physics Jokes:** Q: Why did the chicken cross the road? A: To make a normal vector.

Q: Why did the cat fall off the roof? A: It didn’t have enough mew. From: []

= Lesson 11 =

Projectile motion
- x and y axes are independent - ay= -9.8 m/s - ax= netFx=r equalibrium - use trig to find initial velocity - for ground-to-ground projectiles, Y displacement is ALWAYS 0 -two types of problems:

Homework
**Reading Summary** After reading the material, answer the following questions:
 * Method 1: Directed Reading**
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * 2) What (specifically) 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.
 * 3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 4) What (specifically) did you read that was not gone over during class today?

1. - An object being acted on only by gravity is a projectile regardless of direction - without gravity, a shot object would continue in a straight line at a constant velocity because there would be no forces acting upon it 2._ 3._ 4._
 * What is a Projectile?**

1. - horizontal and vertical motion are independent of each other I.E.> - I.E. a horizontally shot object's horizontal velocity will not change (assuming negligible air resistance) but the vertical velocity will change with gravity 2._ 3._ 4._
 * Characteristics of a Projectile's** **Trajectory**

1. - A to-scale vector diagram will demonstrate the independence of the x and y axes> - the horizontal acceleration stays constant regardless of angle, but, for example, if the ball is shot upwards the y velocity will increase before going to 0 and decreasing 2._
 * Describing Projectiles with Numbers- Horizontal and Vertical Velocity**

3._ 4._

1. - vertical displacement can be found using: **y = 0.5 • g • t2** - horizontal displacement can be found using: **x = vix • t** - vertical displacement for an agled launched projectile can be described as: **y = viy • t + 0.5 • g • t2** 2._
 * Describing Projectiles with Numbers- Horizontal and Vertical Displacement**

3._ 4._

1.**-** to find the time it takes an object to come back down you double the time it took to go up - to find horizontal displacement: **x = vix • t** - to find peek height: **y = viy • t + 0.5 • g • t2**
 * Initial Velocity Components**

2._ 3._ 4. - to find the time an object takes to move up use: (we may have covered this briefly mostly focused on objects with no initial vertical velocity in class)

1.Problem type 1: - object starts elevated - object has initial horizontal velocity - unknowns: initial speed, initial height, time, horizontal distance Problem type 2: - no initial elevation - object is launched at an angle giving it initial horizontal and vertical velocities - unknowns: time, peak height, horizontal distance Both - you need to calculate the X and Y aspects separately (see equations --->) 2._ 3._ 4._
 * Horizontally Launched Projectile Problems**

1._ 2._ 3._ 4.Steps to solving: (we solved in class but we just input data, using or going over a step method)
 * Non-Horizontally Launched Projectile Problems**
 * 1) use the given values (vi, angle) to find horizontal and vertical parts using trig
 * 2) list known an unknown values in a table
 * 3) determine what you have to solve for
 * 4) solve for time (usually using: vfy = viy + ay*t)
 * 5) solve for horizontal displacement (usually using: x = vix*t + 0.5*ax*t2 )
 * 6) solve for peak (usually using: y = viy*t +0.5*ay*t2)

**Cartoon: Calculating Projectile Motion for Real-Life Situations:** website: [] image: [] = = = Lesson 12 =

Projectile Motion Lab
Purpose: To Determine the initial velocity of the ball and to calculate the placement of a cup if the ball is to land in it. Data: Vi=1.029 Calculations: Theoretical vs Experimental Calculations:
 * ||  |||||| Measurement Values ||
 * Trial # || ax || ay || dx || dy ||
 * 1 || 0 || -9.8 || 0.384 || 0.777 ||
 * 2 || 0 || -9.8 || 0.332 || 0.777 ||
 * 3 || 0 || -9.8 || 0.394 || 0.777 ||
 * 4 || 0 || -9.8 || 0.389 || 0.777 ||
 * 5 || 0 || -9.8 || 0.383 || 0.777 ||
 * 6 || 0 || -9.8 || 0.385 || 0.777 ||
 * 7 || 0 || -9.8 || 0.388 || 0.777 ||
 * Average || 0 || -9.8 || 0.379286 || 0.777 ||
 * Photogate Values ||
 * || time ||
 * trial 1 || 0.012 ||
 * trial 2 || 0.0114 ||
 * trial 3 || 0.0109 ||
 * trial 4 || 0.0132 ||
 * average || 0.011875 ||
 * Vi (photogate) ||
 * 1.347368 ||  ||
 * 1.347368 ||  ||
 * Theo-Exp|/Theo= % Error
 * 1.35-1.03|/1.35= 23.7%

Analysis and Experimental Error: I think the most likely cause for error was the slight angle the ball was going at. Looking at the indents the ball made on the tin foil after all the trials, I could see that the ball was not going in a line exactly perpendicular to the table edge. The slight angle of the ramp could account for the seemingly smaller distance of the experimental value. I had to use the experimental values to calculate the place to put the cup because I needed to know where the ball would go based on it's actual trend not its theoretical trend. Using my calculations, I was able to get the ball in on the first try.

Homework
**Cartoon: Alternate Uses for Projectile Motion** Website: [] Image: []

= Lesson 13 =

Incline Lab
Question: What is the Relationship of the incline to the acceleration of an object? Hypothesis: They are proportional. Calculations:

Data: Graph: Analysis: The slope of the graph should be 9.8, and the x value should be a very small negative number to account for the ignored friction. The x-value found by our best fit line looks correct but the Y value is very far off. We think this is because of human error; the person dropping the cart had to tell the person timing who had to react and react again when the cart hit the end. The time was too small probably because of the communication between the two people was bad- the end time was probably close to accurate because if that was inaccurate it would lengthen the time. The group that had the same person timing as letting go had less error because there was less room for communication error. Overall, our results were very precise (we got fairly constant results) but the results were not accurate, as the times were too short due to human error.
 * h (meters) || theta || d || m || t1 || t2 || t3 || t4 || t5 || taverage || acceleration || sin(theta) ||
 * 0.042 || 1.98 || 0.5 || 0.5 || 1.59 || 1.69 || 1.68 || 1.69 || 1.65 || 1.66 || 0.362897 || 0.034568 ||
 * 0.056 || 2.64 || 0.5 || 0.5 || 1.4 || 1.37 || 1.4 || 1.38 || 1.38 || 1.386 || 0.520563 || 0.046091 ||
 * 0.079 || 3.73 || 0.5 || 0.5 || 1.22 || 1.12 || 1.12 || 1.12 || 1.19 || 1.154 || 0.750911 || 0.065021 ||
 * 0.102 || 4.82 || 0.5 || 0.5 || 0.96 || 0.91 || 1 || 0.9 || 0.94 || 0.942 || 1.126933 || 0.083951 ||
 * 0.138 || 6.52 || 0.5 || 0.5 || 0.75 || 0.72 || 0.78 || 0.85 || 0.78 || 0.776 || 1.660644 || 0.11358 ||



Homework
**Reading Summary:** Angles Must Be Accounted For in Finding Net Forces You can find this using a to-scale head-to-tail force diagram (example to the right). When adding forces you must include direction; 10 N+ 10N does not always equal 20N, it depends on the forces' direction. A Force at an Angle Must Be Divided into components You can find the components using SohCahToa, as seen bellow
 * Addition of Forces**
 * Resolution of Forces**

Equilibrium Means Balance Not EqualityIn If an object is in equilibrium the forces are balanced and there is no acceleration. This does not mean that all the forces are equal, but rather that the upward force and downward forces are equal, and the rightward and leftward forces are also equal. Normal force is not always equal to gravitational force, because there can be other upward forces as well. Object Acceleration is Dependent on Inclination and Forces Disregarding friction, the more tilted a tilted surface, the faster an object will go down it. The horizontal component of weight pushes an object in the direction of the lower side of the surface and the vertical component pushes the object in to the surface. Normal force partially counteracts this, pushing up perpendicular to the inclined surface. When you add other values, calculation is made easier by looking at the inclined forces as vertical/horizontal and the N, S, W and E forces as inclined. (as seen below) Two Approaches for Dealing with Two Objects You can either view the two objects as a single system or as two separate systems. Only the second approach can find tension.
 * Equilibrium and Statics**
 * Net Force Problems Revisited**
 * Inclined Planes**
 * Double Trouble in Two Dimensions- Two Body Problem**

**Cartoon:**

Image: [] Website: []

= Lesson 14 =

Newton's Law of Universal Gravitation (LUG)
- Everything is gravitationaly attracted to every other thing - The earth's pull is too great for us to notice others - Mass of earth= 6 *10^24 kg - Mass of a person- 70 kg - Gravity is proportional to mass and inversely (squared) proportional to distance - big G= universal gravitational constant = 6.67 * 10^11 Nm^2/kg^2 - Force of gravity, Gravitational force, Gravitational attraction, Weight - so w=mg is only true on the **surface** of the earth

Kepler's Laws of Motion
1. Law of ellipses- Planets move in elliptical orbits around the sun - eccentricity- how off circle (between 0 and 1) - earths orbit= 0.09 2.Law of Equal Areas- For any given time period, a planet will carve out equal areas in it's ellipse - so the closer to the sun, the faster the planet moves 3. Law of Harmonies- T^2/R^2 is constant for all planets in our solar system - T= period of time around the sun - R- distance from planet to sun

Homework
**Reading Summary:** What is Gravity Really? Gravity is the thing that pulls bodies towards each other, not just the thing that makes things that go up come down. In Physics we often use the constant acceleration of gravity on earth (9.8m/2^2) and the variable force of gravity (mass * acceleration of gravity). Planets Move in Predictable Orbits The Planets move in an elliptical orbit about the sun. The area of the slice carved by the path of a planet around the sun in a certain time is constant. The ratio of the time period around the sun squared to the average distance from the sun cubed is constant. We have known three basic Laws since the 1600s, they helped Newton develop the idea of universal gravitation, which said that everything has it's own gravity, not just large heavenly bodies, and the force of this gravity is dependent on mass and distance. (i.e. v) Cavendish completed Newton's Idea Cavendish determined that there was a constant, G (6.67259 x 10-11 N m2/kg2), that could be used to find F-grav using mas and distance. The equation was: Gravity Varies, Even in Earth's Atmosphere The value of g (9.8N at the earths surface) is inversely dependent on the distance from the center of the earth.
 * Gravity is More Than a Name**
 * The Apple, the Moon, and the Universe Square Law +** **Newton's Law of Universal Gravitaion**
 * Cavendish and the Value of G**
 * The Value of g**

**Cartoon:** image: []

Website: []

= Lesson 15 =

Circular Motion
- constantly changing direction - changing velocity- changing speed/ changing direction - Uniform Circular Motion (UCM)- constant speed but change in direction -∑F=ma still applies - kinematics equations don't wokr b/c they're 2-D - to find centripetal acceleration: - circular motion is constantly changing- if you let go it go, it goes in a straight line - unbalanced force at the center, acceleration must always point towards the center - can use: tension (ball on string) normal (washing machine) friction (car turning) gravity (planetary orbits) - positive is always the force pulling towards the center of the circle - at max speed normal force is equal to 0

Centripetal Force Lab
__Purpose:__ To find the maximum amount of weight a certain kind of string can hold, the minimum tension it can spin at, and the maximum velocity it can spin at.

__Data:__
 * || Radius || Circumference |||||||| # of Rev |||||||| Times (s) |||||||| Period (s) ||
 * || (m) || (m) || 1 || 2 || 3 || Avg || 1 || 2 || 3 || Avg || 1 || 2 || 3 || Avg ||
 * Tension Top of Circle || 0.5 || 3.1415926 || 19 || 20 || 22 || 20.33 || 16.5 || 18.13 || 19.22 || 17.95 || 0.868 || 0.907 || 0.874 || 0.883 ||
 * Tension Bottom of Circle || 0.5 || 3.1415926 || 19 || 20 || 19 || 19.33 || 6.3 || 8.53 || 7.03 || 7.287 || 0.332 || 0.427 || 0.37 || 0.377 ||

__Calculations:__ Circumference: c=2*pi*r c=3.14 meters Period: Period= time/ # of revolutions P=0.868 s= 16.5/19 Experimental Velocity: Velocity= circumference/average period V=3.14/0.883= 3.56 m/s Theoretical Velocity: Velocity= √(((maximum tension-(mass*g))*radius)/mass) V=√(((9.016-(0.01*9.8))*0.5)/0.01)= 2.21 m/s Experimental Error: __Analysis and Error:__ Each group had a large amount of error for this lab. I think the two greatest sources of error were the spinning and the timing. The person had to keep the object spinning vertically for it to fit the theoretical format, but in reality the object had a tendency to spin slightly conically, adding a horizontal element that was not included in the calculations. The person timing had to keep track of how many spins the object underwent and had to start and stop the time at the correct points, which would have been especially difficult while the object was moving faster. Overall, our results were very precise, especially considering that two different people spun for both the top and bottom elements, but they were not accurate, as demonstrated by the 61% error for each.
 * Experimental Velocity || Theoretical Velocity || Max Tension || Mass || Experimental Error ||
 * (m/s) || (m/s) || (N) || (kg) ||  ||
 * 3.559 || 2.213594362 || 9.016 || 0.01 || 60.77% ||
 * 8.335 || 21.11634438 || 9.016 || 0.01 || 60.53% ||
 * Theo-Exp|/Theo= % Error
 * 2.21-3.56|/2.21= 61%

Homework
**Reading Summary:** (Q- question, A- answer, CI- central idea) Q: How do you find the speed and velocity of an object moving with circular motion? A/CI: You find an object moving in uniform circular motion by using these equations:
 * Speed and Velocity**

**Circumference = 2*pi*Radius** Though objects moving with centipetal force may have a constant speed, their velocity is ever changing because the direction is changing and thus tangential to the circle. (i.e. the picture to the right) Q: How do you find the acceleration of an object moving with circular motion? A/CI: use this equation Note that vi and vf will probably be different angular velocities (as seen in the bellow image)
 * Acceleration**

Acceleration can be measured with an accelerometer. Q: How does Newton's first law affect centripetal motion? A/CI: Examples of how inertia acts in cars with non-centripetal movement: Because objects want to move at the same velocity, they resist the changing velocity of circular motion EX: Friction, Tension, and Gravity unbalance the forces,counteracting inertia (examples bellow) To find the ammount of force used on an object: **Work = Force * displacement * cosine (Theta)** Q:Why is Centrifugal force impossible? A/CI: Centrifugal force is force pushing out from the center, while Centripetal force pushes inwards. Because of inertia people often believe in centrifugal force even if they know about centripetal force. Q: How should equations be used to solve centripetal force problems? A/CI: the equations given to solve algebriacly equations can be used to guide thought, ex.
 * The Centripetal Force Requirement**
 * The Forbidden F-word**
 * Mathematics of Circular Motion**

**Cartoon:** Website: [] Image: []

= Lesson 16 =

Pendulum Lab
Question What happens to the period as you change the radius of a conical pendulm? Hypothesis: The time will get larger as the radius gets larger. Calculations: Analysis and Sources of Error: Overall this was a fairly precise and accurate lab, but there are a few factors that could have caused the error we did have. First and foremost, the reaction time of the students was not perfect. Secondly, it is hard to get a perfectly circular rotation, so the circle was probably a little elliptical, but hopefully this elliptical tendency was negligible. Lastly, it looked difficult to determine exactly what radius the weighted ball was at so even with careful measurement the radius of each could reasonably be off by at least a few millimeters.
 * length (m) || radius (m) || average period (s) || theoretical period (s) || Experimental Error ||
 * 2.64 || 0.1 || 3.315 || 3.259 || 2% ||
 * 2.64 || 0.2 || 3.291 || 3.27 || 0.6% ||
 * 2.64 || 0.4 || 3.277 || 3.24 || 0.9% ||
 * 2.64 || 0.6 || 3.2987 || 3.218 || 2% ||
 * 2.64 || 1.0 || 3.16 || 3.142 || 0.5% ||

Homework
**Reading Summary:**

(Q- question, A- answer, CI- central idea) Q: How does Newton's second law effect centripetal motion? A/CI: Newton's second law shows that Acceleration= Net Force/ Mass. Thus, the force pulling towards the center must be great enough and the mass must be small enough to counteract inertia and cause acceleration. Q: How is centripetal force used to design roller coasters? A/CI: Many roller coasters use centripetal force to make the coaster fun as well as keeping the car on the tracks and moving. In a loop, the radius changes, so overlapping circles are used to describe the motion. The Velocity and direction of acceleration is always changing within these loops. this is beacause of the different forces in different positions.
 * Newton's Second Law-Revisited**
 * Amusement Park Physics**

As seen bellow, bumpy roller coasters operate similarly, only normal force is never pushing down and gravity is never pushing the cart away from the track Banked turns opperate similarly to banked turns on a road, keep the motion circular with less friction required. Q: How does centripetal force determine motion in sports? A/CI: All turns made anywhere use centripetal force: An athlete may lean in to turns so forces can allow greater speed- i.e. because the ice must push up in the same direction the skater pushes down, the normal force of the ice pushes him in to the turn. To solve an equation in which an athlete is leaning you will need to use triganometry **Cartoon:** Website: [] Image: []
 * Athletics**