Group+5.1-4-EB

Niki and Maddy free fall lab Deanna&Jae Free Fall Lab =Lab: A Crash Course In Velocity= Members: Jae Li, Deanna Magda, Niki Kaiden, Maddy Huddleston Period 4 Due: 9/27/10

For the spark timer: Since the constant motion vehicle is moving at constant speed, the dots made by the spark timer will be spaced evenly apart. The dots made by the fast car will be closer together, while the dots made by the fast car will be farther apart.
 * Hypotheses**:

For the crash demo: If both the fast and slow cars are started at the same time in opposite directions, then they will crash closer to where the slow car began because the fast car will travel a longer distance.

For the catching up demo: The fast car will eventually catch up to the slow car because the fast car is moving faster.

Objectives goes before Hypotheses. 1. In pairs, generate a spark tape and use the data to create a position-time graph to find the average speed of a constant motion vehicle (CMV). 2. Both algebraically and graphically, solve the following 2 problems. which are???? Then set up each situation and run trials to confirm your calculations.
 * Objectives**:

Materials needed: ticker tape, spark timer, a meterstick and tape measure, tape, electronic cars (2)
 * Procedure:**

Test 1
 * 1) Slide your ticker tape, shiny side up, into the spark timer and then tape the end of the ticker tape to your fast electronic car. (make sure when you tape the ticker tape to the car, the car is facing in the direction you want it to move and not toward the spark timer)
 * 2) Make sure the spark timer is set to 10 hz and then turn it on.
 * 3) Turn the fast electronic car on and let the ticker tape run through.
 * 4) Record your data on a spreadsheet.
 * 5) Repeat steps 1 thought 4 with your slow electronic car.

Test 2—Collision
 * 1) Lay your tape measure, cm side up, on the ground and make sure it is //at least// 6 meters long.(You can tape it to the ground so it will not move)
 * 2) Place the front of your slow car at the beginning of the tape measure
 * 3) Place the front of your fast car at the 6 meter mark on the tape measure facing the slow car.
 * 4) At the same time, turn both cars on and mark on your measuring tape where they meet.
 * 5) Record your data on a spreadsheet.
 * 6) Repeat steps 1 through 5 as many times as you see fit, however there should be a minimum of 5 trials.


 * [[image:magda_crash_pic.png]] ||

Test 3—Catching up
 * 1) Lay your tape measure, cm side up, on the ground and make sure it is longer then one meter long. (you can tape it to the ground so it will not move)
 * 2) Place the front of your fast car at the beginning of the tape measure
 * 3) Place the front of your slow car at the 1 meter mark of the tape measure
 * 4) Both your cars should be facing the same direction.
 * 5) At the same time, turn your cars on and mark on your measuring tape where the front of the fast car matches the front of the slow car.
 * 6) Record your data on a spreadsheet.
 * 7) Repeat steps 1 though 6 as many times as you see fit, however there should be a minimum of 5 trials.


 * [[image:magda_catching_up_pic.png]] ||

Data Table with Labeled Headings place in order of collection
 * [[image:crash_data_magda.png width="162" height="108"]] ||
 * [[image:catchup_data_magda.png width="181" height="111"]] ||


 * Fast Car v. Slow Car ||
 * [[image:magda_new_data.png width="355" height="385"]] ||

Caculations: where is graph? avg velocity should be from equation of best-fit line Average velocity

__Fast__ (1.00, 28.24) (2.00, 62.42) (62.42 – 28.24)/(2.00 – 1.00)  34.18 cm/s 0.3418 m/s

__Slow__ (1.00, 17.15) (2.00, 36.61) (36.61 – 17.15)/(2.00 – 1.00)  19.46 cm/s

0.1946 m/s
 * [[file:jae li mathwork.doc]] ||

nice work! Good results, too.
 * Calculations done by Jae Li

Tables and Graphs: (pictures & links)


 * Graph of the slow car vs fast car ||
 * [[image:magda_new_graph.png width="720" height="456"]] ||

oh good! This goes before calcs, since should use slopes. Also, set y-int =0

Discussion Questions:
 * Link to spreadsheet: ||
 * [[file:magdaDATA&GRAPH.xls]] ||

 1. Why is the slope of the position-time graph equivalent to average velocity?  1. The slope of the position-time graph is equivalent to the average velocity because the formula for average velocity is distance divided by time, which is essentially what you get for the slope on a position-time graph

 1. Why was it okay to set the y-intercept equal to zero?  1. Because at zero time, the position is at zero

 1. What is the meaning of the R2 value?  1. It helps with analyzing the information collected. The R2 number is a statistical number that’s given to show how accurate your information was. The higher to 1 the number is, the better. This value should not be under .97 (which translates to 97%).

 1. Where would the cars meet if their speeds were exactly equal?  1. If the cars were going at the exact same speed, they would meet right in the middle of the track. Because they are traveling the same rate, it would take them the same amount of time to go to from one place to the next. For this lab, we used a 6-meter track the cars had to meet on so if they were going the same speed, they would meet exactly 3 meters in. 2. Sketch position-time graphs to represent the catching up and crashing situations. Show the point where they are at the same place at the same time.


 * [[image:catching_up_pt.png]] ||
 * [[image:crash_pt.png]] ||

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 110%;">great!



Sketch velocity-time graphs to represent the catching up situation. Is there any way to find the points when they are at the same place at the same time? There is no way to know where they hit each other on the graph because they are both constant velocities. Being that they are both constant both the lines are horizontal lines at the speed each car was going.
 * [[image:catching_up_vt.png]][[image:webkit-fake-url://358306D0-7075-4BF4-ADBC-EB0765244E7A/image.tiff]] ||

Link to the Sketches:
 * [[file:jaesketches-1.odt]] ||


 * Interpreting your results:**
 * Conclusion:**
 * When using the spark timer we discovered that when set to 10 hz the timer would create 10 dots per second. We measured three seconds worth of data for both the slow car and the fast car. We skipped the beginning dots because we knew that in the beginning the car had to accelerate from zero to its constant speed. At constant speed the cars were not truly going at a constant speed, although the space between each dot was similar it was not exactly the same as the ones before and after it. The distance between dots on the slower car were much closer than the ones made by the faster car. Also the total distance traveled by the fast car in 3 seconds was larger than the total distance of what the slow car traveled in 3 seconds. **
 * When doing the crash demo we predicted that the crash would occur closer where the slow car began because the faster car would be able to travel a longer distance. We laid out 6 meters of measuring tape and placed the fast car at the 6 meters (600 cm) mark and the slow car at the 0 cm mark. Each trial we recorded that the crash occurred between 185.22 cm and 196.75 cm. These numbers are clearly closer 0 cm than they are to 600 cm making our hypothesis true. **
 * According to our ticker tapes our fast car was truly faster than our slow car. Also according to our ticker tapes the fast car had reached a greater distance in 3 seconds than our slow car did. With that information in mind if our fast car was placed behind our slow car it would eventually catch up to the slow car. We set our fast car 1 meter behind our slow car and each trial the fast car caught up to the slow car between 214.94 meters and 220.89 meters. Each trial the fast car did in fact catch up to the slow car. **
 * Error:**
 * When we used the ticker tape for the slow car at one point the spark timer skipped a dot giving us a gap approximately double the usual. Also the cars did not go perfectly straight. When doing the trials we used extra yardsticks to try and guide the cars in a straight line to keep our results as accurate as possible. Also doing the trials it would be impossible to assume that two people would start the cars at exactly the same time therefore that is another possible source of error. Also catching the exact moment of collision or of catching up was difficult adding another source of error.**

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 110%;">nicely thought out and explained. Just missing implications.

= = =Representations of Motion Lab=
 * Members: Jae Li, Deanna Mada, Niki Kaiden, Maddy Huddleston**
 * Period 4**
 * Due: 9/20/10**

Objective:
 * What are the different types of motion? What is the best way to represent the motion?**

Hypotheses:
 * By using the five different methods of measuring motion one will be successful in gaining a clear understanding of direction, velocity, and acceleration of the motion measured and find that the velocity vs. time graphs best represent the motion.**

Procedure:
 * Materials**
 * - Laptop**
 * - USB motion sensor**
 * optional:**
 * - Chair**
 * - Textbooks**
 * Consider taking pictures of experimental setup and/or iMovie of procedure. **


 * Ticker Tape Diagram**
 * 1. Put a piece of tape into the ticker tape machine. The piece should not be longer than a foot. Shiny side of tape should be facing up**
 * 2. Pull in machine and turn it on**
 * 3. After first spark mark is made, pull tape through at different speeds, depending on what trial you are completing**
 * a). To increase motion away and towards: Pull tape through slowly at first and then continue to increase speed.**
 * b). To decrease motion away and towards: Pull tape through fast at first and then continue to decrease speed**
 * c). Constant motion away and towards: Pull tape through without changing the speed at all**
 * d). No motion: Hold tape and do not pull it**


 * Data Collections:**
 * 1. Plug in USB motion detector into laptop and open Data Studio**
 * 2. Hold a flat object in front of the person being motion detected so the motion detector will not pick up the switching movement of your hips**
 * a). Use the same person for each trial so results are consistant**
 * 3. Record the data and person being detected will do different movements, depending on which trail you are completing**
 * a). No Motion: Stand still and do not move**
 * b). Increase speed away or towards: Stay at a constant speed for several seconds then increase your speed**
 * c). Decrease speed away or towards: Start at a fast pace and then slowly decrease your speed**
 * d). Constant speed away or towards: Stay at a constant speed throughout the entire trial**

Data


 * Constant Speed ||
 * [[image:1._CONSTANT2.png]] ||
 * Positive Acceleration ||
 * [[image:2._POS_ACC2.png]] ||
 * Negative Acceleration ||
 * [[image:3._NEG_ACC2.png]] ||
 * No motion ||
 * [[image:4._no_motion.png width="480" height="318"]] ||
 * Changing Direction ||
 * [[image:5._CHANGE_OF_DIR.png]] ||
 * Good graphs.... I wish they were in order. **
 * This graph above doesn't belong here. **

Motion Graphs
 * __No Motion__**
 * v=0, a=0**


 * __Increasing Speed Toward__**
 * <v**
 * <a**


 * __Increasing Speed Away__**
 * v>**
 * a>**


 * __Constant Speed Toward__**
 * <v**
 * a=0**


 * __Constant Speed Away__**
 * a=0**
 * a=0**


 * __Decreasing Speed Toward__**
 * <v**
 * >a**


 * __Decreasing Speed Away__**
 * >v**
 * <a**

Data Analysis and Interpretation

**SIDE NOTE: You can see in the middle of the 3 “no motion” graphs there is a slight change in the strait line, this is because Niki coughed.**
 * 1) **How can you tell that there is no motion on a…**
 * 2) **Motion diagram**
 * 3) **If there is no motion then “a” will equal 0 on a motion diagram and there will be no velocity vector**
 * 4) **Ticker tape diagram**
 * 5) **If there is no motion then there will be a cluster of dots on a ticker tape diagram. In our diagram there are two lone dots showing that the paper did not move through the sparker. (See Ticker Tape picture #)**
 * 6) **position vs. time graph**
 * 7) **If there is no motion then the slope of the line will be a horizontal line at what ever position you are at when not moving. Niki started 1 meter from the motion sensor and as seen on the graph she did not move away from that 1 meter standpoint.**
 * 8) **velocity vs. time graph**
 * 9) **If there is no motion then the slope of the graph will be a horizontal line on the x-axis. Looking at graph 4 you can see that the averages of the peaks equal 0, meaning Niki was not moving.**
 * 10) **acceleration vs. time graph**
 * 11) **If there is no motion then there will be a line on the x-axis. On run 4 you can seen the line on the x-axis.**


 * 1) **How can you tell that your motion is steady on a…**
 * 2) **Motion diagram**
 * 3) **If you have a velocity vector moving in any direction but your “a” is equal to 0 then you know you are moving at a constant speed.**
 * 4) **Ticker tape diagram**
 * 5) **You can tell your motion on a ticker tape diagram is constant when the intervals between each dot or burn are a constant distance.**
 * 6) **position vs. time graph**
 * 7) **If the slope is the same throughout the graph then you know that you are going at a constant speed because the distance per second is constant throughout the whole graph.**
 * 8) **velocity vs. time graph**
 * 9) **If the object in motion is going at a constant speed then the graph will be a horizontal line at that speed. In our graph you can see that Niki was walking at a constant speed because if you were to average the points on the graph they would create a** **strait** **line.**
 * 10) **acceleration vs. time graph**
 * 11) **An acceleration vs time graph of a constant speed will be a horizontal on the x axis or equalling 0 because the acceleration altering.**


 * 1) **How can you tell that your motion is fast vs. slow on a…**
 * 2) **Motion diagram**
 * 3) **If you are going faster then the vectors in your diagram will progressively get bigger towards the direction you are traveling**
 * 4) **Ex. v-> v--> v---> v> v-> v-->**
 * 5) **If you are going slower then the vectors in your diagram will progressively become smaller in the direction you are traveling**
 * 6) **Ex. v--> v-> v> v---> v--> v->**
 * 7) **Ticker tape diagram**
 * 8) **If your ticks or dots on your tape are farther apart then you are going fast, the faster you go the further apart your dots will become**
 * 9) **If your ticks or dots on your tape are closer together then you are going slow, the slower you go the closer together the dots will become**
 * 10) **position vs. time graph**
 * 11) **The larger and steeper your slope is the larger your velocity is, so your position becomes further away from 0 faster.**
 * 12) **The smaller and shallower your slope is the smaller your velocity is, so your position becomes further away from 0 slower.**
 * 13) **velocity vs. time graph**
 * 14) **The larger or steeper the slope is, the larger your velocity is meaning that the faster you are going, the steeper your slope will be.** **X**
 * 15) **The smaller or shallower your slope is the smaller your velocity is meaning the slower you go the shallower your slope will be.** **X**
 * 16) **acceleration vs. time graph**
 * 17) **The faster you are accelerating, the faster your slope is going to rise or fall, creating a steep slope on your graph.** **X**
 * 18) **The slower you are accelerating, the slower your slope will rise or fall creating a shallow slope.**


 * 1) **How can you tell that you changed direction on a…**
 * 2) **Motion diagram**
 * 3) **It does not show a change, it can show slowing down or speeding up but not a change in direction.**
 * 4) **Ticker tape diagram**
 * 5) **You cannot tell if you changed direction on a ticker tape because the tape is only being pulled through the sparker in one direction.**
 * 6) **position vs. time graph**
 * 7) **If you change direction, your line will rise to a maximum and then fall back down. This happens because you are first walking away from the censor, putting a greater distance between you and the censor, so the graph will crawl upwards as time goes on, and then you are walking back so your position away from the censor is decreasing so your line will decrease. This is clearly seen in the “changing directions” graph.**
 * 8) **velocity vs. time graph**
 * 9) **If the line on your graph crosses over the x-axis from the positive side to the negative and vise versa then the you have changed directions. As seen in “changing directions” graph the line was over the x-axis and then crossed under it when Niki starting walking the other way.**
 * 10) **acceleration vs. time graph**
 * 11) **If you are looking at an acceleration vs time graph then you cannot know when you change direction because you are not graphing position or speed, you are only graphing a change in acceleration which could happen at any time, no matter what direction you are in.**


 * 1) **How can you tell that your motion is increasing on a…**
 * 2) **Motion diagram: The acceleration is in the same direction as the velocity vector.**
 * 3) **Ticker tape diagram: The dots start off close together and become more spaced out.**
 * 4) **position vs. time graph: The position becomes greater at a faster rate. The slope is increases. This is because the person is getting farther away from the detector at a faster rate.**
 * 5) **velocity vs. time graph: The slope increases.** **X** **The velocity increases when the person walks faster.**
 * 6) **acceleration vs. time graph: The slope increases. The person speeds up over time and the graph shows this by increasing in slope.** **X**


 * 1) **How can you tell that your motion is decreasing on a…**
 * 2) **Motion diagram: The acceleration is going in the opposite way of the velocity vector.**
 * 3) **Ticker tape diagram: The dots become closer together.**
 * 4) **position vs. time graph: We did negative acceleration towards. The slope was negative.**
 * 5) **velocity vs. time graph: Your velocity will start to come closer to zero.**
 * 6) **acceleration vs. time graph: the acceleration will start to come closer to zero.** **X**

Discussion questions

**i. It is clear visual in which you can determine easily which direction you are going and if you are accelerating vs. staying at a constant speed**
 * 1) **What are the advantages of representing motion using a…**
 * 2) **Motion diagram**

**i. You can determine the acceleration vs. constant speed very easily**
 * 1) **Ticker tape diagram**

**i. This graph is very good for comparing constant and acceleration motion**
 * 1) **position vs. time graph**
 * ii. You can see how far you got in a certain amount of time and if it is constant, the slope of the line is the average speed **

**i. It is helpful with determining whether or not you stayed at an average speed or if you accelerated at one point**
 * 1) **velocity vs. time graph**
 * ii. If your speed is constant, then the slope is the speed of the moving object **
 * iii. You can also determine if there is negative acceleration vs. a positive acceleration **
 * *Basically you can determine everything with this graph (It’s the best!) :D **

**i. You can determine if something is speeding up vs. slowing down**
 * 1) **acceleration vs. time graph**

**i. It is not very detailed and you do not have any specific numbers**
 * 1) **What are the disadvantages of representing motion using a…**
 * 2) **Motion diagram**

**i. With the acceleration, you must be told the direction in which the ticker tape was pulled through the sparker to analyze your information (negative and positive acceleration)**
 * 1) **Ticker tape diagram**
 * ii. You also cannot determine change of direction because there is no change of direction **

**i. It is very relevant graph in which you need a reference to compare it to** **Unclear**
 * 1) **position vs. time graph**

**i. We could not find anything wrong with the velocity vs. time graph** **Not that there is anything wrong, but that all of these have pros and cons...**
 * 1) **velocity vs. time graph**

**i. If you are going at a constant velocity, the graph cannot specify if you changed direction or not**
 * 1) **acceleration vs. time graph**

**i. Position stays the same. Velocity and acceleration equal zero**
 * 1) **Define the following:**
 * 2) **No motion**

**i. Position changes. Velocity stays the same and acceleration still equals zero**
 * 1) **Constant speed**

**i. Position changes. Velocity and acceleration increase** **X**
 * 1) **Increasing speed**

**i. Position changes. Velocity decreases as acceleration goes in opposite direction of the velocity**
 * 1) **Decreasing speed**

Conclusion:

Results:
 * When using the ticker tape we exhibited no motion, constant speed, and positive and negative acceleration. However the ticker tape did not display direction therefore in order to fully understand the tape one must already know the direction of the acceleration being displayed. When the ticker tape displayed a positive acceleration the spacing between the dots increased. When the tape was showing negative acceleration the spacing between the dots decreased. Because the tapes had no way of showing direction they were clearly not the best choice for measuring motion. **


 * Using the position vs. time graph we were able to determine the displacement of the motion. The position vs. time graph showed how close or far we were from the motion detector. The acceleration vs. time graph showed us the rate of acceleration, which could be found by looking at the slope of the line created. We found that the velocity vs. time graphs were the most useful. Velocity vs. Time graphs include direction as well as displacement and speed making them the most valuable form of data for monitoring motion. **

Error:
 * When using the motion detector we had to be careful because of the sensitivity of the motion detector. We had to hold a binder in front of us so that the movement of our hips or knees etc would not throw off the detector. When we were recording the constant speed using the motion detector Niki coughed and that slight movement was recorded in the data. This is true. however, there are more reasons. **

Implications:** Because we were using the motion detector in the hallway if person walked by that could potentially throw off our data even though we had separated ourselves from the other groups in the room. Also if we had a bigger binder or folder to hold while walking it would have been easier to avoid the movement of knees and hips affecting the motion detector.