Ch2_AronskyA

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=**Constant Speed** =

=**CMV Lab** =

**Objective:** What is the speed of a Constant Motion Vehicle (CMV)?

**Available Materials**: Constant Motion Vehicle, Tape measure and/or metersticks, spark timer and spark tape

Hypotheses:
 * The Yellow CMV is moving 1/2m/s and the blue CMV is moving 1m/s
 * The position of time graph will show us how quickly our CMV will travel a certain distance
 * We should measure to the closest millimeter or second decimal place with an educated guess

**__Excel Graphs:__**


 * Yellow Constant Motion Vehicle ||  ||
 *  Time (s) || Position (cm) ||
 * 0.0 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.0  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.1 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">1.38  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.2 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">2.83  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.3 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">4.15  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.4 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">5.62  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.5 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">7.06  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.6 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">8.51  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.7 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">10.08  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.8 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">11.59  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.9 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">13.82  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">1.0 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">14.61  ||
 * <span style="color: black; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Blue Constant Motion Vehicle ||  ||
 * <span style="color: black; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Time (s) || <span style="color: black; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Position (cm) ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.0 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.0  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.1 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">5.35  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.2 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">11.35  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.3 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">18.25  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.4 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">24.95  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.5 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">32.21  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.6 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">39.43  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.7 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">46.73  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.8 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">54.12  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">0.9 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">61.34  ||
 * <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">1.0 || <span style="color: black; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: right;">69.43  ||

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**ANALYSIS:** <span style="font-family: Tahoma,Geneva,sans-serif;">- The R-squared value is how close the data points are to the trend line. The closer it is to .1, the more accurate it is. The reason the graphs have a straight line is because they are moving at constant speed, therefore the change is velocity is constant per time interval. We discussed that the sources of error may include the measuring with the ruler, the different battery lives, the not completely straight path the CMV follows, and where we start calculating the dots on the ticker tape. To improve our results, we can use new batteries, have a leveled floor, use a different flat ruler or a tape measure.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">**Discussion questions**

<span style="font-family: Tahoma,Geneva,sans-serif;">**1.Why is the slope of the position-time graph equivalent to average velocity?** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">- The slope of the line of best fit takes into account all parts and components of the graph; the slope is the equal to the change in y (position) over the change in x (time). Average velocity is also the change in the distance over the change in time.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">**2. Why is it average velocity and not instantaneous velocity? What assumptions are we making?** <span style="font-family: Tahoma,Geneva,sans-serif;"> - Instantaneous velocity is the measure of the speed of a CMV at one instance, the distance between two points, during the specified period of the given time, whereas average velocity is the speed of the CMV over the entire period of time. We use average velocity as opposed to instantaneous velocity because of the fact that the vehicle needs to be in constant motion as it is on the line of best fit, in order to find the velocity at which it moves. We are assuming that that there aren't any extreme instantaneous velocities that could affect the average velocity.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">**3. Why was it okay to set the y-intercept equal to zero?** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">- It is ok to set the y intercept for this type of graph to zero because the constant motion vehicles are starting at certain position, the constant motion vehicle has at this point not moved it was immobile, and than we are to begin our measuring from the first location. If there has been no time and the vehicle has not moved and it is assumed that the constant motion vehicle’s position (cm) should start at zero

<span style="font-family: Tahoma,Geneva,sans-serif;">**4.What is the meaning of the R2 value?** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">- The R2 value is a value that ranges from 0-1. The value itself represents the line of best fit or the perfect fit between the data and the line drawn through them. It represents how close to 100% accuracy the equation of the line of fit is.

<span style="font-family: Tahoma,Geneva,sans-serif;">**5. If you were to add the graph of another CMV that moved more slowly on the same axes as your current graph, how would you expect it to lie relative to yours?** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">- Comparing the resulting graphs of the two CMVs shows that the blue CMV, which was ultimately faster, had a steeper slope than the yellow CMV. The y of the yellow CMV had a lesser value, causing the slope to lie below the slope of the blue CMV.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">**Conclusion** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">We hypothesized that the blue constant motion vehicle would go 1 meter per second but the results showed that the car actually went 67.186 centimeters per second, which is much slower. For the yellow car, we thought the speed would be half a meter per second, which was also faster than the actual 14.6 centimeters per second.A position-time graph explains the speed of an object, which is shown through the relationship of time and position. There are quite a few sources of error that may have contributed to inaccuracies such as the different battery lives; some batteries in a constant motion vehicle could have been used more often, therefore the car would run slower. Depending on the person reading the measurements, people may have had different viewpoints of the ruler marks, thus different measurements were calculated between groups. Another error could have resulted by someone beginning the measurements on the spark tape at different locations, as there wasn’t a constant speed yet when the car first started moving. Ways to minimize these issues could be done by buying new batteries and replacing the old ones from all the constant motion vehicles, using a ruler that would be easier to read like measuring tape or a foot ruler because they lie flat against the spark tape, and using the same leveled floor for each group.

=<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">Homework: Lesson 1 = <span style="font-family: Tahoma,Geneva,sans-serif;">9/8


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.**
 * From our class discussion, I really understood vectors, especially because we learned about them last year in pre-calc. They are simply used to describe a quantity that has both a magnitude and a direction. For example, a car is moving 40 miles per hour North would be considered a vector quantity. Vector quantities are distinguished from scalar quantities because direction is involved.
 * I also understood the concept of speed, which is a scalar quantity and basically just represents how fast an object is going across a distance (ex: 55 miles per hour). While velocity is a vector quantity and requires both a distance AND a direction. It shows the rate at which an object changes position (ex: 55 miles per hour EAST).Velocity is based upon displacement.
 * Instantaneous speed: the speed at a given instant in time
 * Average Speed: average of instantaneous speeds; distance/time
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**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.**
 * I was not clear about the difference of displacement and distance when we first discussed it, but I realized from reading that displacement is a vector quantity as it requires direction. I saw that distance was a scalar quantity because it just involves magnitude. Displacement is different from direction because it takes the direction change into account and can cancel the changes out. The cross country skier example really helped better my understanding.
 * distance is to speed as displacement is to velocity
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What (specifically) did you read that you still don’t understand? Please word these in the form of a question.**
 * I understand everything I read.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What (specifically) did you read that was not gone over during class today?**
 * Everything was gone over in class basically except instantaneous and average speed.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Constant Speed Notes = <span style="font-family: Tahoma,Geneva,sans-serif;">9/9

<span style="font-family: Tahoma,Geneva,sans-serif;">**Average speed**: total distance and total time, can have different instantaneous speeds <span style="font-family: Tahoma,Geneva,sans-serif;">**Instantaneous speed**: speed going at the moment - speedometer <span style="font-family: Tahoma,Geneva,sans-serif;">**Constant speed**: going the same speed the WHOLE time, instantaneous speed is the same
 * <span style="font-family: Tahoma,Geneva,sans-serif;">V = d/t

<span style="font-family: Tahoma,Geneva,sans-serif;">__Types of Motion__
 * <span style="font-family: Tahoma,Geneva,sans-serif;">At rest
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Constant speed
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Increasing speed
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Decreasing speed

<span style="font-family: Tahoma,Geneva,sans-serif;">__1. Motion Diagram__ <span style="font-family: Tahoma,Geneva,sans-serif;">- at rest: v=0; a=0 <span style="font-family: Tahoma,Geneva,sans-serif;">- constant speed: --> --> --> a=0 <span style="font-family: Tahoma,Geneva,sans-serif;"> - increasing speed: -> --> ---> <span style="font-family: Tahoma,Geneva,sans-serif;">- decreasing speed: ---> --> ->
 * <span style="font-family: Tahoma,Geneva,sans-serif;">velocity is the same
 * <span style="font-family: Tahoma,Geneva,sans-serif;">a --> (acceleration points in the same direction as velocity)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">velocity is getting bigger
 * <span style="font-family: Tahoma,Geneva,sans-serif;"><-- a (acceleration points in opposite direction from velocity)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">velocity is decreasing

<span style="font-family: Tahoma,Geneva,sans-serif;">Signs are arbitrary: kind of made up
 * <span style="font-family: Tahoma,Geneva,sans-serif;">up and right --> positive
 * <span style="font-family: Tahoma,Geneva,sans-serif;">down and left --> negative
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Increasing speed - points in same direction as velocity
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Decreasing speed - points in opposite direction as velocity

<span style="font-family: Tahoma,Geneva,sans-serif;">2. __Ticker Tape Diagram / Spark Diagrams__
 * <span style="font-family: Tahoma,Geneva,sans-serif;">used for taking measurements
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Increasing speed: dots get further apart
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Decreasing speed: dots get closer together
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Constant speed: dots stay same distance apart

=<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">Homework: Lesson 2 = <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;"> 9/9


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.**
 * Because there were only 2 topics covered, ticker tape diagrams and vector diagrams and I didn't fully understand ticker tape diagrams, vector diagrams were very clear for me from the class discussion. A vector diagram is used to represent the velocity of an object while it is moving. The size of the vector arrow depicts the magnitude of a vector quantity. If the arrow size is the same, then there is a constant velocity. When the size is getting bigger, that means that both velocity and acceleration are increasing. When the arrow gets smaller, the velocity is decreasing. The concept of acceleration was also understandable for me. When an object slows down, the direction of acceleration is the opposite direction of the object's motion.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**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.**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">I was a little confused about ticket tape diagrams. I couldn't realize visualize them, but from the reading I understood that dots on the tape represent an object's change in position during a specific time. Large spaces in between the dots shows that the object was moving fast, while small spaces indicate the object was moving slowly. When they are evenly spaced, there is constant speed. A changing distance in between dots means that there is a change in velocity, and therefore in acceleration, which is the rate that an object changes its velocity. When there is constant a constant velocity, there is no acceleration.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What (specifically) did you read that you still don’t understand? Please word these in the form of a question.What (specifically) did you read that was not gone over during class today?**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">I understand all of this material pretty well.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What (specifically) did you read that was not gone over during class today?**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Everything was covered in class.

=<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">Representations of Motion =

<span style="font-family: Tahoma,Geneva,sans-serif;">


 * <span style="font-family: Tahoma,Geneva,sans-serif;">The graph above shows a person walking away from the motion detector, then walking towards it. Run #1 represents when the person is walking away from the detector, while Run #2 is representative of the person walking to the detector.

<span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">This graph is representative of the person walking away from the motion detector. Run #1 shows the person walking fast and Run #2 is the person slowly walking away.

<span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The final graph is of a person at rest. They are standing still with their back facing the detector.

<span style="font-family: Tahoma,Geneva,sans-serif;">** Discussion questions **
 * 1) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">How can you tell that there is no motion on a…
 * 2) **position vs. time graph**
 * 3) horizontal line at starting point
 * 4) **velocity vs. time graph**
 * 5) horizontal line at 0
 * 6) **acceleration vs. time graph**
 * 7) horizontal line at 0


 * 1) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">How can you tell that your motion is steady on a…
 * 2) **position vs. time graph**
 * 3) constant slope
 * 4) **velocity vs. time graph**
 * 5) horizontal line
 * 6) **acceleration vs. time graph**
 * 7) horizontal line


 * 1) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">How can you tell that your motion is fast vs. slow on a…
 * 2) **position vs. time graph**
 * 3) the steeper the slope of the line, the faster the object is moving; and vice versa
 * 4) **velocity vs. time graph**
 * 5) the y-values of the horizontal line would be greater on a faster moving object than the y-values on a slower moving object
 * 6) **acceleration vs. time graph**
 * 7) you can't tell if a person is fast or slow on this graph because there is a constant speed, so the acceleration is 0


 * 1) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">How can you tell that you changed direction on a…
 * 2) **position vs. time graph**
 * 3) When walking away from the motion detector, the slope of the line is positive. The distance between the person and the motion detector is increasing. While walking toward, the slope is negative. The distance between the person walking and the motion detector is decreasing.
 * 4) **velocity vs. time graph**
 * 5) The line will reflect over the x-axis when the direction is changed. It was positive while walking away from the motion detector, but negative walking to the detector.
 * 6) **acceleration vs. time graph**
 * 7) You can't tell the change of direction in this graph because acceleration does not keep track of direction; it keeps track of displacement.


 * 1) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">What are the advantages of representing motion using a…
 * 2) **position vs. time graph**
 * 3) You can see the slope, or the change in position over the change in time. It clear to see how far the person is from the motion detector relative to how long they were walking. The slope of the line is the average speed.
 * 4) **velocity vs. time graph**
 * 5) This graph is useful when seeing the velocity difference between a person moving fast and slow. The faster the person is walking, the greater the velocity is. Therefore, it shows the relationship between speed and motion. It also shows you the velocity of an object at a certain interval of time as you are able to see the velocity when a person is walking towards and away from the sensor.
 * 6) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">**acceleration vs. time graph**
 * 7) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">You can determine if something is speeding up or speeding down, thus it is a representation of acceleration that is both increasing and decreasing. It also shows if velocity is negative or positive.


 * 1) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">What are the disadvantages of representing motion using a…
 * 2) **position vs. time graph**
 * 3) I don’t think there is a disadvantage unless the walking path of the person is disrupted, but this graph it doesn’t give you acceleration.
 * 4) **velocity vs. time graph**
 * 5) This graph was not truly accurate because the sensor was sensitive to other movements which interfered with how the graph depicted the lines and created inaccuracies.
 * 6) **acceleration vs. time graph**
 * 7) It doesn’t show the exact velocity, or the change in position of the object over time, thus direction is not shown.
 * 8) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">Define the following:
 * 9) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">**No motion**
 * 10) At rest, the object is not moving
 * 11) 0 velocity and 0 acceleration
 * 12) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">**Constant speed**
 * 13) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">Constant change in position per time interval
 * 14) <span style="color: black; font-family: Tahoma,Geneva,sans-serif;">acceleration is 0

=<span style="font-family: Tahoma,Geneva,sans-serif;">LAB: Acceleration Graphs = <span style="font-family: Tahoma,Geneva,sans-serif;">9/13/11 <span style="font-family: Tahoma,Geneva,sans-serif;">Partner: Brianna Behrens

<span style="font-family: Tahoma,Geneva,sans-serif;">**Objectives:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">What does a position-time graph for increasing speeds look like?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">What information can be found from the graph?

<span style="font-family: Tahoma,Geneva,sans-serif;">**Available Materials:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape

<span style="font-family: Tahoma,Geneva,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**Hypotheses**: <span style="font-family: Tahoma,Geneva,sans-serif;">**Procedure**: <span style="font-family: Tahoma,Geneva,sans-serif;">1) place the track on one textbook to create a slant. <span style="font-family: Tahoma,Geneva,sans-serif;">2) thread spark tape through the spark timer and attach it to the dynamics cart <span style="font-family: Tahoma,Geneva,sans-serif;">3) turn the spark timer on and allow the cart to travel down the track without falling at the end <span style="font-family: Tahoma,Geneva,sans-serif;">4) take out the used spark tape and measure the distance between the first ten dots (0-1, 0-2, 0-3 and so on) <span style="font-family: Tahoma,Geneva,sans-serif;">5) graph the results
 * <span style="font-family: Tahoma,Geneva,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The graph will look like a J curve because of the increasing slope.
 * <span style="font-family: Tahoma,Geneva,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The graph will show the change of position of the cart during a specific time interval

<span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2011-09-13 at 12.49.mov" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data**: <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">Graph of the Acceleration of the Cart Over Time <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:** <span style="font-family: Tahoma,Geneva,sans-serif;">**a)** **Interpret the equation of the line (slope, y-intercept) and the R****2** **value.** <span style="font-family: Tahoma,Geneva,sans-serif;">**b)** **Find the instantaneous speed at halfway point and at the end. (You may find this easier to do on a printed copy of the graph. Just remember to take a snapshot of it and upload to wiki when you are done.)** <span style="font-family: Tahoma,Geneva,sans-serif;">**c)** **Find the average speed for the entire trip.**
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">It is a polynomial equation with a R2 value of 0.99907, which is very close to 100% meaning it's more accurate than the linear R2 value of 0.91725. The linear line doesn't fit best, if there was a constant slope then it would be a linear equation but because the cart is accelerating the speed is not constant and as a result the graph shows a curved line. See graph for more values.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Halfway: 10 cm/s
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">End: 20.75 cm/s
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Speed: distance/ time = 10.85/ 1 = 10.85 cm/s

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">This position time graph contains both the linear and polynomial trend line along our points. The orange line represents the line tangent to the halfway point while the green line represents the line tangent to the last point.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">polynomial equation: y= 8.2662x2 + 2.4565x; R2: 0.99907
 * <span style="font-family: Tahoma,Geneva,sans-serif;">linear equation: y= 8.9613x; R2: 0.91725

<span style="font-family: Tahoma,Geneva,sans-serif;">**Discussion Questions:** <span style="font-family: Tahoma,Geneva,sans-serif;">
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What would your graph look like if the incline had been steeper?**
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">See graph below--> the slope would have been larger and steeper


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**What would your graph look like if the cart had been decreasing up the incline?**

<span style="font-family: Tahoma,Geneva,sans-serif;">


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**Compare the instantaneous speed at the halfway point with the average speed of the entire trip.**
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">They are almost the same value being that the instantaneous speed is 10 cm/s while the average speed is 10.85. The instantaneous speed was taken at the halfway point, showing the speed of the car as it was in the middle of the acceleration process. The average speed is the mean of all the speeds, showing what they average out to be. Therefore, both values show approximately the middle speed, which is why they are so similar.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">**Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?****Draw a v-t graph of the motion of the cart. Be as quantitative as possible**
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif;">Instantaneous speed is the speed the object is at during that specific time. The tangent line only intersects with one point out of the ten on the graph; therefore, when taking the slope of that line (with only that point) you are figuring out the velocity, and the velocity will be the same throughout that straight line because it remains constant.

<span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion**: <span style="font-family: Tahoma,Geneva,sans-serif;">The results of this lab proved our hypothesis to be correct as we originally thought that the graph would have the shape of a “J” and that we would be able to gather information about the cart’s velocity from the results. The slope, or y-value, of the linear trendline was 8.9613x, while the R2 value was 0.91725. The slope of the polynomial trendline was 8.266x2 – 2.4665x, and the R2 value was 0.99907. Therefore, the polynomial trend line better fit our data because the cart was accelerating, thus the line is curving. Many different errors could have had possible effects on the results of this lab; inaccuracies can be due to misreading of the ruler during the process of taking measurements; an unleveled work station, textbook, and ramp; and mistiming of starting the sparktimer. The lab procedures and results can be more accurate by including a second person in the measurement readings, in order to get a more exact number. A flatter workstation would have also corrected another source of human error. Lastly, we could take multiple runs during the lab to minimize the errors from the mistiming of the spark timer.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Homework: Acceleration = <span style="font-family: Tahoma,Geneva,sans-serif;">9/14


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">Acceleration is only occurring if an object is changing it's velocity. It is a vector quantity that shows the rate at which the object is changing its velocity; it doesn't have to do with going fast. If an object is staying at its constant speed, then it's not accelerating. If the velocity is increasing 5 m/s per second then there is a constant acceleration, but the object covers different distances each second interval. I knew that if an object's velocity was decreasing, then the acceleration would be in the opposite direction and will be negative. So when increasing velocity, the acceleration is going in the same direction and will be positive.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">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.
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif;">Seeing the formulas again definitely helped me remember how acceleration is calculated. The reading clarified that when an object is speeding up but in a negative direction (negative velocity), there will be negative acceleration because the acceleration goes in the same direction as the velocity if its increasing. The sample problems helped with this. [[image:http://www.physicsclassroom.com/Class/1DKin/U1L1e2.gif width="263" height="38"]]
 * 5) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 6) <span style="font-family: Tahoma,Geneva,sans-serif;">Can you help clarify how the distance of travel is directly proportional to the square of the time of travel?


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">We went over everything basically but not a lot on positive and negative acceleration.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Big 5 Notes = <span style="font-family: Tahoma,Geneva,sans-serif;">

=<span style="font-family: Tahoma,Geneva,sans-serif;">**Graph Notes** =

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">constant speed ^

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">increasing and decreasing speed ^

=<span style="font-family: Tahoma,Geneva,sans-serif;">Homework: Lesson 3 and 4 = <span style="font-family: Tahoma,Geneva,sans-serif;">__**Lesson 3: Position Time Graphs**__ <span style="font-family: Tahoma,Geneva,sans-serif;">slow rightward constant velocity ||= <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">fast rightward constant velocity ||
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">I understood how to read and graph position time graphs from class. The slope on these graphs is equivalent to the velocity of an object. I knew how to calculate slope before the reading so finding the velocity is simply done by finding the slope (position (m)/time (s) or rise over run). If an object is at rest, there is a horizontal line at the origin so the slope is equal to 0 as there is no velocity because the object is not changing its position. When there is a constant slope, or a straight line, that means there is a constant velocity throughout the time intervals. On the other hand, when there is a changing velocity, that means that the object is accelerating, therefore the resulted graph represents almost a J-curve and can be seen as a polynomial equation because of the curved line. If the velocity is positive, the slope will be positive so if the velocity is negative, the slope will also be negative. The steeper or larger the slope, the faster the object is moving.
 * = <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a7.gif height="125"]]

<span style="font-family: Tahoma,Geneva,sans-serif;">**Constant Velocity** ||~ <span style="font-family: Tahoma,Geneva,sans-serif;">**Fast, Leftward(-)** <span style="font-family: Tahoma,Geneva,sans-serif;">**Constant Velocity** ||
 * ~ <span style="font-family: Tahoma,Geneva,sans-serif;">**Slow, Leftward(-)**
 * = <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a8.gif height="124"]] ||= <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a14.gif height="123"]] ||

<span style="font-family: Tahoma,Geneva,sans-serif;">negative velocity - slow to fast ||= <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">negative velocity - fast to slow ||
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">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.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">I was a little shaky with graphs that have a negative changing velocity and curved lines. The reading put it into words for me that when an object had a small velocity, it would begin with a small slope, and end with a big velocity, hence a big slope. This shows that the object is moving in a negative direction (ex: away from sensor) but is increasing its velocity. It has a negative acceleration because it is going in the same direction as the negative velocity because velocity is increasing. Another thing that happens is an object starts off with a high velocity, a big slope, then ends with a with a small velocity, a small slope. This means that this object is moving in a negative direction but slowing down. As a result, the acceleration is positive because it is moving in the opposite direction of the negative velocity that is decreasing. Seeing the graphs and reading about them really helped me understand negative changing velocity graphs.
 * = <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:http://www.physicsclassroom.com/Class/1DKin/U1L3a16.gif height="136"]]
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">I understand everything.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif;">Everything was gone over.

<span style="font-family: Tahoma,Geneva,sans-serif;">__**Lesson 4: Position Time Graphs**__ > <span style="font-family: Tahoma,Geneva,sans-serif;">
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.**Positive Velocity** - **Zero Acceleration**
 * 2) I also understood how to read velocity time graphs from class. In these graphs, the slope is equal to the acceleration of an object. If an object is at rest, there is a horizontal line on the origin because there is no velocity, thus no acceleration and the slope is equal to 0. So if an object has a constant velocity, the graph will show a horizontal line as there is no increased or decreased speed, therefore, no acceleration (rate at which an object changes position). If an object had a positive changing velocity, then the slope would be positive because of the positive acceleration. But, if the acceleration is negative, the graph has a downward sloping line even if it has positive velocity. By finding the slope of the line, you are able to determine if the acceleration is negative or positive. This expemplifies how the shape of the time graph reveals information about an object's acceleration.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">**Positive Velocity - Positive Acceleration**
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:http://www.physicsclassroom.com/Class/1DKin/U1L4a5.gif height="129"]]

<span style="font-family: Tahoma,Geneva,sans-serif;">
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">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.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">Once again I wasn't too confident with negative changing velocity time graphs. Seeing the graphs all next to each other helped clarify my confusion. If an object is moving in a positive direction (away from sensor for example) then it has a positive velocity, but if it has a negative direction (toward sensor) then it has a negative velocity. When an object has a positive velocity, the line for the graph is above the x-axis in the positive region, so therefore, a negative velocity would result in a line below the x-axis. If a line crosses over the x-axis, it has changed directions. When speeding up, or increasing velocity, the line representing the object's acceleration is changing from near the 0 velocity point to further away. Consequently, when an object is slowing down, decreasing velocity, the line approaches the x-axis.

<span style="font-family: Tahoma,Geneva,sans-serif;">


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">I understand everything.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif;">We didn't go over finding the area on a velocity-time graph but it was simple to understand how to do so from the reading.

<span style="font-family: Tahoma,Geneva,sans-serif;">

=<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 140%;">LAB: Crash Course in Velocity = <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 140%;">(Part 2)

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: large;">9/20 <span style="font-family: Tahoma,Geneva,sans-serif;">Partners: Joe Miller and Brianna Behrens

<span style="font-family: Verdana,Geneva,sans-serif; font-size: 16px;">In this lab we have to find two things. The first thing is we have to find where our two CMV's will meet if they are 600 cm apart. The second thing that we need to find out is if the slow (yellow) CMV is 100 cm ahead of the blue how long and where will the blue CMV catch up.

<span style="font-family: Tahoma,Geneva,sans-serif;">** Available Materials ** : <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Constant Motion Vehicle, Tape measure and/or metersticks, Masking tape (about 30 cm/group), Stop watch, spark timer and spark tape

<span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2011-09-20 at 13.52

<span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2011-09-20 at 13.58.mov" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">**DATA:**

<span style="font-family: Tahoma,Geneva,sans-serif;">Collision
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">trial || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">distance(cm) ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">1 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">125.15 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">2 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">123.36 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">3 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">122.87 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">4 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">127.67 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">5 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">121.52 ||

<span style="font-family: Tahoma,Geneva,sans-serif;">Catching up
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">trial || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">distance(cm) ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">1 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">125.55 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">2 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">126.46 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">3 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">131.86 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">4 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">127.63 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13pt;">5 || <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 13pt; text-align: right;">121.52 ||

<span style="font-family: Tahoma,Geneva,sans-serif;">** Objectives ** :

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Both algebraically and graphically, solve the following 2 problems. Then set up each situation and run trials to confirm your calculations.


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Find another group with a different CMV speed. Find the position where both CMV’s will meet if they start //at least// 600 cm apart, move towards each other, and start simultaneously

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">- Position of the yellow (slower) CMV was 104.32 centimeters, while the position of the blue (faster) CMV was -495.93 cm.


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Find the position where the faster CMV will catch up with the slower CMV if they start //at least// 1 m apart, move in the same direction, and start simultaneously.

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">- The blue CMV (faster) will catch up to the yellow CMV after 126.36 cm.

<span style="font-family: Tahoma,Geneva,sans-serif;">** Discussion questions ** <span style="font-family: Tahoma,Geneva,sans-serif;">
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;"> **Where would the cars meet if their speeds were exactly equal?** **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.**
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">If the speed of the CMVs were exactly equal, this would mean that they would travel the same amount of distance over the same amount of time because speed is equal to total distance/total time. Therefore, in a distance of 600 cm, the cars would pass each other at 300 cm, which is the middle. The CMVs would then have traveled the same distance from their starting point at the same rate. If the cars are 1 meter apart and are going at the same speed, the cars will never meet.

<span style="font-family: Tahoma,Geneva,sans-serif;">


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">**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?**

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;"> <span style="font-family: Tahoma,Geneva,sans-serif;">By using a velocity time graph, it is not possible to see when the cars are in the same place at the same time. The CMVs appear to begin at the same point, yet they are really 100 cm or 1 m apart.

<span style="font-family: Tahoma,Geneva,sans-serif;">Analysis: We can judge how accurate we are by finding the percent of error in this lab. We have to do each trial individually. Percent difference tells us how precise our measurements are.

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">The percent error for the collision problem was between 16-22% which was not as low as we had hoped. <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">The results for the catch up problems were much better than those of the collision and they ranged from 0.6-4.35%.
 * PERCENT ERROR:**


 * PERCENT DIFFERENCE:**



<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;">**Conclusion** <span style="font-family: Tahoma,Geneva,sans-serif;">The results we obtained were not as accurate as we liked them to be, as seen in the percent error. We got the result that the cars would collide at the positions 104.32 cm (yellow car) and -495.73 cm (blue car). The experimental results were much closer to the result we got mathematically for the catch up problem, than the experimental results compared to mathematical result of the collision problem. The faster blue car would catch up to the yellow CMV after 126.36 over the time of 1.82 seconds. We determined this because when we used the percent error formula and plugged in our data the results for the collision scenario were off by between 16-22% while the catch up was between .6-3.5% error. When we ran the trials for the CMVs, the positions we got were slightly off from the ones we calculated algebraically. This was mainly caused because the fast blue CMV would not travel in a straight line, therefore, it prevented us from getting correct measurements where the cars would meet. Other sources of error could have resulted from our original speed measurements during part 1 of this lab if they weren't exact. For example, if there were problems with reading the dots on the ticker tape or if the trial wasn't done on a completely leveled surface, it could have contributed to inaccuracies to this lab. Over time the CMV's could also have been used and in turn the batteries could have depleted some charge which would cause the CMV to move at a slower pace. One of our other sources of error found in our calculations was that for part A, instead of the two distances adding up to 600, it added up to 600.05. This was because we used significant figures, thus cutting off any "useless" decimals.To minimize error, we could have perfected our original measurements of speed to allow us to have an accurate position in this part of the lab. We could also have done more trials with the CMVs to find out where they collided or caught up to each other more precisely. We could have used different measuring techniques to help make our answers a little more exact when estimating the final significant figure. The video taping was also ineffective because we couldn't really tell where the CMV's met from looking at the video. Error could be found in timing and reaction time so we can use a method such as a USB to DataStudio or more advanced technologies to make measurements more accurate. Another way to improve this lab could be done by replacing the batteries of the CMVS with new ones and redoing both parts of the lab. There are many ways to redo this lab to make it more efficient and accurate.

=<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Egg Drop Project =

<span style="font-family: Tahoma,Geneva,sans-serif;">partner: Madison Steele

<span style="font-family: Tahoma,Geneva,sans-serif;">**Description** <span style="font-family: Tahoma,Geneva,sans-serif;"> - Our final project consisted of a cone made of paper with 3 straws going through the middle and 3 straws going through the top of cone. The straws directly on top of each other were taped. We also made a double parachute made of two pieces of paper and attached it to the cones with string.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Calculations**

<span style="font-family: Tahoma,Geneva,sans-serif;">**Results/Analysis** <span style="font-family: Tahoma,Geneva,sans-serif;"> Our egg was completely intact after the drop. Originally, our device was made of a paper cone that was stuffed with newspaper for cushioning and had a piece of paper for a parachute. This device had weighed much more and the egg had cracked once it hit the ground. We decided to create a structure that would not allow the egg to ever hit the floor. The addition of straws ensured that the egg would never be on its side, and thus not crack. There was low air resistance because of the double parachute, which was seen through the acceleration as it was 4.8 m/s2 compared to the maximum acceleration rate of 9.8 m/s2.

<span style="font-family: Tahoma,Geneva,sans-serif;">**What would we do differently?** <span style="font-family: Tahoma,Geneva,sans-serif;"> We could try to make the device have an even lower mass of 28 grams so it wouldn't fall as fast, but other than that I would keep our structure the same because it was effective in preventing the egg from cracking.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Homework: Lesson 5 = <span style="font-family: Tahoma,Geneva,sans-serif;">10/3

<span style="font-family: Verdana,Geneva,sans-serif;">**Topic Sentence**: Free fall is an object moving under influence of solely gravity. All objects free fall at the same rate of 9.8 m/s/s regardless of their mass. Any object that is being acted upon only by the force of gravity is said to be in a state of ** free fall **.
 * Introduction to Free Fall **
 * Free-falling objects do not encounter air resistance.
 * All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s

Free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, so a [|ticker tape trace] of its motion would depict an acceleration. 9.8 m/s/s, is known as the ** acceleration of gravity ** - the acceleration for any object moving under the sole influence of gravity. The symbol ** g **denotes it.
 * The Acceleration of Gravity **

A position versus time graph for a free-falling object is shown below. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. A velocity versus time graph for a free-falling object is shown below.
 * Representing Free Fall by Graphs **

Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. The velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen. The formula for determining the velocity of a falling object after a time of ** t ** seconds is ** v **** f **** = g * t ** The distance fallen after a time of ** t ** seconds is given by the formula : ** d = 0.5 * g * t **** 2 ** 9.8 m/s/s is the same for all free-falling objects regardless of how long they have been falling, or whether they were initially dropped from rest or thrown up into the air. Free-fall is the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. More massive objects will only fall faster if there is an appreciable amount of air resistance present. The acceleration of an object is directly proportional to force and inversely proportional to mass. Thus, the greater force on more massive objects is offset by the inverse influence of greater mass. Subsequently, all objects free fall at the same rate of acceleration, regardless of their mass.
 * How Fast? and How Far? **
 * The Big Misconception **

= Free Fall Lab = 10/4

<span style="font-family: Tahoma,Geneva,sans-serif;">**Partner**: Brianna Behrens <span style="font-family: Tahoma,Geneva,sans-serif;">**Objective**: What is acceleration due to gravity?

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">**Materials**: Ticker Tape Timer, Timer tape, Masking tape, Mass, clamp, meterstick. <span style="font-family: Tahoma,Geneva,sans-serif;">**Procedure:** Tape ticker tape to a small 100 g circle weight after putting the ticker tape through a spark timer. Hold the spark timer and the weight over the railing in the main lobby. Then, drop the weight to send the ticker tape through the spark timer until the weight hits the ground. Measure the distances from the beginning of the ticker tape's dots to each dot. Record these distances and use excel to graph our results.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Hypothesis**: Acceleration due to gravity should be 9.8 m/s/s. The velocity time graph tells you the acceleration due to gravity from the slope of the line, as the slope of a v-t graph is equal to acceleration, and the graph should look like:


 * Data:**

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations:** <span style="font-family: Tahoma,Geneva,sans-serif;">- sample instantaneous velocity and mid time calculations <span style="font-family: Tahoma,Geneva,sans-serif;">- the percent error calculation came out to be 8.81% <span style="font-family: Tahoma,Geneva,sans-serif;">- the percent difference calculation came out to be 11% **Graphs:**  <span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:**
 * Class Data:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The position-time graph has a polynomial trendline with a very high R2 value of .99999, showing that our results are very good. We were able to derive the polynomial equation y=Ax2+Bx from the d=1/2at2+vit equation. This is why A=1/2acceleration and B=initial velocity. As a result our acceleration was 891.2 cm/s2 which is very close to the acceleration found from our v-t graph. Our initial velocity on the x-t graph was 83.709 cm/s, which is also similar to the 82.894 cm/s found on the v-t graph.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Our velocity-time graph had a very high R2 value of .99892, which is close to desired 1.0 value. The experimental acceleration, which is the slope of the velocity, is 894.54 cm/s2, compared to the theoretical is 981 cm/s2. The slope is found from the equation of the linear trendline which is y=895.54x+82.8984, following the form y=mx+b. B, the 82.984 is the initial velocity. We got y=mx+b equation from the Vf=at+Vi, explaining how b=Vi. The initial velocity should be zero but is not because the timer and the drop of the object might not have been at the same time, the object could have been in motion when the spark timer made the first dot.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">**Discussion Questions:**

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;"> **1.Does the shape of your v-t graph agree with the expected graph? Why or why not?** <span style="color: #000000; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: left;"> The shape of the velocity-time graph was similar to the one predicted in our hypothesis. However, this graph has a positive slope because we used positive data (velocities), showing that the object moving in the opposite direction. The expected graph was hypothesized to have a negative slope. However, the shape of the trendlines are the same as they both accelerate. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;"> **2. Does the shape of your x-t graph agree with the expected graph? Why or why not?** <span style="color: #000000; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: left;"> The shape of the position-time graph does match the expected graph. There is a changing velocity, thus there is acceleration, which in this case is 9.8 m/s2. We predicted that the shape of the graph would be a “J” curve to show an increased velocity. After graphing the data, we were able to see that we were correct in our prediction. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;"> **3. How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)** <span style="color: #000000; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: left;"> The class average was 805.9 cm/s2, compared to our 894.54 cm/s2 result. Our percent difference was 11%, which does show that our value still falls within the 20% difference range. The results showed that the falling object’s acceleration was lower than the value of “g” at 981 cm/s2. The average is lower than the acceleration of gravity measurement because different groups had lower values as human error played a role in affecting the acceleration. Calculations show that the smallest percent difference was 0.16% and the largest was 12.59%, therefore, our percent difference was on the higher end of these percentages. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;"> **4. Did the object accelerate uniformly? How do you know?** <span style="color: #000000; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: left;"> By looking at the velocity time graph, we are able to see that the object did basically fall in a consistent rate. The acceleration is approximately uniform because acceleration is equal to the slope of the velocity time graph, thus there was almost a constant slope shown in the trendline. As a result, we can assume that the rate was almost uniform. If it had been completely constant, the linear trendline would have an R2 value of 1 but ours was extremely close as it was 0.99892. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 90%;"> **5. What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?** <span style="color: #000000; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 90%; text-align: left;"> Free fall is an object moving solely on the influence of gravity, but in this lab, it is hard to make gravity have the only impact. During the experiment, we had to hold the tape to make sure it was straight when the object would fall, while another person held the spark timer and dropped the weight. This caused friction between the ticker tape and the spark timer, causing the acceleration to go at a slower rate. Thus the results would be expected to be lower. The person holding the tape could have also affected the object’s fall, adding to inaccuracies. We don't know when the spark time made a dot, it could have already been moving so the initial velocity might have not been zero. It might have been in motion, but was not moving that quickly.The acceleration due to gravity could have been higher due to mistaken measurements. <span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion** <span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: left;">When creating a hypothesis for this lab, we had concluded that the data would form a linear line that would be representing an increasing velocity toward the origin in the velocity time graph. This hypothesis ended up being only somewhat correct, because the velocity-time graph actually provided data showing that the velocity was increasing away from the origin because we had positive data of the velocities. Since we truncated the negative values, the v-t graph was in a positive direction. We also hypothesized that the position-time graph would look like it was increasing away from the origin in an upward curve, which ended up being the way that our x-t graph looked like. We predicted that the graph would look like this because the slope would show an increased velocity over time. The slope of our line in the velocity time graph was 894.54 cm/s/s, which is equal to the acceleration. However, the slope was theoretically supposed to be approximately 981 cm/s/s, so the percent error was 8.81% and the percent difference was 11%. The percent error was not as low as we wanted it to be due to experimental errors during the lab procedure. The biggest problem came from the friction between the tape and the spark timer. When releasing the tape through the timer, a person was holding the tape to keep it straight, therefore, the tape was moving more slowly each time the timer made dots, skewing our data. As a result, gravity was not the sole influence on the free fall object. The first dot on the ticker tape wasn't precise as the free fall object began its drop because it could have been made when the object was already in motion. When we were measuring the distance of each dot on the ticker tape, which was taped to the ground, the measuring tape or the spark tape could have moved slightly because they were relatively long, throwing off our data. While using the measuring tape, we had to estimate the hundredths value, also creating inaccuracy. In order to change this experiment to address the errors, it would be helpful to have a more precise way of measuring the change in position. For example, an electronic device could have picked up how much tape had passed through the timer without actually making contact with the tape, and the results could have been recorded on a computer. This would also solve the inaccuracies caused by friction when measuring, and we wouldn't have to use measuring tape to find the distance between the dots. Then our experiment could have been even better!

Quantitative Graph Interpretation (D, E, F, G) D.  E.  F.   G.

= Free Fall Notes =



<span style="font-family: Tahoma,Geneva,sans-serif;">Class problem: