Ch2_Knapelr

=toc= =Chapter 2=

Constant motion Vehicle lab
Lab: A Crash Course in Velocity (Part 1) Honors Physics 9/6/11 Lab partner: Molly lambert
 * Objective: ** What is the speed of a Constant Motion Vehicle (CMV)?

The slope is the average speed. The meaning of the equation of the line is v=d/t. R2 tells if the line is a good fit into your data. If it is above 95% then your data is on the path it should be.
 * Hypothesis: **
 * 1) I think Cmv (yellow) is going 2 seconds per centimeter **
 * 2) How far the position changes over a certain amount of time **
 * 3) You must measure very precise to get the best answer possible **
 * Data table and position-time graph for speed of Yellow CMV**

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


 * Interpreting Your Results: **
 * Be sure to provide concrete evidence for the success of your experiment.
 * Any graphs that you make should be done in Excel, not by hand.
 * You need to collect at least 10 data points.

> The slope of the position-time graph is equivalent to the average velocity because slope is centimeters/seconds and the average velocity was the number of centimeters over 1. > It is the average velocity because its an average of all the positions and seconds, if it was instantaneous than the velocity would be the same for each position, but as we see they are not all equal. > It is okay to set the y-intercept equal to zero because we started the experiment at 0 where the position and seconds both were equal to zero. > R2 tells if the line is a good fit into your data. If it is above 95% then your data is on the path it should be. > The results of the second CMV would be similar to the line our CMV created but it would lie beneath our line because the position would be lower but the time would be the same. >
 * Discussion questions **
 * 1) Why is the slope of the position-time graph equivalent to average velocity?
 * 1) Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * 1) Why was it okay to set the y-intercept equal to zero?
 * 1) What is the meaning of the R2 value?
 * 1) 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?

In essay format, answer the following questions: 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?
 * Conclusion **

Through the experiment we found the results to be that the yellow slow CMV moves at 10.538 cm per second. Both of our hypotheses were much lower than the actual results, we believed that the CMV traveled at a much slower rate of 2 or 3 cm per second. We both saw the relationship between the positions of the CMV and the time it took to get there, that the graph created as well as the precision needed in order to measure. The main sources that contributed to inaccuracies were that the CMV’s were not identical due to their differing battery strengths, the elevated rulers made it difficult to measure, and the CMV did not drive in a straight line. In order to minimize these issues, we would put new, identical batteries in each CMV, use a flat or translucent ruler, and test the CMV on a flatter more level surface. Constant speed

Homework #1 9/8/11
Lesson 1
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. I understood when they talked about the difference between distance and displacement. I got how distance is the full amount of feet(or what ever unit) you traveled, while displacement is the amount of space between the origin and where you end up.
 * 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 was confused about the difference between vector and scalar and i wasn't sure which one to use in a situation, but the reading cleared that up. You use vector for a number and location and scalar is just a number.
 * 3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question. There is nothing that i still do not understand
 * 4) What (specifically) did you read that was not gone over during class today? **We did not learn that mechanics is the study of the motion of an object or that kinematics is a description of the objects in motion using different things like words, diagrams, number, graphs, and equations**

Class notes 9/9/11
Average speed - Take the total distance and the total time and thats the average speed Constant speed - Going the same speed all the time Instantaneous speed - The speed you are going at that moment

Equation - V(m/s)= Change in distance/Change in time

Types of motion: Motion diagram Rest V=0, a=0 Constant --> --> --> --> v v v v a=0 Speeding up(increasing) -> --> ---> > -> v v v v v a> (Accelerations points in the same direction as velocity) Slowing down(decreasing) -> > ---> --> -> v v v v v <-a (for decreasing speed acceleration always points opposite direction from velocity)

Sings are arbitrary(random) - Someone made it up and we agreed with it. Not right or wrong. Arrow points down - its has a negative sign Arrow points up - it has a positive sign

Homework #2 9/9/11
Lesson 2
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. I understood the ticket tape diagram and that when the dots are more spread out it means the object is moving faster than if they were closer together. I also understood that vector diagrams show a direction an object is moving.
 * 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 was confused in each different scenario for the vector diagram, how the acceleration was related to velocity, but now i understand.
 * 3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question. What are vector diagrams used for besides showing which direction an object is moving?
 * 4) What (specifically) did you read that was not gone over during class today? The only thing that we read about that we didn't go over in class was that diagrams and graphs are very useful in physics.

Class notes
Ticker tape diagram
 * Tape being pulled through a machine that places a dot at every certain time interval. Fast to slow --> decreasing speed**
 * Slow to fast --> increasing speed**


 * Vector diagram**
 * Shows the direction of an object using arrows. the size of the arrow displays if the object is increasing or decreasing speed. It is another way to graph motion.**
 * Big to small --> decreasing speed**
 * Small to big --> increasing speed**

Activity
Graphing acceleration Graphs representing constant motion 9/12/11
 * 1) How can you tell that there is no motion on a…
 * 2) position vs. time graph – the line is straight with no curves up or down
 * 3) velocity vs. time graph – Velocity the line is at 0
 * 4) acceleration vs. time graph – Acceleration the line is at 0
 * 5) How can you tell that your motion is steady on a…
 * 6) position vs. time graph – The slope is the same throughout both lines
 * 7) velocity vs. time graph – The line is at 0
 * 8) acceleration vs. time graph – The line is at 0 and is not going up or down
 * 9) How can you tell that your motion is fast vs. slow on a…
 * 10) position vs. time graph – The graph for faster is steeper
 * 11) velocity vs. time graph – For slower the line is shorter for the same distance
 * 12) acceleration vs. time graph – The line is shorter for the same distance
 * 13) How can you tell that you changed direction on a…
 * 14) position vs. time graph – Opposite slopes. The starting position is less/closer for going away from the motion detector.
 * 15) velocity vs. time graph – Walking away from the motion detector is above the x-axis and walking towards the motion detector is below the x-axis.
 * 16) acceleration vs. time graph – You are not able to tell the difference
 * 17) What are the advantages of representing motion using a…
 * 18) position vs. time graph – It is easier to see the differences in speed and direction
 * 19) velocity vs. time graph – You can see not only the speed but the distance better
 * 20) acceleration vs. time graph – you can see the difference in speeds between two things
 * 21) What are the disadvantages of representing motion using a…
 * 22) position vs. time graph – if you sway back and fourth or don’t walk in a straight line then the graph isn’t linear
 * 23) velocity vs. time graph – It is hard to read and describe the information
 * 24) acceleration vs. time graph – If your speed changes at all there are spikes in the graph
 * 25) Define the following:
 * 26) No motion – When your acceleration and velocity is 0 and your position stays the same.
 * 27) Constant speed – you do not speed up or slow down, it stays the same and your position has the same slope throughout the run.

This graph shows when i am at rest. These graphs show constant motion slow vs. fast. Run 1 was the slow one, while run 2 was the fast one.

This graph shows constant speed going towards and away the motion detector. Run 1 represents when i was walking away from the motion detector, while run 2 depicts when i was walking toward it.

Acceleration lab 9/13/11
Lab partner - Molly Lambert
 * Objectives:**
 * What does a position-time graph for increasing speeds look like?
 * What information can be found from the graph?
 * Hypothesis:**
 * 1) **The slope gets steeper as the car approaches the bottom of the ramp**
 * 2) **The graph shows the relationship between the position of the car and its speed. Further the position the faster it goes.**

Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape
 * Available Materials:**

This is our data and graph a= half acceleration b= Initial velocity a) Interpret the equation of the line (slope, y-intercept) and the R2 value. 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.) c) Find the average speed for the entire trip.
 * Important Notes:**
 * Be sure to write your hypothesis BEFORE doing the experiment.
 * All data should be recorded in an organized spreadsheet in Excel.
 * You need to document your procedure. Decide with your lab partner how you intend to do this.
 * Analysis:**

Discussion questions If the incline had been steeper than the graph would look more like the linear line of best fit and less like the polynomial line of best fit. The slope would be steeper 2. What would your graph look like if the cart had been decreasing up the incline? It would be steeper at the bottom and then curve as it got higher to the top since it would slow down as it went up the incline 3. Compare the instantaneous speed at the halfway point with the average speed of the entire trip. The average speed and the instantaneous speed at the halfway point were only 7.59 cm/s away from one another. The average speed and the instantaneous speed both represent the middle. The instantaneous being the median and the average speed being the mean 4. Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense? Instantaneous is speed you are at that second, so when tangent intersects with a point on the graph it is the slope for that point only. Therefore, the instantaneous speed equal the slope of the tangent line. 5. Draw a v-t graph of the motion of the cart. Be as quantitative as possible. v-t graph
 * 1) What would your graph look like if the incline had been steeper?

As a result, the further along the car was on the ramp the higher the speed was. As the car approached the bottom the ramp, the speed gradually increased. The ticker tape dots got farther apart because of this and this proved our hypothesis. We were correct in thinking that the graph shows a steeper slope as the car approached the bottom of the ramp and that it showed the relationship between the cars position and speed. There were many sources for error. One was that the ticker take sometimes does not go through the spark time in a straight line causing false results. Also, when releasing the car we could have added force to the car by pushing it, which would increase the speed. We would make sure that the tape was lined up straighter before beginning. If we could redo the lab we would try to release the car without adding any extra force.
 * conclusion**

This picture shows me doing the calculations for instantaneous speed for both the halfway and last point on the line. media type="file" key="Movie on 2011-09-13 at 13.01.mov" width="300" height="300" This video shows the car all during our experiment. It has the ticker tape taped to the back so as it rides along the ramp a dot is made every .1 of a second. THe car starts at rest then gets faster and faster as it goes down the ramp until it is eventually stopped by an outside force.

Homework 9/14/11
Lesson 3
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. I knew that acceleration had to deal with speed/velocity and slowing down or speeding up. I also understand that a vector quantity, like acceleration is, has to deal with direction as well as speed.
 * 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 was confused about what acceleration actually meant. I knew it was when you sped up or slowed down, but know i understand that it is a vector quantity and is the change in velocity.
 * 3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question. I understand everything in this section.
 * 4) What (specifically) did you read that was not gone over during class today? We did not go over constant acceleration. We also didn't go over free falling objects.

Class notes
9/14-9/15

Increasing and Decreasing speed graphs At rest and constant speed graphs

Homework 9/15/11
Lesson 4
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. I understood that position-time graph's slope represent the velocity and that if the velocity is positive than so id teh slope. Therefore; slope is equal to velocity. I understand that when you draw a velocity-time graph if it is positive(away and increasing speed) than it is about the x axis and if it is negative (increasing but moving towards) it is below the x axis.
 * 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 was confused about the different shapes of all the graph, but mostly i understand the meaning behind the way they go now.
 * 3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.When does moving towards the motion detector make the line go above the x axis?
 * 4) What (specifically) did you read that was not gone over during class today? We never went over how to find area from these types of graphs.

The big 5 - equations
1. v=d/t 2. V = vi+vf/2 3. d= 1/2(vi+vf)t 4. vf=vi+at 5. d=vit+1/2at^2

**Lab CMV #2 9/20/11**

 * Partners:** Molly Lambert, Lindsay Marella, Maggie Leffler
 * Objectives:** Both algebraically and graphically, solve the following 2 problems. Then set up the situation and run trials to confirm your calculations.

Hypothesis: 1. the cars will crash closer to the side where the slower cmv started 2. The faster car will catch up not long after where the slower car started.

Calculations for Part A media type="file" key="Movie on 2011-09-22 at 11.21.mov" width="300" height="300" This video shows the Blue Cmv placed 1 meter behind the yellow Cmv. The blue car caught up to the yellow Cmv and we marked the point at which they met down and then looked back at our calculations to see if our math was correct. My calculations

media type="file" key="Movie on 2011-09-22 at 11.14.mov" width="300" height="300" This video shows when the Cmv's are plays 6 meters apart and show when they crash into one another. Calculations for Part B My calculations Discussion questions:
 * 1) Where would the cars meet if their speeds were exactly equal? If one car started in front of the other than the two cars would never meet. If they were facing each other and going the same speed than they would meet in the middle.
 * 2) Sketch position-time graphs to represent the catching up and crashing situations. Show the point where they are at the same place at the same time.[[image:Photo_on_2011-09-25_at_20.55.jpg]]
 * 3) 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?[[image:Photo_on_2011-09-25_at_20.55_#2.jpg]]

Percent error and Percent Difference

Conclusion: In Conclusion the cars would meet up at about 256 cm and then the Blue CMV would pass the yellow one. This is because after testing if several times we found this to be our average. They would also crash about 350cm away from where the blue car started. This is because we also tested this many times and found it to be our average. Our data gained from the experiments were not always close to the number we found when doing the problem mathematically. There were many mistakes that one could have made while doing this experiment. The two people holding the CMV might have let go at different times causing the data to be off a little. Also, depending on where we rounded the numbers when doing the equations the answers could have been a little off. Other reasons that contributed to us having high percent error and percent difference is that when we tested the CMV's the blue one seemed to be slower than then it was in the CMV lab part 1. Also, the yellow CMV's battery kept falling. The next time that i would make sure that the two people release the cmvs at the same time and ensure that the speed of both CMV's are going the same speed as the time they were before.

Egg drop project
This is our egg drop project. It is a cone made out of paper with straws at the bottom and top to secure the egg from wiggling or moving.

Our results when we dropped our contraption from the roof was that the egg survived, was intact, and did not break.

Analysis: When we calculated the acceleration we got a very high number of 14.05m/s which is impossible. It should be close to or around 9.8m/s, but it was not. There may be flaws in our calculations. Also, the fact that their were only two times to find the average time may have ruined our calculations. Or maybe one person took the time down wrong. Molly may have released the cone and then the person timing may have started their clock. There are many faults that could have happened to lead to this miscalculation. In the experiment i would not have done much different since the fact that it worked. I might have used less paper to try and make it weigh less and also tighten up the cone so that i wouldn't need the straws to keep it in place.

Freefall notes
Class notes 10/3/11 Freefall - An object moving under the influence of gravity only (Up or Down) ignore air resistance!

Never at constant speed with free fall Can use any equation except v=d/t Free fall well problem

Homework lesson 5 - 10/3/11
Free fall is when an object, that does not encounter air resistance, is being acted upon by gravity resulting in the object falling to the ground at a rate of 9.8 m/s, which can be graphed by a ticker tape diagram to show its acceleration. The acceleration of gravity is the acceleration for any object moving under the sole influence of gravity, which numerical value is 9.8 and symbol is g. Larger objects do not accelerate at a greater rate than smaller objects Acceleration of an object is directly proportional to its force and inversely proportional to its mass which is why larger objects do not fall faster than smaller ones.

Freefall Lab
10/4/11

Objective: 1. What is acceleration due to gravtiy?

Hypothesis: 1. (a) Acceleration is -9.8m/s (981cm/s) (b) v-t graph (c) The slope of the line is the acceleration This is all of our data and both our position time graph and velocity time graph. Analysis 1. (^^) 2. The position time graph starts off with a flatter slope and then gradually gets steeper. This is because the object was accelerating as it fell from the bannister. In this graph the a(387.93) represents half of the acceleration and the b(52.006) represents the initial velocity. The velocity-time graph is a diagonal line because the object was accelerating. For This graph the a(775.37) represents the acceleration and the b(52.763) represents the initial velocity. 3. 4. Discussion Questions No, because i thought that it would be in the negative side of the graph, but since we made our data positive it was not. Yes because it shows acceleration in speed and that it was i thought would happen. It started off slow and then got faster. My data was close to the middle of the data for the rest of the class. For percent difference i got 3.87% which means that it was relatively close to the average of the class. The percent is how far away my data was from the class average. Yes it did accelerate uniformly. You can tell this because the line is very close to a straight line and has a r value of .99. It may be lower than it should be because of friction with the spark timer and also there being a restraint. Air resistance may cause for acceleration due to gravity to be higher than it should be.
 * 1) Does the shape of your v-t graph agree with the expected graph? Why or why not?
 * 1) Does the shape of your x-t graph agree with the expected graph? Why or why not?
 * 1) How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)
 * 1) Did the object accelerate uniformly? How do you know?
 * 1) What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?

Conclusion We found that after one second the weight dropped 519.10cm by measuring the furthest point from the start. We also found that our acceleration by looking at the slope of the line and it turned out to be 775.37m/s. Our calculations were under the expected acceleration of 981cm/s. We had a percent error of 20.96% and a percent difference of 3.78%. This may be due to the fact that we didn't drop it right when a dot was made and therefore the initial velocity was not zero. Another source of error may be from the person holding the ticker tape. they may have been holding it tightly and it may have caused friction. They might have been a restraint, which would have caused the acceleration to be less than what it is supposed to be. I would change this by using a motion detector; therefore, their would be no friction, which would have given us better and more accurate data points. Also, measuring more precise may have given us better data points.