Ch2_GirginL

=CMV Lab= toc 9/6/11 Lerna Girgin, Sarah Gordon

Objective: What is the speed of a Constant Motion Vehicle (CMV)? Hypothesis: The CMV travels at 12 cm per second.



Discussion questions It is equal to the average velocity because the slope of the line is the same as the speed. (Speed= distance/ time) It was not instantaneous velocity because we are calculating the speed from the beginning to the end, instead of each individual point in between. We are assuming that the car is traveling at a constant speed. It was okay to do that because we started at time zero and worked all the way up to one second. This way, our distances would start at zero and work its way up too. It shows how well the line of best fit actually fits the data. You want the R squared value to be as close to 1 as possible, so we had a good R squared value (.99839) For the graph of another CMV that moved slower than ours, the line on that graph would be slanted farther down. It would take up more time to get to a specific speed compared to our CMV.
 * 1) 1. Why is the slope of the position-time graph equivalent to average velocity?
 * 1) 2. Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * 1) 3. Why was it okay to set the y-intercept equal to zero?
 * 1) 4. What is the meaning of the R2 value?
 * 1) 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?

Conclusion <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">After obtaining the results for the lab to test the speed the CMV traveled at, my hypothesis was proven wrong. For the yellow CMV labeled “slow”, the result was that the vehicle traveled at a speed of 12.897 meters per second. These results did not comply with my hypothesis created at the start of the lab, which stated that the CMV would travel at a speed of one foot per second. The actual results came out to show that the CMV traveled __ faster __<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> than what my hypothesis suggested. According to the data from the lab, the CMV was at 1.11 meters at .1 seconds, and at one second, it traveled 13.14 meters, which equals to 43.11 feet. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Like any experiment, errors in the results were inevitable during the lab for a few reasons. To start, the CMV did not have full batteries. This impacted the speed of the car because it was not at its fullest potential, throwing off the more accurate results. In addition, the half-meter stick that was used was thick and it became hard to read the measurements on the paper. This also made it difficult to line up the ruler from 0 to the corresponding number. Furthermore, the first several dots did not have the same intervals because the CMV at that time was just powering up. These intervals should not be used in the lab because they are not constant and would throw off the results. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">If this lab were redone, a few things would have to be changed. Before turning on the CMV with the spark timer, the batteries would be replaced with new, unused ones so that the CMV could travel at its fasted potential speed. The half-meter stick that was used would have to be replaced with a regular one-foot ruler. This ruler would be thinner and be about the same level as the paper, making it easier to read the measurements. It would also help in lining up the 0 of the paper with the first centimeter line on the ruler. Also, when measuring the spark tape, the first several dots would not be measured, but the next several dots because these dots would all have the same intervals. This would show more precise measurements for the graph because the objective is to figure out the speed of a //constant// CMV. = =

=Class Notes Graph Shapes 9/7/11= =<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Class Notes: Constant Speed = <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">The differences between:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"><span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">average speed - total distance over total time

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"><span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">constant speed - find it by look at the speedometer, the current speed

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"><span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">instantaneous speed -the speed at any given instant in time

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">***Equation for all of them is v = change in distance over change in time -** **units are m/s***

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Types of Motion: <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1. at rest <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2. constant <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3. increasing <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4. decreasing

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">These can be represented with a motion diagram

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">motion diagram <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">v = 0 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">a = 0

<span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">2. constant speed to the right would look like this <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">v v v <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">> --> > <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">a=0

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">you're not changing the speed so there is no acceleration

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">velocity looks the same distance apart because it is the same

<span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">3. increasing speed would look like this <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">v v v v v <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">---> > --> ---> ---> <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">a> <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">acceleration points in the same direction as velocity

<span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">4. decreasing speed <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">v v v <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">-> --> > <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"><-- a <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">acceleration speed points opposite direction from velocity

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Increasing speed down would make the arrows face downward <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">the sign for velocity would be negative and so would the acceleration if speed was increasing and direction was negative

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Signs are arbitrary (random) = = =<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Homework 9/8/11 Lesson 1: ABCD =
 * <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: left;">1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.==

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: left;">From our class discussion I understood the difference between scalars and vectors. Scalars have to with quantities or size and do not involve words that describe direction. If you want to talk about someone moving from point A to point B, you would use numbers to describe the distance and the distance only. Vectors are different because they are descriptions of displacements, or the end result from point A to point B. To describe this change, you would use words like the student moved 5 yards to the back of the classroom.

2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: left;">From the homework, I understand the concept of having no displacement much better. Before, I thought that you would not have a displacement if you stayed where you were, but it also works if you travel a distance but come back to where you started. The teacher diagram helped me understand this because it showed how going one place, but then retrieving your steps can leave the displacement being zero. This is known as canceling the direction, which in turn makes the displacement zero.

3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: left;">How do you find the resulting displacement and distance of travel of a certain object or person when the information is on a number line?

4. What (specifically) did you read that was not gone over during class today?

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: left;">When an object often goes through changes in speed, that is when you need to find the //average// velocity or speed. || = = =<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Homework 9/9/11 Lesson 2: A,B,C = <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;">2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding. <span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;">When I was reading about ticker tapes, the caption near the diagram explained that the farther the dots are apart, the faster the object is going. In class, I thought that if the dots were close, the object was going fast. This is mainly because I didn't really understand how the ticker tape was used. I thought that the dots intervals were dependent upon how fast the spark timer was going, but now that website explained the intervals, I fully understand it now.
 * <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;"><span style="font-family: arial,helvetica,sans-serif;">1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. <span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 110%; text-align: left;">From the class notes I understood how the vector diagrams worked. A vector diagram presenting accelerating speed shows the object a few times with one arrow on each drawing pointing to the direction the object is moving towards. The arrows start out small and become larger and larger with each picture. Above the arrows are V's that stand for velocity. In addition, a vector diagram presenting constant speed shows the object and its arrows at the same length, expressing how its speed remains the same.



<span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;">3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question. <span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;">Is motion always represented with diagrams or sometimes with formulas? <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;">4. What (specifically) did you read that was not gone over during class today? <span style="color: #ff0000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 130%; text-align: left;">On the website I saw a picture of an object being thrown in the air on a vector diagram. The arrows aligned in the form of how the object was formed. <span style="color: #000000; display: block; font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px; text-align: left;"> || =<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Motion on Graphs =

<span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a velocity graph, you know there is no motion because there is one line that has no outliers. <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On an acceleration graph, the line would also be straight with no outliers.
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">How can you tell that there is no motion on a…
 * 2) Position vs. time graph-
 * 3) In my graph, there was one line that extended to the length of time, in seconds, my partner was standing for. Also, the line was perfectly straight and was comprised of dash marks.
 * 4) velocity vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">acceleration vs. time graph

<span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a position time graph, the line would be diagonal and depending on the speed, the diagonal line would either be steeper or flatter. <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a velocity graph, you know that your motion is steady when the line never rises or falls. <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On an acceleration graph, you know that your motion is steady when the line also never rises or falls.
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">How can you tell that your motion is steady on a…
 * 2) position vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">velocity vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">acceleration vs. time graph

<span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a position graph, you know that your motion is fast vs. slow because when the object is moving fast the line is shorter, but when the object is moving slow, the line is spread out farther. Also, when your object is moving fast, the line will increase its position on the graph faster than when the object is moving slow the line will increase its position slower. <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a velocity graph you know your motion is fast because the dots on the line are closer together, but the line on a velocity graph going slow would have its dots spread farther apart.
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">How can you tell that your motion is fast vs. slow on a…
 * 2) position vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">velocity vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">acceleration vs. time graph

<span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a position graph, if you change direction, there would be two lines. If the two directions were moving away from something and toward something, one line would be going from left to right going down, and the other would be going left to right going up. In other words, moving away from an object is positive, and moving towards an object is negative. <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On a velocity graph, you can tell you changed direction if there are two lines, one over the zero mark, and one under the zero mark. Where the first line ends, the second line, where you changed direction, would start. <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">On an acceleration graph, there would be two lines, each a different color on the zero mark line.
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">How can you tell that you changed direction on a…
 * 2) position vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">velocity vs. time graph
 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">acceleration vs. time graph


 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">What are the advantages of representing motion using a…
 * 2) position vs. time graph
 * 3) With a position graph, the advantage is seeing whether it object is moving away or towards something.
 * 4) velocity vs. time graph
 * 5) With a velocity graph, you can see whether your speed is constant or if it is increasing or decreasing.
 * 6) acceleration vs. time graph
 * 7) With an acceleration graph, you can see if the object slowed down or sped up during the move.


 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">What are the disadvantages of representing motion using a
 * 2) position vs. time graph
 * 3) The disadvantage with a position graph is that it doesn't show acceleration.
 * 4) velocity vs. time graph
 * 5) Because the sensor picked up interferences, this graph showed outliers and the path of other objects.
 * 6) acceleration vs. time graph
 * 7) In an acceleration graph, velocity is not shown or position change.


 * 1) <span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">Define the following:
 * 2) No motion- This is when the object is not moving, or at rest and because of this there would be 0 acceleration and velocity.
 * 3) Constant speed- This is when an object moves with the same speed throughout its path.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Our graphs:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Lab: Cart on an Incline = <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">9/13/11 <span style="font-family: 'Times New Roman',Times,serif;">Lerna Girgin, Sarah Gordon

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Objectives <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Hypothesis: <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">We think that the graph's slope will be steeper as time (x) increases.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">What does a position-time graph for increasing speeds look like?
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">What information can be found from the graphs?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">media type="file" key="labvid-1.mov" width="300" height="300"



<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Analysis:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**a)** **Interpret the equation of the line (slope, y-intercept) and the R2 value.** The y intercept shows the point right before the cart started moving down the track. The R squared value shows how well the polynomial graph fits the data. IN this case, the polynomial graph fits really well because it is close to 1. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">b) Find the instantaneous speed at halfway point and at the end. <span style="font-family: 'Times New Roman',Times,serif; font-size: large; line-height: 27px;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Halfway point = 20 cm/s
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">End point = 150 cm/s

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**c)** **Find the average speed for the entire trip.** The average speed is total distance/ total time. The total distance= 23.27mm and the total time is 1 second. Therefore the average speed is 23.27mm/s

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Discussion Questions:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">If the incline was steeper the graph would look like this:
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">What would your graph look like if the cart had been decreasing up the incline?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">The instantaneous speed at the halfway point was 20 cm/s while the average speed of the entire trip was 23.27 cm/s. The instantaneous speed was less than the average speed of the entire trip which is normal because the car accelerated the farther it went down the incline. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">The instantaneous speed is the slope of the tangent line because it calculates the velocity at the half point mark. <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px; line-height: 23px;">
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Draw a v-t graph of theof the cart. Be as quantitative as possible.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Don’t forget to write a brief conclusion. (Discuss, in essay format: What results did you get? Was your hypothesis accurate? (Be specific, using data from the lab to support claims.) What sources of error may have contributed to inaccuracies? What could you do to minimize these issues if you had to redo this lab?)**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Our hypothesis was that the position time graph would have a steep line because each interval would be constant. This was proven wrong because the cart had accelerated as it moved down the incline. From our data, we found that at .2 seconds, the cart moved to 1.77cmm, but at .3s it moved 3.17 cm. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> If this were a linear graph (if the cart remained at constant speed) the difference between each interval should be around 1.4 mm. However, the y value (distance) increase as time increases. So it makes sense that the interval between time= .8s and time=.9s, the distance increased to 3.7cm instead of 1.4cm. In the end, our graph ended up having a polynomial fit, with a slope 18.097 and a y intercept at 0. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">To get more precise results, the class should have had the books all laying in the same direction. Not having the books in the same direction could create some differences because the incline would be steeper if the track is right on the top of the book. For that same reason, we should have measured the book and put the track at the halfway point of the book. Also, if the person holding the cart accidently applied force to the cart while letting go it could have changed the slope of the line. As always, measuring can generate error. One way to minimize inaccuracy in measuring would be to have both lab partners measure the distance, instead of just one person doing it.

=Class Notes: Kinematics 9/14/11=



=<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Homework 9/14/11 Lesson 1: E =
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. I already understood the difference between constant acceleration and constant velocity. Constant acceleration means that an object is increasing its speed in the same interval throughout, thus it is called constant. An object having constant velocity, however, is not increasing its speed. It is staying at its current speed throughout the move. In a car, the constant velocity can be seen on a speedometer.
 * 2) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding. The reading clarified what the use of negatives and positives in acceleration really mean. In class I thought that a negative acceleration meant that the object stopped moving, therefore it became negative. Now I know that a negative acceleration means that whichever direction the object was originally moving, it is now moving away or backwards from it.


 * 1) What (specifically) did you read that you still don’t understand? Please word these in the form of a question. How do you find the square relationships between x and y values?
 * 2) What (specifically) did you read that was not gone over during class today? Free-falling objects and what types of accelerations they could have (constant or accelerating speed)

=Class Notes 9/15/11=



= Homework 9/15/11 Lesson 3: ABCDE Lesson 4: ABCDE =

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. You get a negative velocity from a negative slope. You get this slope by picking two coordinates from the line and use rise over run. You get a positive velocity from a positive slope. You also get this from using the rise over run slope.





2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding. I wasn't sure what a curved line on a graph meant and a straight line meant. I thought that you could use either to plot your data.

3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question. Why is a negative acceleration defined as moving in the negative position but speeding up? Same for positive acceleration.

4. What (specifically) did you read that was not gone over during class today? Positive acceleration on a velocity time graph was moving in the positive direction and speeding up.

= CMV Lab Part II = 9/20/11 Lerna Girgin, Sarah Gordon, Jake Greenstein, Katie Dooman The two CMVs will catch up at 186.87 cm in 6.74s. A) When the yellow (fast) and the yellow (slow) CMVs were positioned 600 cm or 6 m apart, the crashed or intersected at 120 cm. B) When the yellow (slow) CMV was positioned 1 m ahead of the faster CMV, the faster CMV caught up to the slower one at 150 cm.
 * Hypothesis:** The two CMVs will crash at 190.5 cm in 14.77 s.
 * Results**

Lab Calculations



Data Table Catch-Up || Percent Error Intersection || Percent Difference Catch-Up || Percent Difference Intersection ||
 * || Intersection || Catch-Up || Percent Error
 * Experimental || 190.5 cm || 186.8 cm ||  ||   ||   ||   ||
 * Test 1 || 210 cm || 150 || 19.70 || 10.24 || 2.44 || -2.69 ||
 * Test 2 || 200 cm || 152 || 18.63 || 5.00 || 1.14 || 2.20 ||
 * Test 3 || 205 cm || 160 || 14.35 || 7.61 || 4.07 || 0.24 ||
 * Test 4 || 203 cm || 153 || 18.09 || 6.56 || 0.50 || 0.73 ||
 * Avg. Experimental || 204.5 || 153.75 ||  ||   ||   ||   ||

Crashing media type="file" key="crashing video.mov" width="300" height="300"

Crashing (close up)

media type="file" key="Movie on 2011-09-20 at 13.47.mov" width="300" height="300"

Catching Up

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1. If the speeds of the cars were exactly equal and they were positioned apart 600 cm or 6 m, they would meet up at 300 cm or 3 m. This would work with any two objects positioned apart and having the same velocity.
 * Discussion Questions**

2.



3.



**Conclusion:** Before starting the experiment with the CMVs, our group created hypotheses for when and where the CMVs would crash and when and where one CMV would catch up to the faster one. Our hypothesis for when the CMVs would crash was at 190.5 cm in 14.77 s. Although our equations for this hypothesis were logical, the actual results with the CMVs were a bit different. Our predicted 190.5 cm was a little higher than where the CMVs actually met up at which was 120 cm. Our hypothesis for when the one CMV would catch up to the other was at 186.87 in 6.74 s. Again when we tried our experiment with the actual CMVs, our results came to be 150 cm. The possible reasons our calculations and actual results were different could be because one of the CMVs, the yellow, fast one, didn't go in a straight line and it was hard to see where the point where they intersected was exactly. Another reason could be because the CMVs weren't running on full batteries. If they were, their velocities might have proved to catch up and crash at the expected point. Also, the error could have come from placing the back of the yellow (slow) CMV at 6 m instead of the head being there. If the head was placed at 6 m the catch up time and position would have been later on instead of 150 cm. If we could redo this lab, we would put both of the SMVs on the metal track that was available in the classroom. That way, the yellow fast CMV could only go in a straight path. Second, we would put new batteries in both CMVs so they would move at their highest potential velocity. Third, we would place the head of the yellow (slow) CMV at 6 m instead of the back.

Errors:



=Egg Drop Project= 9/28/11 The project was successful in keeping the egg intact throughout the fall which lasted 2.18 seconds. :)
 * Results:**

//Calculation of "a"//
 * Analysis:**

//Comparison of acceleration to 9.8 m/s/s// When an object is free falling, it is said to always have an acceleration of 9.8 m/s/s, however, this was not true for our final project. The project had an acceleration rate of 3.58 m/s/s when it was dropped from the second floor. This is less than 9.8 m/s/s because our project had a parachute which didn't allow for a big acceleration. It only accelerated this much because the parachute slowed it down and allowed it float to the ground.

//What would be done differently?// Because our project was able to keep the egg intact when it was dropped, we wouldn't change much about the project except maybe its weight. Its weight now is 84.44 g. Instead of using 4 straws on each side, we could have used 3 still making sturdy, but lighter in weight.

=Homework 9/3/11 Lesson 5=


 * TOPIC SENTENCE**: The motion of free fall depends only on gravity.

A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of ** free fall **. There are two important motion characteristics that are true of free-falling objects:
 * 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 (often approximated as 10 m/s/s for //back-of-the-envelope// calculations)

Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a [|ticker tape trace] or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an [|earlier lesson], that if an object travels downward and speeds up, then its acceleration is downward.

Another way to represent this acceleration of 9.8 m/s/s is to add numbers to our dot diagram that we saw [|earlier in this lesson]. The velocity of the ball is seen to increase as depicted in the diagram at the right.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 13pt;">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 <span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: center;">** v **** f **** = g * t **

<span style="font-family: 'Times New Roman',Times,serif; font-size: 13pt;">The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by use of a formula; the distance fallen after a time of **t** seconds is given by the formula. <span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: center;">** d = 0.5 * g * t **** 2 **

<span style="font-family: 'Times New Roman',Times,serif; font-size: 13pt;">The answer to the question (doesn't a more massive object accelerate at a greater rate than a less massive object?) is absolutely not, if we are considering free-fall. More massive objects only fall faster if there is air resistance present. <span style="font-family: 'Times New Roman',Times,serif; font-size: 13pt;">All objects free fall at the same rate of acceleration, regardless of their mass.

Class Notes on Free Fall 10/3/11



= = =__FreeFall Lab__= October 4, 2011


 * Objective:** What is acceleration due to gravity? What does a velocity-time graph of the falling object look like? How can you get acceleration due to gravity from a velocity-time graph?
 * Hypothesis:**
 * This type of acceleration is 9.8 m/s/s
 * The V-T Graph would look like this


 * By using the above graph you can find the slope and get the acceleration.

Data:

Graphs X-T Graph



V-T Graph



Sample Calculations Analysis

Looking at the equations of the V-T and the X-T graphs, we saw that our R squared value was decent for both. The V-T graph had an R squared value of .972. The X-T graph had an R squared value of .9972 which is a really good fit. Since slope (m) on a V-T graph exhibits acceleration, the acceleration we achieved from the falling metal was 708.55 cm/s/s. The slope of an X-T graph shows velocity so the velocity we got for the falling metal was 34.49 cm/s. The B value we got for the V-T graph was -91.659 which resulted from the time it took to react. The B value for the X-T graph was 3.88 because the spark timer did not start putting in the dots when the object was falling, due to reaction time.

Discussion Questions


 * 1) The shape of my V-T graph did not agree with the expected graph because unlike the actual graph, mine had a negative slope. The V-T graph from the experiment had a positive slope but the trend line still came up to be straight.
 * 2) The shape of my X-T graph matches because it is a curved like starting with a small slope to a higher slope. This makes sense because as the object is falling and falling, the acceleration increases.
 * 3) The percent difference we got compared to the class average was 12.45% whereas the class average was 805.9. This average acceleration is largely due to friction.
 * 4) Yes, the object accelerated uniformly and you can know this by looking at the R squared value.
 * 5) There really isn't anything one could do to cause acceleration to be higher than it should be because it is acted upon the force of gravity, which doesn't change. A factor that would make acceleration lower than it should be could be friction due to someone holding the ticker tape as the object was sliding through the spark timer.

Conclusion

Before starting the lab, my three hypothesizes were that the acceleration of the falling object would be 9.8 m/s/s, the V-T graph would have a negative slope, and by looking at the V-T graph you could find acceleration by using the slope. My hypothesis about the acceleration being -9.8 m/s/s was wrong and the actual results came to be 705.55 cm/s/s. My expected V-T graph was also wrong and the actual V-T graph came out to have a positive slope. My hypothesis about finding acceleration was correct because you can find acceleration by looking at the slope of a V-T graph. The percent error we got on this lab was 28.08% which is a very high number and the percent difference was 12.45% which is also a pretty high number. A reason for this big of an error comes from a few things. First, we might have made a mistake while measuring the ticker tape which definitely could have thrown off our results. In addition, friction played a big part in this lab because one person had to lightly hold the ticker tape while it was going through the spark timer so that it would remain flat. Because of this, the object wasn't really free falling, thus not having an acceleration of 9.8 m/s/s. To make the lab results more accurate and precise, we would use a flat ruler, like we used in the CMV lab. This way, we could clearly see the marked times and measure the dots more accurately. Also, while the ticker tape was going through the spark timer, we would try not to hold the tape so much. This would give it a better chance to accelerate like a normally free falling object.

=Class Notes FreeFall and Speed of Sound=