Chapter 2:
Week 1:
Constant Motion Vehicle Lab Report:

Constant Motion Vehicle:
Lab: A Crash Course in Velocity (Part 1)
Honors Physics

Constant Motion Vehicle Lab:

Excel Graphs:

Constant Motion Vehicle Laboratory (Joe, Andrea, and Brianna) 9/6/11:
1) Hypothesis
- 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

2)Outline your procedure as you conduct it.

- Pick up all of our materials

- Measure out approximately an arms length of spark tape

- Place the spark tape partially through the spark timer and tape it to the CMV

- Start the spark timer and the CMV

- Allow the CMV to run and retrieve the spark tape

- Begin to record and measure the length between the dots on the spark tape

- Each dots represents .1 of a second so go for 10 or 1 second

- Make sure to start a little bit into the tape to help account for the time needed for the CMV to reach its constant speed



The yellow constant motion vehicle graph is displayed here. The line of best fit has a slope of 14.6 which means the equation is y=14.6x. The R2 is supposed to be as close to 1.0 as possible. We came out with 0.99703 which is rather close.

Yellow Constant Motion Vehicle
Time (s)	Position (cm)
0.0	0.0
0.1	1.38
0.2	2.83
0.3	4.15
0.4	5.62
0.5	7.06
0.6	8.51
0.7	10.08
0.8	11.59
0.9	13.82
1.0	14.61

The blue constant motion vehicle graph is displayed here. The line of best fit has a slope of 67.186 which means the equation is y=67.186x. The R2 is supposed to be as close to 1.0 as possible. We came out with 0.99588 which is rather close.

Blue Constant Motion Vehicle
Time (s)	Position (cm)
0.0	0.0
0.1	5.35
0.2	11.35
0.3	18.25
0.4	24.95
0.5	32.21
0.6	39.43
0.7	46.73
0.8	54.12
0.9	61.34
1.0	69.43

Discussion question

1. Why is the slope of the position-time graph equivalent to average velocity?

- The slope of the line of best fit takes into account all parts and components of the graph; the slope is the average of the distance and time. This means that it is also velocity.
2. Why is it average velocity and not instantaneous velocity? What assumptions are we making?
- 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.
3. Why was it okay to set the y-intercept equal to zero?
- 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.
4. What is the meaning of the R2 value?
- 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.
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?
- 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.

Conclusion
Essay:
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. 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.

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Class notes 9/7/11:

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Physics Classroom Notes Section 1 A,B,C, and D: 9/8/11

Method 2a: Directed Reading (as a Follow-Up)

After reading the material, answer the following questions:
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
- During class one of the terms that we went over was displacement. Displacement is a vector that refers to an objects total change in position.
- The second term that I already understood well was the term Distance. Distance is a scaler and is the measure of total distance an object or thing covers.
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.
- One of the terms that I was a little shaky about when I left class was Scaler. After the reading I feel that I have a better understanding of the term. A scaler is a quantity that is described by numerical values/distance ONLY. The thing that was throwing me off was I felt like in class we weren't able to do more than one or two examples and I just felt, not confused but unsure of the topic.
- The second term that I was unsure about related to the first term, it was Vector. After the reading I feel that I have a better understanding of the term. A Vector is a quantity that is described by both a numerical value/distance and a specified direction of travel. The thing that was throwing me off was I felt like in class we weren't able to go more than one or two examples and I just felt, not confused but unsure of the topic.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
- After having taken notes in class and having reinforced the information with a reading I feel that all the material that we covered I have a pretty strong understanding of.
4. What (specifically) did you read that was not gone over during class today?
- One of the things that was in the reading that we did not talk about in class was the concept of instantaneous and average speed. Both are rather self explanatory when you know the other terms. The reading referenced the two terms but did not have any concepts that required the ideas in order to occur.

Some valuable formulas:
image from PhysicsClassroom.com

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Notes from Class 9/9/11: (Constant Speed Notes and graphs of constant speed and at rest)

Average Speed: is when you take the total distance and divide by the total time

Constant Speed: is when you are going at the same speed all the time (ex: you drive 50 mph all the way to work)(cruise control)

Instantaneous Speed: is the speed you are currently going

Equation for all three terms is: V: Total distance/total time


Types of Motion:
1. At rest
2. constant
3. Increasing
4. decreasing

Represent these with a motion diagram: (USING NUMBER 1-4 from above list)
1. V=0 A=0
2. ------>------>------> above each arrow is a V for velocity Acceleration=0
3. -->---->------->---------> above each arrow is a V for velocity Acceleration: ------> (acceleration points in the same direction as velocity)
4. --------->-------->----> above each is a V for velocity Acceleration: <------(Acceleration points in opposite direction from velocity)

When you want a traveled distance to be represented in a different area like down the diagram is simply rotated. Velocity points in the direction of motion.

Signs are arbitrary.
The direction that the arrow points is determined positive or negative based upon the coordinate plane.

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Physics Classroom Notes Section 2 A, B, C 9/9/11:

Method 2a: Directed Reading (as a Follow-Up)

After reading the material, answer the following questions:
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
- During class specifically in the lab we went over the concept of using ticker timers to record a designated amount of time. The tape or ticker tape is attached to a moving vehicle. The ticker tape that has a mark which signifies a .10 time elapse. By measuring the distance in between the dots we can determine various things about the vehicles path.
- The lesson also talked about how distance can be measured using the ticker tape. We had already gone over the formulas. When we measure the distance we know the time and we can use that to find average speed and average velocity.
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.
- When I left class I was still a little bit unsure of the vector/motion graphs. I felt like I understood what they represented but I was unsure about the variations in the lines and how to determine the acceleration.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
- I want to know: How can i decipher the graph of an object when its path is not a straight line?
EX:
4. What (specifically) did you read that was not gone over during class today?
- The only thing that was different than what we had gone over in class was what the website called things. In class we referred to as the arrow graphs/motion graphs online they referred to them as vector graphs. This was the only thing that was slightly different than what we had done.

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3 graphs of constant motion Activity:

This graph signifies a person at rest:










This graph shows constant speed walking away from the graph. The test shown represent both fast (run 9) and slow (run 8).












This graph represents a person at constant motion moving toward the sensor (run 12) and away from the sensor(run 11).


Graphs:
Discussion Questions:

1. How can you tell that there is no motion on a…
   1. position vs. time graph
   2. velocity vs. time graph
   3. acceleration vs. time graph

A) On the at rest graph we can tell that there is no motion because when we look at the graph the line has very few fluctuations that go above or below zero. The line is nearly horizontal with a slight positive slope.

1. How can you tell that your motion is steady on a…
   1. Position vs. time graph

- The line rose at a gradual rate and than evened out and continued for a short time at the same pace

1. Velocity vs. time graph

- There is a very small inline that leads to a pretty steady line slightly above 0.

1. Acceleration vs. time graph

- For the most part the line remains exactly on 0. It does fluctuate slightly above or below 0 on a few occasions.

1. How can you tell that your motion is fast vs. slow on a…
   1. position vs. time graph

- The faster the motion is, the shorter it takes to go a greater distance or have a larger change in position. The slower a motion is, the longer it takes for something to change or move positions.

1. velocity vs. time graph

- The faster motion will have a faster/higher velocity then the slower motion, so the faster motions line should be slightly above that of the slow motion line.

1. acceleration vs. time graph

- Because during the experiment the fast and slow walk were constant, the acceleration remains close to 0 throughout.

1. How can you tell that you changed direction on a…
   1. position vs. time graph

- When the line, or position, starts at a high number and then gets lower as time goes on, the motion that is being preformed is moving towards/closer the sensor, but when the position starts at a low number and gets higher, the motion being performed is moving farther away from the sensor.

1. velocity vs. time graph

- The velocity for the line going away from the sensor was at a slightly higher rate than the line of the test coming toward the sensor.

1. acceleration vs. time graph

- Because there is no acceleration during either of these motions, you couldn’t tell that there was a change in direction because the acceleration would remain around 0 in both ways.

1. What are the advantages of representing motion using a…
   1. position vs. time graph

- The movement of an object staying still will not change its position. This means that the graph has a straight line representing no change in its position. It can also show if there is a large change in position indicating that an object is moving faster than another. Also it can show the displacement depending on how far an object moves forward and back. It will show how much distance is covered at a certain speed.

1. velocity vs. time graph

- It can show that an object is moving towards a certain point and back by the negative and positive intervals of the graph. Negative would be moving closer to the original position and positive would be moving away from the original position.

1. acceleration vs. time graph

- It shows whether an object is increasing its speed, decreasing its speed, or staying at a constant rate for a certain amount of time over the course of a distance.

1. What are the disadvantages of representing motion using a…
   1. position vs. time graph

- Occasionally, one of the plotted points will be on the zero or another number, which represents either change in the moving position or no change at all from the starting point. Another potential disadvantage would be the initial and final discrepancies that cause the graph to have large peaks and valleys. When the sensor starts off and finishes we can sometimes see peaks and valley.

1. velocity vs. time graph

- A possible disadvantage for representing our data using a velocity graph would be that there are some peaks and valleys in the beginning and end of the data. It is also difficult to see the data because of its closeness together unless you adjust the scale.

1. acceleration vs. time graph

- A possible disadvantage for representing our data using an acceleration graph would just be because the acceleration for this specific lab was 0 its very hard to see any truly outstanding differences between the data.

1. Define the following:
   1. No motion- when an object is at rest and is not changing its position. Speed, velocity, and acceleration equal 0.
   2. Constant speed- when an object goes at the same continuous speed from one position to another.

QUIZ 1 ENDS HERE

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Acceleration Graphs Lab:

Joey Miller, Julie Van Malden, Remzi Tonuzi
1) Objectives:

• What does a position-time graph for increasing speeds look like?
• What information can be found from the graph?

2) Hypothesis:
- An upward incline with a positive slope
- The graph will show us how fast an object travels a certain distance. The graph will display the distance at which our cart travels in 1.0 second.


3) Procedure:

- Step 1- Get materials

- Step 2- Lean Ramp on textbook and put cart at the top of the ramp

- Step 3- Feed ticker tape through timer and attach to cart

- Step 4- Turn on ticker time and release car

- Step 5- Turn off ticker timer and interpret results



Analysis:
a) Interpret the equation of the line (slope, y-intercept) and the R2 value.

1. When we constructed our line of best fit we tried two different lines before we came to the correct one (a polynomial). When we compare the two lines we find that the polynomial is closer to 1.0 (0.99979) than that of the linear, which was only about 0.934… This means that the polynomial line contains almost 100% of our points compared to only about 93.4%. Our polynomial line has a slope of 13.67 and a y intercept of 0.7452.

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.)

1. These are the tangent lines for the halfway point speed and the end point speed. Using these I used the coordinate points, (.37,2) and (.77, 8) from the tangent line for the slope of the instantaneous speed at the halfway point. I also used the coordinates (.79,8) and (.55,0) from the tangent of the end point line to find the slope/ instantaneous speed at the end.
2. The instantaneous speed is about 15 cm/s

i. Slope of tangent line= (8-2)/(.77-.37)= 6/.4= 15 cm/s

1. The instantaneous speed at the end is about 33.3 cm/s

i. Slope of tangent line= (8-0)/(.79-.55)= 8/.24 = about 33.3 cm/s

c) Find the average speed for the entire trip.

1. Average speed = total distance/ total time
2. Average speed= 14.48 cm/ 1 s
3. The average speed is 14.48 cm/s

Discussion Questions:

1. What would your graph look like if the incline had been steeper?
   1. Graph shows the original line and the updated steeper version:

2.What would your graph look like if the cart had been decreasing up the incline?
- Graph shows the original, steeper version, and decreasing line:

3. Compare the instantaneous speed at the halfway point with the average speed of the entire trip.

1. Avg. Speed = ∆d/∆t = 14.48 cm/1 sec

i. Avg. Speed: 14.48

1. Inst. Speed = work above

i. Inst. Speed = 15cm/s

1. The Instantaneous speed is at any point in the graph while average speed is the overall speed of the entire trip. The instantaneous speed happens to be at the halfway point and accounts for a slow increase of speed while .5 cm later the speed begins to increase more.

4. Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
- If a line is tangent to a curve it touches at only 1point. If you know the slope of the tangent line you know the slope of the point that you chose on the curve which is included on the tangent line.


5. Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
- Below is an example of a V-T graph

1. 

Conclusion Essay:

After starting the lab we measured our results for 1.0 second and came up with pretty decent numbers. When we placed a polynomial line of best fit we found that our equation for the line was: (y=13.67X^2+0.7452x) and our R2 value was extremely close to being 1 it came out as (0.99979). For this laboratory we created two individual hypotheses. The first was: An upward incline with a positive slope and the second was: The graph will show us how fast an object travels a certain distance. It will display the distance at which our cart travels in 1.0 second. Both of our hypotheses seemed to be accurate with the data we received. You can see the labels on the graph represent position and time that proves our second hypothesis and you can see an upward curve with a positive slope, which proves our first hypothesis. Some sources of error that could have affected our results are the fact that the ticker timer starts and a person may not release the car at a perfect time, which creates a few extraneous dots. Another error that could have occurred was in the measuring of the distance between one dot and the next on the ticker tape, which could have led to slightly off results. In order to minimize these errors there are a few things that can be done. The first thing that I would recommend doing is starting on the ticker tape a few dots in on the tape to assure that it was recording the time when the cart was moving and not just the wait time in between the launch and timer start process. The second way we could minimize error is to use other methods of measuring the space in between the ticker tape dots. We could have used different measuring devices like a flat ruler or a tape measure. Another option is to have two people measure it and see if the results they produced were comparable.

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Notes from class 9/14/11

Kinematics:
V=distance/time Used for constant and average speed only.

V= (Inital Speed-Final speed)/2 average speed only

V=d/t---=----V=Is-Fs/2

Combination of the two formulas would be: distance=1/2(Vi+Vf)*time (use when accelerating)


Acceleration- how fast your speed is changing
a= Vf-Vi/time vf=initial speed vi=final speed can be used also as Vf=Vi+a*t

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Physics classroom reading section1E 9/14/11

Method 2a: Directed Reading (as a Follow-Up)
After reading the material, answer the following questions:
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
- When class concluded I felt that I had a pretty good understanding of what the term acceleration meant. Acceleration is a vector quantity that is described as a change in velocity.
- The second thing that I felt confident in were the formulas that are used for acceleration. I felt that after having learned them and having used them in several examples I understood how to use them and what each variable represented.
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 major thing that I was not confident in was the motion graphs when an object is decelerating. After having read the website and looked a few more examples i feel a little bit more confident.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
- The material that we covered in class was all reinforced by the website. I felt I had a good understanding of most things before but now i feel a little bit more confident in the material.
4. What (specifically) did you read that was not gone over during class today?
- I know that we have talked about acceleration and what its graph look like but the website talked about the idea of constant acceleration and I don't think we went into any sort of detail about what it was.

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Class Notes 9/15/11:

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Physics Classroom Lesson 3 Notes 9/15/11:

Method 2a: Directed Reading (as a Follow-Up)

After reading the material, answer the following questions:
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
- Lesson 3 primarily focused on graphs and what determines how they appear. The main graph that it talked about was the position time graph which I already had a pretty strong understanding of before the reading.
- The second thing the article talked about was the importance of using the slope to determine what the line will look like. The slope of a position time graph is generally understood to be the velocity.
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 don't really feel confused about any of the topic that we covered in class or went over in the reading. Once you understand what the graph represents and how to figure out the slope of the line the drawing of the graph is not that difficult. I feel like i need to see more example though to make my understanding more complete.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
- I felt pretty confident in my overall understanding of the topics covered in class. I think that the ideas are relatively simple, with some more practice I think I will feel confident with the material.
4. What (specifically) did you read that was not gone over during class today?
- I did not really notice anything that i read that we had not already gone over in class.

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Physics Classroom Lesson 4 Notes 9/15/11:

Method 2a: Directed Reading (as a Follow-Up)
After reading the material, answer the following questions:
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
- The idea of acceleration time graphs and what they are and how they look. I felt very confident with those ideas before the reading.
- The second concept would be the graphing of velocity time graphs and how they are supposed to look. Once you understand the basic idea of the graph and know that the slope of the graph itself will be the acceleration, graphing it is not that difficult.
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.
- One of the things that I did not have a strong grasp on before the reading was the idea that each graph in some way is related to the other graphs like (position, velocity, or acceleration time graphs). Originally I was unsure what the graphs reflected when put together. However now after having completed the reading I can see how they correspond to each other and what their significance is.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
- The reading talked about using area formulas: One of the things that i am still not sure of it why we need to use the area formulas when we graph our line. I hope that we can go over what exactly the purpose to finding the area is. I understand the area formulas them self but i do not understand there purpose in relation to the time graphs.
4. What (specifically) did you read that was not gone over during class today?
- We really did not go over what we use area for in the time graphs and what it represents.


-Velocity Time Graph

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A Crash Course in Velocity:

Joe, Andrea, Brianna

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.

Procedure:
1) Get paper and begin to work out the arithmetic
2) Insert proper formulas and solve both scenarios
3) Get paper and graph both of the scenarios showing the point of intersection
4) Measure 600 cm and test out the first scenario making sure to record the process. Take note of where exactly the CMV's collide
5) Measure 100 cm and test out the second scenario making sure to record the process. Take note of how long and where the CMV caught up.
6) Make a velocity time graph showing what occurred on the catch up scenario
7) Finish Lab report



A)



B)




Data Explination:
- Position of the yellow (slower) CMV was 104.32 centimeters, while the position of the blue (faster) CMV was -495.93 cm.
- The blue CMV (faster) will catch up to the yellow CMV after 126.36 cm.



Data Tables:
Collision

trial	distance(cm)
1	125.15
2	123.36
3	122.87
4	127.67
5	121.52

Catching up

trial	distance(cm)
1	125.55
2	126.46
3	131.86
4	127.63
5	121.52

Discussion Questions:
1)
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.

2) Position Time graphs Catching up and Collision:




Two videos for collision Scenario:




Video for Catching Up:


3) Velocity Time Graph With explanation: (IGNORE TEXT IN PICTURE BELOW GRAPH, READ TYPED COPY)

- 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 CMV appears to have begun at the same point, however they are in reality separated by 100 cm or 1m.




Percent Error Calculations: (after initial formula there should be a x100) :)

The percent error for the collision problem was between 16-22 which was not as great as we had hoped.

The results for the Catch up were much better than we had hoped they ranged from .6-4.35 which made our results almost spot on!






Conclusion:

We felt that our results we ok. The results for the collision scenario were further off than that of the catch up. We determined this because when we use the percent error formula and plug 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. This shows us that our data from the collision scenario was not as good as the data from the catch up. One of the things that affected our results was the CMV itself. The blue CMV (fast) was very fast and did not like to travel in a straight line. So when we tried to measure where the two CMV's met we were unable to get as precise a measurement as I would have liked. The things that may have contributed to our error would be a few specific things. The first would have to be our initial finding for the time and distance traveled by our CMV's. Another thing that could have contributed to error is when we made the initial measurements for how far the CMV traveled we could have measured slightly off which in turn would have effected our results for this laboratory. 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. If we were to redo this lab the first thing we would have done is made sure that our measurements for our CMV's position from the previous lab was as exact as possible. We could have used different measuring techniques to help make our answers a little more precise. Another thing that I would have tried to make better was the video recording. I felt that recording the video took a long time which made the work load after school greater. If I were to redo this lab I would have tried a different method for recording the video itself. If we had time we could also replace the batteries of the CMV and redo both tests.

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Egg Drop Project Results:

Mass of device: 26.23g (without egg)
Time to impact: 1.02 seconds (most likely off because of bad acceleration calculations)

The egg drop project was neither a complete success nor complete failure for my design. The device was itself was relatively lightweight which was one of my main objectives when constructing it. The design was able to keep the egg from leaking any liquid, however it did cause the egg to have one crack near the bottom of it. I was a little disappointed that the design did not work as it had the previous day by keeping the egg completely unharmed. I was however happy that it did not allow the egg to break. The main reason for the semi-successful drop was the design shape. The design shape was a cone that had layers of paper and straws in the bottom. The idea behind the cone shape is that the bottom is the heaviest part of the device and that causes it to fall straight. When the cone hits the ground the bottom compresses and the paper and straws absorb the impact from the fall. The straws which formed a cross shape then supported the device once it hit the ground in order to keep it from falling on its side.

Calculations:

Based on the results that I got when i plugged my data into the formula D=v1+.5*a*t^2 I found that my time must have been recorded wrongly. The resulted acceleration is not a possible value; some sort of error weather in reaction time or something of that nature affected my results.



If I were to complete this project again I would do a few things differently. The first thing would have to be think simpler. I made a total of 6 different designs all of which I tested to determine the best. With most of them I either made the device to light which cause the device to flip and crush the egg or too heavy and overcomplicated which caused the egg to be drawn down toward the ground and crushed. With my final design if I had the chance to modify it before another launch I might have added a parachute to help slow its descent (the only reason I didn't do it originally was because I though such a small parachute would do not good). I also might have added some more padding to help better protect the egg from the impact of the fall.

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Quantitative Graph Interpretation Packet:

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Class notes 10/3/11:

Freefall- an object moving under the influence of gravity only. Can be up or down!!!

Object goes up: is 0 speed at max: then goes down (acceleration is opposite, if up than acceleration is down etc.)
- ignore air resistance when completing these problems (freefall will imply no air resistance)

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Physics Classroom Notes Lesson 5 10/3/11:

Method 1 Lesson 5:
Lesson 1:
Topic Sentence: When an object is in a state of freefall it is moving at 9.8m/s and is under the sole influence of gravity, no other forces act upon it.

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 accelerates downwards at a rate of 9.8 m/s/s


Lesson 2:
Topic Sentence: 9.8m/s is known as acceleration of gravity, this can be display in a few ways using graphs or even dot diagrams.

9.8 m/s It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. When it comes to representing this material there are a few ways to go about it. You can use dot diagrams or you can use velocity-time graphs.

Lesson 3:
Topic Sentence: We can represent freefall by using position-time graphs and velocity-time graphs
One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs.

Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. 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. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity.


Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. 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. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction.

Lesson 4:
Topic Sentence: There are two formulas that you can use to figure out the times in seconds and the distance when you are doing freefall equations.

Free-falling objects are in a state of acceleration. Specifically, they are accelerating at a rate of 9.8 m/s/s. This is to say that the velocity of a free-falling object is changing by 9.8 m/s every second. If dropped from a position of rest, the object will be traveling 9.8 m/s at the end of the first second, 19.6 m/s at the end of the second second, 29.4 m/s at the end of the third second, etc. Thus, 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
vf = g * t
where g is the acceleration of gravity. The value for g on Earth is 9.8 m/s/s. The above equation can be used to calculate the velocity of the object after any given amount of time when dropped from rest. 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.
d = 0.5 * g * t2
where g is the acceleration of gravity (9.8 m/s/s on Earth).

Lesson 5:
Topic Sentence: Heavier objects do not accelerate at greater rates than smaller objects.

After all, nearly everyone has observed the difference in the rate of fall of a single piece of paper (or similar object) and a textbook. The two objects clearly travel to the ground at different rates - with the more massive book falling faster.
The answer to the question (doesn't a more massive object accelerate at a greater rate than a less massive object?) is absolutely not! That is, absolutely not if we are considering the specific type of falling motion known as free-fall. 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. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. 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.

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Freefall Lab:

Joey Miller and Katie Dooman

Purpose-Determine the acceleration of gravity when we drop a 100g object off the balcony above the lunch room.

Hypothesis:
I predict that the acceleration of gravity will be 9.8m/s^2.
I believe the velocity vs. time graph will show a linear line with a negative slope representing the object speeding up away from the origin.
I predict g will be equal to the value of the slope of the line on the VT graph.

Procedure: Drop 100 gram mass. Use a spark timer, plugged in, and hold it over the edge of where you are dropping the mass. Take a piece of masking tape, attach ticker tape to mass, letting it drop to the ground. Try not to wrinkle the tape or coil it up. Make sure it's all laying out and no one is standing on the end. Then lay the ticker tape out and get a measuring tape to get the data with which we will make the v-t graph and do the lab.



Sample Calculations:




% Error


%Difference



Graphs:
Velocity Time Graph for freefall lab:



Position Time Graph for Freefall Lab:



Analysis:

Our velocity time graph contains a positively slope linear line that represents our object speeding off away from the origin. When we graphed the VT graph we got the equation y=842.38x+35.399 (y=mx+b). The slope of the line m (842.38) represents the acceleration due to gravity of our freefalling object. The next thing to look at is how exact our results are and the answer is overall they were ok. The ideal slope of the line could have been 980.00 cm/s^2 and based on our graph we were off by about 14.08%. The next thing that we can examine is b or the y intercept of our line, which was 35.399. Our y intercept was not zero because we cannot guarantee that our initial velocity will be zero the dropping part of the lab is not specific/controlled to the point were it could be exactly zero. The closer the R^2 value it to 1 the better, our R^2 value was .98907 which is an ok value.

The Position Time Graph shows a positively curved line accelerating away from the origin. The equation of the trend line for our graph was y=399.15x^2+62.193x (when y=Ax^2+bx). The slope or A (399.15) represents about half of the acceleration the object has during freefell. Another way to find this is to take half of the VT graphs slope and you should get a value close to this one. B represents the initial velocity when we dropped our object.




Discussion Questions:

1. The shape of my VT graph seems to agree with my expected graph. So it turn my hypothesis is mostly correct. Both the actual graph and my prediction include a linear line, which represents the acceleration (increase of speed). In our hypothesis we thought the slope would be negative however during this lab it was considered positive.
2. Yes, my prediction seemed to agree with the shape that our XT graph displayed. Both my prediction and the displayed graph showed a positive curved slope going away from the origin.
3. The percent difference between the results for the class (average experimental) and our (individual) experimental value is 4.53%. Our value in turn was (4.53%) higher than the class average.
4. The (100g) object accelerated constantly. We found this out by examining the V-T graph, which shows a linear line. The slope of the V-T graph shows acceleration; over equal intervals so thus it is evident that the acceleration is constant.
5. The acceleration due to gravity could be higher than normal if the data was gathered incorrectly or if the person read the start or end point of the data incorrectly. The acceleration due to gravity would be lower than normal if the tape attached to the (100g) object was being dragged. The tape also goes through the spark timer, which creates additional friction, which in turn slows the object. We also have to consider the manor in which the spark timer was held (vertically or horizontally) and if the tape encountered any “road blocks” (a hand, foot, or notebook).

Conclusion:
The first hypothesis was pretty correct. Our results came out as 842.38cm/s^2 or 8.42cm/s^2. The known value is 980cm/s^2 or 9.80m/s^2 so overall our results were pretty close. In relation to the known value we had a percent error of 14.08%, which is not great but not bad either. The second part of our hypothesis was also correct. Our actual graph displayed a linear line accelerating (speeding up) away from the origin and we predicted the same, as the velocity was considered positive. Our third hypothesis was also correct. We determined g from the slope of the VT graph; this is evident from our acceleration of gravity result: 842.38cm/s^2 or 8.42cm/s^2. One possible source of error occurred when the tape passed through the spark timer. When the tape passes through the timer it creates friction, which slows the tape down in turn dropping the objects acceleration/speed. The only way that I could think of to help reduce the friction would be to directly feed the tape rather than allowing it to slide through the spark timer. Another source of error would occur in the measuring of the spark dots. When we measure the dots we need to try to be as exact as possible and not allow the long tape to move. A way that we could minimize error is to measure with a more exact device or even multiple measuring tools (tape measure, yard stick, etc.).