Ch3_LefflerM

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 * //__Chapter 3: 2D Motion! __//**

10/12/11: Lesson 1; A&B
Class Work:
 * Hand in Homework Journal
 * Take Test

HW:
 * Vectors, //Lesson 1//, only parts **a** and **b**. Use [|Method 1].

A vector quantity is a quantity that is fully described by both magnitude and direction unlike a scalar quantity which is a quantity that is fully described by its magnitude. Vector diagrams depict a vector by use of an arrow drawn to scale in a specific direction. When Drawing a Vector Diagram Make sure to include: a scale is clearly listed a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a //head// and a //tail//. the magnitude and direction of the vector is clearly labeled. In this case, the diagram shows the magnitude is 20 m and the direction is (30 degrees West of North). The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow. The arrow is drawn a precise length in accordance with a chosen scale. On such a scaled vector diagram, a vector arrow is drawn to represent the vector. The arrow has an obvious tail and head. The magnitude of a vector is represented by the length of the arrow. A scale is indicated (such as, 1 cm = 5 miles) and the arrow is drawn the proper length according to the chosen scale. The arrow points in the precise direction.
 * Vectors and Direction**
 * Conventions for Describing Directions of Vectors**
 * Representing the Magnitude of a Vector**

Two vectors can be added together to determine the resultant The two methods that will be discussed in this lesson and used throughout the entire unit are: the Pythagorean theorem and trigonometric methods __the head-to-tail method using a scaled vector diagram__
 * Vector Addition**

Can be used for ONLY! adding two vectors that make a 90**°** angle
 * The Pythagorean Theorem**

The direction of a //resultant// vector can often be determined by use of trigonometric functions. SOH CAH TOA The measure of an angle as determined through use of SOH CAH TOA is __not__ always the direction of the vector
 * Using Trigonometry to Determine a Vector's Direction**



The magnitude and direction of the sum of two or more vectors can also be determined by use of an accurately drawn scaled vector diagram. Using a scaled diagram, the **head-to-tail method** is employed to determine the vector sum or resultant
 * Use of Scaled Vector Diagrams to Determine a Resultant**

The head-to-tail method involves [|drawing a vector to scale] on a sheet of paper beginning at a designated starting position. Where the head of this first vector ends, the tail of the second vector begins (thus, //head-to-tail// method).

An example of the use of the head-to-tail method is illustrated below. The problem involves the addition of three vectors: The head-to-tail method is employed as described above and the resultant is determined (drawn in red). Its magnitude and direction is labeled on the diagram. SCALE: 1 cm = 5 m
 * 20 m, 45 deg. + 25 m, 300 deg. + 15 m, 210 deg.**
 * SCALE: 1 cm = 5 m**

10/13/11: Lesson 1; C & D
Class Work:
 * Go over Test.
 * Practice measuring with a protractor [|Worksheet]
 * Notes on Vector Basics [|Worksheet]

HW:
 * Complete questions #8 - 15 on Vector Basics notes page (back)
 * Vectors, //Lesson 1//, only parts **c** and **d**. Use [|Method 1].

The **resultant (R)** is the vector sum of two or more vectors. Vector R can be determined by the use of an [|accurately drawn, scaled, vector addition diagram].
 * Resultants**

Displacement vector R gives the same //result// as displacement vectors A + B + C. "To do A + B + C is the same as to do R." In summary, the resultant is the vector sum of all the individual vectors. The resultant is the result of combining the individual vectors together. The resultant can be determined by adding the individual forces together using [|vector addition methods].
 * Vector Components**

That is, it can be thought of as having two parts. Each part of a two-dimensional vector is known as a **component**.

Any vector directed in two dimensions can be thought of as having two different components. The component of a single vector describes the influence of that vector in a given direction

10/14/11 Class Work: HW:
 * Practice Estimating Vectors #16-25.
 * Practice the Graphical Method: Head to Tail, #22 in notes packet.
 * Graph Paper [|PDF] if you prefer
 * Use the graphical method to find the resultant magnitude and direction for #23 & 24 from notes packet, to scale, in your classwork notebook

Weekend 10/15/11 and 10/16/11

10/17/11: Lesson 1; E
Class Work: HW: Finding the magnitude of a vector is known as **vector resolution**. The two methods of vector resolution that we will examine are the parallelogram method __the trigonometric method__
 * Go over HW.
 * Notes on Analytical Method.
 * Add vectors that are noncollinear and non-perpendicular. [|Worksheet]
 * Ch3# p65 #1,2,4,5
 * Read and summarize at The Physics Classroom, Vectors, //Lesson 1//, only part **e**. Use [|Method 1]
 * Vector Resolution**


 * Parallelogram Method of Vector Resolution**
 * Make a scale (2m=1cm) make sure to multiply out the scale
 * Draw vectors using the head to tail method connect the tail of the first vector to the tail of the last vector. That is your resultant.
 * Measure the Resultant
 * Find the angle of the resultant


 * Trigonometric Method of Vector Resolution**
 * find the R x and the R y

R=√25^2 + 43^2 R=49.74 ~ 50 m/s
 * Vector || x-component || y-component ||
 * 43m/s @ 90° || 43cos 90°=0 || 43sin90°=43 ||
 * 25m/s @ 0° || 25cos0°=25 || 25sin0°=0 ||
 * R || Rx=25 || Ry=43 ||


 * find Θ**
 * Θtan=(Ry/Rx)
 * Θ=Tan^-1 (43/25)
 * Θ=59.83 ~ 60°

The amount of influence in a given direction can be determined using methods of vector resolution.

10/18/11: Period 6: Lesson 1; G & H
Classwork:
 * Practice the Graphical and Analytical Methods. [|Worksheet]
 * Complete Vector Addition practice page [|HERE], BOTH methods!

HW:
 * Vectors, //Lesson 1//, only parts g and h. Use [|Method 1].
 * Text p65 #7,8,9,10

When a moving object is acted upon by a wind, it will either add to or take away from it’s velocity.
 * Relative Velocity and Riverboat Problems**

Ex. Adding velocity Ex. Taking away velocity

If the wind is not going in the same or opposite direction Example Calculations:
 * Add the vectors, using head to tail method
 * Can either use the graphing method, or the Pythagorean theorem to find the R value

(100 km/hr)2 + (25 km/hr)2 = R2 10 000 km2/hr2 + 625 km2/hr2 = R2 10 625 km2/hr2 = R2 SQRT(10 625 km2/hr2) = R
 * 103.1 km/hr = R**

A trig function can be used to find the Θ tan θ= (Ry/Rx) tan θ= (25/100) θ = tan -1 (25/100)
 * theta = 14.0 degrees**

A force vector that is directed upward and rightward has two parts also known as **components** which describe the affect of a single vector in any given direction. The vector sum of these two components is always equal to the force at the given angle.
 * Independence of Perpendicular Components of Motion**

The two perpendicular parts or components of a vector are independent of each other. A change in the horizontal component does not affect the vertical component

10/18/11: Period 7 Lab Classwork:
 * Use your data from "Orienteering Activity" to calculate final displacement using graphical and analytical methods of vector addition.
 * Compare resultant to the measured displacement.
 * Trade data and try to find the correct endpoint by calculating the final displacement and measuring it out.
 * Calculate the vector resultant using the graphical method.
 * Compare your results from experimental measurement to graphical and to analytical. It is best to use %error.

HW:
 * Post your work on this activity on your wiki.

=Activity: Vector Mapping= Partners: Maddi S. and Remzi T. 10/18/11 Data: Analytical Method: Graphical Method: Percent Error: Conclusion: Percent error for the graphing method was very ow due to the fact that it was graphed using the GSP function that is installed on the computers. The percent error for the analytical was much higher than the 1.65% that was calculated for the graphing. To change this problem a good idea would be to not round to only two decimal places. Also the final spot for this experiment was under a tree, which could have put the person measuring the final displacement in an uncomfortable situation. Doing this lab on a flat surface would be a good way to also make results more even.

10/19/11: Lesson 2; A & B
Classwork:
 * Go over HW.
 * Solve river-boat and wind-plane problems. [|Practice]

HW:
 * Text p65#11,13,14
 * Vectors, Lesson 2, parts a & b only. Use [|Method 3].
 * //Optional Gizmo: Vectors (Go to "Lesson Materials" to find worksheets in either PDF or Word format.) Due by Friday 10/21//.

Lesson 2; Part A Preview: Questions and Test: State: Main idea: projectiles are objects which the only force acting upon them is gravity. A projectile has a parabolic trajectory.
 * What is a projectile?
 * Types of projectiles
 * Horizontal vs. Vertical motion
 * What is a projectile?
 * A projectile is an object upon which the only force acting is gravity.
 * What are the types of projectiles?
 * Projectiles can be: dropped from rest, thrown vertically, or thrown upward at an angle to the horizontal (no air resistance).
 * What is the only force that acts upon a projectile?
 * Gravity is the only force that acts on a projectile.
 * What is a parabolic trajectory?
 * It is the shape of the movement of the projectile, a parabola (quadratic).
 * What makes the projectile have a parabolic trajectory?
 * Gravity is the force which acts upon the vertical motion.

Lesson 2; Part B

Preview: Questions and Test: State: Main Idea - Horizontal and Vertical motion act separately from each other. Because there are no horizontal forces, the horizontal motion is constant.
 * How projectiles move
 * Acceleration of a projectile
 * How does gravity change the path of the projectile?
 * Gravity makes the projectile change its path downwards, so if the path were described as x and y the x would not change and the y would decrease.
 * (From my previous answer) What are the x and y called?
 * x is horizontal motion and y is vertical motion
 * How is horizontal and vertical motion used in projectiles?
 * There are not horizontal forces, the only forces are from vertical motion.
 * How does gravity effect non-horizontal launches?
 * If there was no gravity effecting them, they would never stop, they would never come back to earth.
 * What is constant for the horizontal motion? The vertical?
 * Horizontal motion: acceleration and velocity
 * Vertical motion: acceleration is always -9.8 m/s 2

10/20/11: Lesson 2; C
Classwork:
 * Quiz on Vector Addition
 * Go over HW
 * Notes on Projectiles

HW:
 * Conceptual Practice [|Worksheet]
 * Vectors, Lesson 2, part **c only. Use [|Method 3].**
 * //FYI: Ch 3 Test is scheduled for 11/3/11.//

Lesson 2; Part C

Preview: Questions and Test: State: Main Idea - It is important not to confuse the horizontal and vertical parts of a projectile, each part of the vertical and horizontal motion are very different. Gravity is very important to the path of a projectile.
 * In-depth analysis of horizontal and vertical components.
 * Calculations of horizontal and vertical components.
 * How do vertical and horizontal velocity components differ?
 * The horizontal velocity is never changing, the vertical velocity decreases by 9.8 m/s every second.[[image:Screen_shot_2011-11-10_at_3.53.45_PM.png width="351" height="233"]]
 * What equation can we use to find the vertical displacement of a projectile?
 * y=v i t + (1/2)at 2
 * Y being the vertical displacement.
 * Can we use the same equation for the horizontal displacement?
 * Yes we can, the only difference is that it will look more like h = v i t
 * H being the horizontal displacement, we don't have the other part of the equation because the acceleration is 0, which cancels out the last part of the equation.
 * What if there was no gravity acting on the projectile?
 * [[image:Screen_shot_2011-11-10_at_4.04.47_PM.png]]
 * If a projectile was shot at an angle and there was no gravity where would it go?
 * [[image:Screen_shot_2011-11-10_at_4.16.47_PM.png]]

10/21/11 Classwork:
 * Problem Solving for Horizontally-Launched Projectiles [|Worksheet]
 * Finding hang time and range [|Worksheet].
 * Finding initial velocity. [|Worksheet]
 * Activity: Ball in Cup, Part 1. [|Guidesheet]

HW:
 * Text p65 #17,18,21
 * Read at the Physics Classroom, Vectors, Lesson 2, part **c** only. Use [|Method 3].
 * Optional Gizmo Vector Addition (Go to "Experiment Guide" to find worksheet.) Due by Monday 10/24.

Weekend 10/22/11 and 10/23/11

10/24/11 Classwork:
 * Activity: Ball in Cup, Part 1. [|Guidesheet]
 * How fast does the launcher shoot the ball at "medium range"? (Be sure to launch horizontally.)
 * After changing the initial height of the launcher, calculate where to place the cup on the floor so that ball lands inside of the cup 3 times in a row. (You may adjust the position of the cup.)
 * Calculate the %error of the theoretical position of the cup with the actual position of the cup.

HW:
 * Post calculations, video, and data on your wiki.
 * Text p 65-68 #23,27,63

=Activity: Ball in Cup; Parts 1 and 2= Partners: Remzi T. and Maddi S 10/24/11 Objectives:
 * Measure the initial velocity of a ball.
 * Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion.
 * Take into account trial-to-trial variations in the velocity measurement when calculating the impact point.

Pre-Lab Questions: Procedure: media type="file" key="Ball in Cup.mov" width="300" height="300"
 * If you were to drop a ball, releasing it from rest, what information would be needed to predict how much time it would take for the ball to hit the floor? What assumptions must you make?
 * Initial velocity (0), height of person. You would assume that the acceleration would be -9.8 m/s/s, and that the ball would go strait down.
 * If the ball in Question 1 is traveling at a known horizontal velocity when it starts to fall, explain how you would calculate how far it will travel before it hits the ground.
 * You would need to solve for both the horizontal and vertical displacement. In order to do that, you would need to set up an x and y chart. We know vertical initial velocity, acceleration, and displacement for the vertical component, so you can find time from that. Using this equation y=v i t + (1/2)at 2 to find the time. The time for the vertical component and the horizontal component is the same. So using the time and the same equation, you can find the horizontal displacement.
 * A single Photogate can be used to accurately measure the time interval for an object to break the beam of the Photogate. If you wanted to know the velocity of the object, what additional information would you need?
 * We would need to know the amount of time it took, as well as the displacement.
 * Write your procedure and get approval from Mrs. Burns before you proceed any further!
 * What data will you need to collect? Remember that you must run multiple trials. Keep in mind your end goal!
 * We would need to find the height of the shooter, as well as the distance that each ball goes.
 * How will you analyze your results in terms of precision and/or in terms of accuracy?
 * Percent difference is a good way to find how precise the shooter was. To find how accurate the shooter is, an average of the dots on the carbon paper, as the theoretic value and the actual value of where ball landed plugged into the percent error formula, will show how accurate the shooter is.
 * Carbon paper measurement
 * Shoot ball at "medium range"
 * Put carbon paper on floor where ball seems to be landing
 * Shoot the ball onto the carbon paper multiple times.
 * Measure distance from shooter to each dot on carbon paper.
 * Take the average of distances
 * Change height of launcher, calculate where the ball will land at new height and into the cup

Calculations: Initial Velocity: 6.85 m/s Change height, find new displacement: Percent Error: Theoretical landing position: 2.6462 m Actual landing position: 2.55 m Conclusion: The percent error was very small because the height of the cup was taken into consideration. Also if the calculations had taken into consideration the path of the ball to the left or right, it may have been easier to get the ball in the cup.
 * Initial velocity calculations:

10/25/11 - Period 6 Classwork:
 * Go over HW
 * Problem Solving: Ground to Ground Launches.
 * Hang time
 * Range
 * Maximum height
 * initial velocity

HW:
 * Text p 65 #19,22,26,30
 * Copy and paste the questions that you created for Lesson 2 (a,b,c) summaries into this wiki page. Be sure to read what is already posted and DO NOT ADD questions already posted.

10/25/11 - Period 7 LAB Classwork:
 * LAB: Shoot Your Grade [|Instructions]

HW:
 * Continue Planning and doing initial calculations. You will be given more time tomorrow. Do HW listed on other link on the calendar.

10/26/11 Classwork:
 * Go over HW
 * Continue "Shoot Your Grade" lab

HW:
 * Continue to update and post your work as you go.

10/27/11 Classwork:
 * Quiz on Vector Addition and //Basic// Projectiles
 * Go over HW
 * Problem Solving: Off-a-Cliff-at-an-Angle Launches.
 * Hang time
 * Range
 * Maximum height

HW:
 * Text p 65 #31,32,62

10/28/11 Classwork:
 * Go over HW
 * Problem Solving Practice with Projectiles
 * Continue working on "Shoot Your Grade" Lab, if time allows.

HW:
 * Text p 65 #64,71,72
 * Test is scheduled for Friday 11/4/11; HW Notebook will be collected at the same time.

11/1/11 - Period 6 Classwork:
 * Gordo-rama!
 * Analysis
 * Post results and calculations on wiki

HW:
 * Post results and calculations on wiki

=Gordo-Rama!=

Partner (in Crime): Katie Dooman Date: 11/1/11

Side: Behind: Frontal: Calculations: Analysis: The reason why the Jack Skellington King of The Pumpkin Patch cart did not do so well was because the wheels were not strait, and it weighed to much. Given the chance to do this lab again, the cart would be made of a light weight chip board, or a box type recyclable. Also the wheels would be of a lighter material, possibly foam, which would subtract from the overall weight.

11/1/11 - LAB Classwork:
 * Continue LAB: Shoot Your Grade

HW:
 * Lab Analysis and Conclusion
 * Optional GIZMO: Monkey and Hunter, due Friday 11/4.

11/2/11 __Classwork__:
 * Go over HW.
 * Practice Problem Solving

__HW__:
 * Study for Quiz tomorrow.
 * Optional GIZMO: Monkey and Hunter, due Friday 11/4.
 * Test postponed until Monday 11/7. HW notebooks will be collected at the beginning of the test period.
 * Wikis for chapter 3 will be due around the same time, rubric coming shortly.

11/3/11 __Classwork__:
 * Quiz on Projectiles Problem Solving
 * Go over Quiz
 * Go over HW problems.
 * Lab, if time allows.

__HW__:
 * Study for Test; HW Notebooks will be collected on Monday.

11/4/11 Classwork:
 * Hand in Gordorama rubric... mass.
 * Q&A
 * Continue LAB: Shoot Your Grade

HW:
 * Post Lab Report on your wiki, due Tuesday... [|Rubric]
 * Test on Monday... Practice [|HERE] (No Answer Key Currently Available). HW Journal due Monday. Wiki ch3 due Wednesday... [|NEW Rubric].

11/5/11 - 11/6/11 Weekend

11/7/11 Classwork:
 * Hand in HW Notebooks for Chapter 3 check.
 * TEST on Ch 3.

HW:
 * Proofread Ch3 wikis, and prepare them for grading this coming weekend. Use this [|NEW RUBRIC].

=Shoot Your Grade= Partners: Maddi S. and Remzi T. Started: 10/25/11 Completed: 11/8/11 __Hypothesis:__ If all of the five hoops and cup are aligned and hanging correctly from the ceiling, the ball should soar through them, then landing in the cup.

__Purpose with Rational:__ The purpose of this lab is to launch a ball from a ball launcher stationed at a 20 degree angle, through five precisely positioned hoops, as well as into a cup. To accomplish this, calculations are necessary for the initial velocity, final displacement of the ball, as well as the (x,y) coordinate of each hoop also including the cup. The assumption is that every launch will be very similar and not hit any of the hoops, so that the ball continues in it's original path.

__Materials and Method:__ Materials provided by Ms. Burns for this lab were, ball shooter, ball, masking tape rolls (hoops), thin black string, measuring tape/sticks, and a plumb bob. The ball shooter was used to shoot the ball, the masking tape rolls were used as hoops for the ball to go through. The measuring tape was laid out on the floor to help find the x coordinates of the masking tape hoops, along with the plumb bob to make sure that the masking tape was put up at the correct displacement from the base of the shooter.

The Procedure used for this lab was to first off verify the initial velocity by shooting the ball a multitude of times and recording the displacement. Then averaging the shots all together using it as the displacement for finding the initial velocity. The next step was to choose the coordinates of each of the masking tape hoops. For each x value for the placement of the hoops chosen, the y value had to be solved for using the equation d=V i t+(1/2)at 2. First the time is solved for using d=V i t+(1/2)at 2, then since time is the same for both x and y, it is allowable to plug the known variables into the same equation for the y displacement. After finding the coordinates hang the hoops in their spots using a measuring tape along with the plumb bob to accurately hang them in the proper position. The cup should then be placed at the average of the displacements. Finally shoot the ball from the shooter at the medium velocity to verify the calculations.

__Observations and Data from Initial Velocity:__ To find the initial velocity from the shooter at a 20 degree angle on the medium setting, the first step is to shoot the ball onto a piece of carbon paper multiple times to get a variety of points. Once the points are measured in relation to the base of the counter on which the shooter was sitting on, average them together to find the average displacement.

Using known variables for both x and y, plus the data collected in to carbon paper displacement test, the height of the counter, and the angle of the projectile; the initial velocity is not hard to find. Plugging in to the equation d=v i t+(1/2)at 2, everything is known but V i t. Solve for V i t, for the X component, then find time using the same equation for the Y component. Finally sub in V i t for the X component to find the resulting velocity.

__Observations and Data from Performance:__ Best Trial (4 hoops): media type="file" key="Shooter Best.mov" width="300" height="300" Trials and Hoops Achieved: __Physics Calculations:__ Previously Known or Assumed Data-
 * Vertical Acceleration is -9.8m/s 2, this is due to gravity and is used as a constant.
 * The Acceleration for the Horizontal motion is always 0, this is because the only force working on a projectile if gravity, which is one of their properties.
 * Theta is 20 degrees, which was assigned
 * Height of desk that the launcher is on; 1.167 m

Sample Calculations: Initial Velocity- X and Y positions for Hoops:

Excel Calculations: __Error Analysis:__ __Conclusion:__ Was the purpose satisfied?
 * Was your hypothesis correct?
 * The hypothesis was correct regardless of the fact that the ball did not make it through all five hoops and into the cup. The ball did manage to make it through four of the five hoops, which shows that the calculations for initial velocity were correct. Also when the ball did go through the hoops it was right in the middle which shows that the center of the hoops were the proper height for the distance from the shooter.

Experimental Error -
 * How much? Where did the error occur? Why did the error occur?
 * The percent error for this lab, overall was quite low. There were, however, some areas where room for error was high. When putting up the hoops there was only one way to adjust it. To adjust the hoops there were strings on either side that needed to be pulled on to make the hoop go up, down, left or right. The strings were not a very exact way of making the height and would sometimes move more than anticipated. A huge source of error was if the strings were pulled on to much, it would create a rut in the ceiling tile, making the string slip because of the weight of the hoop pulling it down. The uncertainty of the shooter was also a maker of error. After each launch, the spring would heat, and then loosen a little making the ball's trajectory a little different each time. The force from the launch would sometimes be so powerful that the shooter would tilt at an angle, which would mess up the next run if it wasn't re-alligned properly.

Implications for Further Discussion -
 * How would you change to lab to address the error? What is a relevant real-life application of this concept?
 * To lesson the impact of error on this lab, the most probable thing to do would be to have stands for the hoops to rest on. It would make it easier for the hoops to stay in place. A hoop stand would be a cane like object, who's legs would move up and down, controlled by a measuring tape type stopper. The hoop would attach to the stand by being inserted into a groove on a flat platform. Also by clamping both sides of the shooter, it would be much more unlikely for the shooter to tilt from the force of the ball being shot.
 * Games like angry birds, or little wing, use projectiles as the main part of their game. They force users to make decisions as to what they want to initial velocity, angle, and displacement to be. This impacts where the bird will hit and if it will destroy the tower. Without this small amount of physics the game wouldn't be fun. Physics gives the user a chance to think about how fast to launch the bird, which is important if the level the user is on is the only thing between losing and physics domination.