Group+2.1-4-EB

Sean and Phil Ross and Chris

Philip Litmanov - Sean Krazit - Ross Dember - Chris Bickel
 * \.-•`º´•-./** **THE FEARSOME FOURSOME \.-•`º´•-./**

Lab: Representations of Motion Due: 9/20/2010

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

Hypothesis: The different types of motion are no motion, constant motion, increasing speed, and decreasing speed. The best way to represent motion is a position vs. time graph as you can tell the velocity, acceleration (when slope changes drastically), and displacement.

Procedure:

1. Place the motion sensor on a flat surface about waist height. 2. Plug the motion sensor into the computer's USB drive and open up DataStudio. 3. Click on Create Experiment in DataStudio. 4. Open position vs. time, velocity vs. time, and acceleration vs. time graphs. 5. Hold a book or folder or any flat object around your waste (so the sensor picks up a fluid motion) and do the following: - For **No Motion**, stand in front of the sensor with the flat object and don't move. Click "Start" in DataStudio and after a few seconds press "Stop". - For **Increasing Speed Toward**, stand about 10 feet away from the sensor with the flat object. Click "Start" and begin walking toward the sensor, increasing your speed as you approach it. When done, press "Stop". - For **Increasing Speed Away**, stand right in front of the sensor with the flat object. Click "Start" and begin walking away from the sensor, increasing speed you get further and further. When about 10 feet away, click "Stop". - For **Constant Speed Toward**, stand 10 feet away from the sensor with the flat object. Click "Start" and begin walking toward the sensor with constant speed. When in front of the sensor, click "Stop". - For **Constant Speed Away**, stand in front of the sensor with the flat object. Click "Start" and begin walking away from the sensor with constant speed. When 10 feet away from the sensor, click "Stop". - For **Decreasing Speed Towards**, stand 15 feet away from the sensor with the flat object. Begin walking toward the sensor and when 10 feet away, click "Start". Decrease speed until in front of the sensor and click "Stop". - For **Decreasing Speed Away**, stand in front of the sensor with the flat object. Begin walking away from the sensor and when 5 feet away, click "Start". Decrease speed until 15 feet away from the sensor and click "Stop". 6. For the Ticker Tape graphs: - For **Constant Motion**, Swipe paper through the insert of machine in consistent, sweeping motion. - For **Decreasing Speed**, Start swiping paper through slot relatively fast, then noticeably slow down. - For **Increasing Speed**, Start swiping relatively slow than noticeably speed up.

Data: A=0 || V --->-->---> A -> || V <-<-<--- A < || V ->->->-> A=0 || V <-<-<-<- A=0 || V --->--->> A <-- || V <---<--<- A ---> ||
 * || **No Motion** || **Increasing Speed Toward** || **Increasing Speed Away** || **Constant Speed Toward** || **Constant Speed Away** || **Decreasing Speed Towards** || **Decreasing Speed Away** ||
 * **Motion Diagram** || V=0
 * **Ticker Tape Diagrams** ||  |||| [[image:Accelerating.jpg width="213" height="20"]] |||| [[image:Constant.jpg width="189" height="20"]] |||| [[image:Increasing.jpg width="191" height="17"]] ||
 * **Distance vs. Time Graph** ||  ||   ||   ||   ||   ||   ||   ||
 * **Velocity vs. Time Graph** ||  ||   ||   ||   ||   ||   ||   ||
 * **Acceleration vs. Time Graph** ||  ||   ||   ||   ||   ||   ||   ||


 * No Motion**




 * Increasing Toward**




 * Increasing Away**




 * Constant Toward**




 * Constant Away**




 * Decreasing Toward**




 * Decreasing Away**



Very good graphs! They are very well "walked"!

Data Interpretation:

1. How can you tell that there is no motion on a…

a. Motion diagram - **Velocity and acceleration equal zero** b. Ticker tape diagram - **All of the dots are in one spot.** c. position vs. time graph - **There will be a horizontal straight line at y = the distance from the motion detector.** d. velocity vs. time graph - **There will be a horizontal straight line on the x axis because there is no velocity, therefore no displacement.** e. acceleration vs. time graph - **There will be a horizontal straight line on the x axis because there is no acceleration therefore no change in velocity.**

//**2. How can you tell that your motion is steady on a…**// a. Motion diagram - **There will be one velocity arrow, no acceleration arrow because a = 0.** b. Ticker tape diagram - **The marks are all the same distance apart.** c. position vs. time graph - **Slope doesn't change.** d. velocity vs. time graph - **There will be a horizontal line at y = set velocity.** e. acceleration vs. time graph - **There will be a horizontal line on the x axis because there is no acceleration.**

//**3. How can you tell that your motion is fast vs. slow on a…**// a. Motion diagram - **You can't tell. You can only tell if it's accelerating or constant**. b. Ticker tape diagram - **The closer together the dots are, the slower the motion. Dots with large amounts of space in between show a fast motion** c. position vs. time graph - **If your motion if fast, the line will have a steep slope. If slow, it will have a shallow slope.** d. velocity vs. time graph - **If the velocity decreases to zero, and then continues in the opposite direction which it came from, it has changed directions.** e. acceleration vs. time graph - **If the acceleration line’s slope is decreasing and reaches zero and then continues in that direction it has changed direction.**

//**4. How can you tell that you changed direction on a…**// a. Motion diagram - **through a change in the direction of the velocity arrow.** b. Ticker tape diagram - **You cannot.** c. position vs. time graph - **The sign of the slope of the line changes sign: positive to negative or negative to positive.** d. velocity vs. time graph - **If the velocity decreases to zero, and then continues in the opposite direction from which it came.** e. acceleration vs. time graph - **If the acceleration line is decreasing and reaches zero and then continues that direction, the object has changed its direction.**

How can you tell that your motion is increasing on a…
 * 1) Motion diagram- **Acceleration and Velocity point are both positive or negative.**
 * 2) Ticker tape diagram- **Dots are bunched together than start to spread apart.**
 * 3) position vs. time graph- **The slope starts to get larger and increases in absolute value.**
 * 4) velocity vs. time graph- **Slope increases in absolute value as time moves to the right.**
 * 5) acceleration vs. time graph- **Slope is steep and increasing in absolute value.**

**//How can you tell that your motion is decreasing on a…//**
 * 1) Motion diagram- **Acceleration and velocity have one being positive and the other negative.**
 * 2) Ticker tape diagram- **Dots are spread then start to bunch more.**
 * 3) position vs. time graph- **Slope get less “steep” and decreases in absolute value.**
 * 4) velocity vs. time graph- **Slope decreases in absolute value.**
 * 5) acceleration vs. time graph- **Slope is getting closer to zero (having no acceleration) then going from positive to negative (depending on the sign on velocity.**

Discussion:


 * 1) What are the advantages of representing motion using a…
 * 2) Motion diagram- It is a simple method that g ets the point across . Shows direction.
 * 3) Ticker tape diagram- Shows acceleration and velocity very well and is easy to understand and read.
 * 4) position vs. time graph- Shows the displacement, velocity, and acceleration can be determined from the velocity slope.
 * 5) velocity vs. time graph- Shows the velocity and acceleration just by looking at the slope.
 * 6) acceleration vs. time graph- Shows acceleration and displacement if you find the area of the graph.


 * 1) What are the disadvantages of representing motion using a…
 * 2) Motion diagram- Has no quantitative purpose.
 * 3) Ticker tape diagram- Does not give a rate, only generalization of the acceleration.
 * 4) position vs. time graph- Does not give you acceleration just by looking at the graph.
 * 5) velocity vs. time graph- Does not show the displacement.
 * 6) acceleration vs. time graph- Does not show velocity, only change in it.


 * 1) Define the following:
 * 2) No motion- An object's motion that has a velocity and acceleration of zero.
 * 3) Constant speed- A motion with a velocity and no acceleration.
 * 4) Increasing speed- A motion with a velocity and acceleration that are either both positive or both negative.
 * 5) Decreasing speed- A motion with a velocity and acceleration where one is positive and the other is negative.

**Conclusion:**
The results from our motion lab presented data that supported our hypothesis. Our goal was to prove that a position vs. time graph is the best way to represent motion. We feel that our results showed that a motion sensor is extremely sensitive, and picks up even the most minute detail of motion, showing its accuracy. The position vs. time graphs, once one understands their nature, are extremely easy to read and interpret.

There are a few different ways that error plays into this experiment, much of it human error. First, because we were //walking// toward and away from the sensor, the results were less accurate. When humans walk, we don’t maintain a robotic, constant speed, and instead accelerate and decelerate many times, usually when steps are taken. This is evident in all of our graphs, but let’s examine the graph of **constant motion toward** space? . Because Sean was walking at a constant motion toward the sensor, his speed was not changing. Thus, the acceleration should be a flat line. The line does indeed hover at around zero like we expected, however it has tiny peaks and valleys. These are the points at which steps were taken, and the speed was increased and decreased very slightly. Also, because we had to manually stop and start the sensor by clicking a button on the computer, we were not completely accurate at our stops and starts. Standard human reaction time is about .2 - .25s, therefore we may have started the sensor too early or too late, causing unwanted data or misrepresented graphs. Another form of error, this time not human related, would be the terrain. Of course, there is no way to tell if the floor of the classroom and the surface of the counter on which the sensor was positioned were parallel. If they were not, then the distance Sean actually traveled when walking as opposed to the distance the sensor recorded would be different, and would thus give us an incorrect representation of both velocity and acceleration. well-stated!

When it comes to real life, we found that a Position vs. Time graph is the most efficient way to judge an objects motion. Motion detectors are utilized by roadside police officers to judge a car’s speed. The machine would use a Position vs. Time graph to calculate the car’s velocity, and notify the police officer if a driver is speeding. Position vs. Time graphs are also used in sports. In the game of baseball, stats are kept on how fast a pitcher throws a ball. Using the same technology from the aforementioned police officer’s machine, one is able to use a speed gun to determine the mph/h of a pitchers toss. In summation, a Position vs. Time graph is the most applicable of all the graphs we’ve encountered in this lab. It shows the direction of motion as well as allows you to calculate the velocity and tell if an object is accelerating or at a constant speed, making it the most versatile of all the graphs we used.

Lab: A Crash Course in Velocity Due: 9/27/10


 * Hypotheses:**

Hypothesis for graph: The faster car will have a steeper slope than the slower car because the faster has a high velocity.

**Purpose:** Show the difference between the velocities of two different CMVs graphically, algebraically, and experimentally. goes before hypothesis. and this isn't such a great purpose... I think I provided them on lab instruction sheet. I usually do.

//Collecting Initial Data://
 * Procedure:**
 * 1) Attach spark tape to the slow speed Constant Motion Vehicle with tape
 * 2) Thread other end through spark machine.
 * 3) Begin CMV.
 * 4) Turn on spark machine.
 * 5) Remove and repeat for fast CMV.
 * 6) Find the distances between spark marks of each, and record in Excel.
 * 7)  Create position-time graph to find the average speed of each CMV in Excel.

//Collision Test://
 * 1) Place the two CMVs 600cm apart, facing eachother
 * 2) Start the CMVs.
 * 3) Record the time and distance at which they collide.

//Catch Up Problem://
 * 1) Place the slow CMV ahead of the fast CMV, facing the same direction.
 * 2) Start the CMVs.
 * 3) Record the position at which the faster CMV catches up with the slower CMV.

great graph!!!!

OR aren't these calcs for other lab?

For the catching up problem, Ross and Sean set up the cars in the same spot every time, with the front* of the fast car lined up with the beginning of the first ruler. The back of the slow car was lined up with the end of the same 1m ruler. Sean counted down every time to keep a constant reaction time difference between himself and Ross. Catching-up equation: V fast ﻿= 3.7 cm/s V slow = 1.8 cm/s d fast ﻿= 3.7t d slow = 1.8t d fast = d slow ﻿ + 100 3.7t=1.8t + 100 1.9t=100 t=52.6 seconds
 * || Slower ||  || Faster ||
 * Trial 1 || 133 ||  || 233 ||
 * Trial 2 || 133.2 ||  || 233.2 ||
 * Trial 3 || 132.2 ||  || 232.2 ||
 * Trial 4 || 142 ||  || 242 ||
 * Trial 5 || 134 ||  || 234 ||
 * Trial 6 || 137 ||  || 237 ||
 * Trial 7 || 128.5 ||  || 228.5 ||
 * Trial 8 || 122 ||  || 222 ||
 * Average || 132.7 || Average || 232.7 ||

d fast ﻿= d slow ﻿+100 d slow ﻿=.18t 37(5.26) = 194 cm. 18(5.26)=94.7 cm.

Collision Problem:



Avg distance for fast car = 404.5cm Avg distance for slow car = 195.5cm

For the collision problem, Ross and Sean set up the cars 600cm apart, with the front of the fast car at the beginning of the tape measure, and the front of the slow car at the 6m mark. Sean counted down every time with this experiment as well. When the two cars collided, Sean put his hands on both to keep them from moving. Ross and Phil would then draw the best possible line from where the two fronts collided to the tape measure.

Equaiton:

V fast ﻿= 37 cm/s V slow = -18 cm/s d fast ﻿= 37t d slow = -18t

d fast ﻿=d slow - 600 37t= -18t+600 55t=600 t= 10.9 seconds d fast ﻿= 37t d slow = -18t 37(10.9)= 404 cm. -.18(10.9)= -196 cm. (so distance is 196 cm.)


 * Front/back = the respective side on the top part of the car. If we would've used the actually body of the car, it would've made the calculations for distances slightly more complicated.

percent error between theory and actual positions?


 * Discussion Questions**


 * 1) Why is the slope of the position-time graph equivalent to average velocity? - Slope = rise/run. Rise = y (position) and Run = x (time). Slope = (y2 - y1)/(x2 - x1) or (pos2 - pos1)/(time2 - time1). Therefore, by taking two points on the position-time graph and finding the slope, we get the velocity. For example, taking the points (0,0), or the object's starting point, and (10, 5), we get a slope of 2. This means that the object traveled 2 meters in 1 second, which equates to a velocity of 2 m/s. In our situation, if the points were graphed exactly, the line would not be linear - it would be curved. Due to this fact, it is necessary to use a best fit or trend line to represent the average between these points. Since the slope of a position-time graph represents velocity, the slope of the trend line would be equivalent to average velocity because the trend line the average of all the points.
 * 2) Why was it okay to set the y-intercept equal to zero? - It was okay to set the y-intercept equal to zero because when time was zero, the spark timer had not started yet, therefore the position would also be zero.
 * 3) What is the meaning of the R2 value? - The R2 value represents how accurate the trend line of the position-time graph fits the actual individual points. An R2 value of 1 means that the trend line fit perfectly in respect to the individual points.
 * 4) Where would the cars meet if their speeds were exactly equal? - If the speeds of the cars were exactly equal, they would meet exactly at the half-way point between them. If they were to start at 600cm apart and their speeds were equal, the would meet right in the middle at 300cm.
 * 5) 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.
 * 6) Catching up
 * 7) [[image:P-t_catchingup.jpg]]
 * 8) Crashing
 * 9) [[image:P-t_crashing.jpg]]
 * 10) Sketch velocity-time graphs to represent the catching up situation. Is there any way to find the points when they are at the same place at the same time? - There is no way to find the points when they are at the same place at the same time in a velocity-time graph.
 * 11) [[image:V-t_catchingup.jpg]]


 * Conlusion**

We were correct on all three of our hypothesis. By looking at the position-time graph, it shows that the faster car had a steeper slope. Furthermore, as shown in the discussion, the slope of a position-time graph is the velocity, and the faster car would have the faster velocity. For the collision equation, the car traveling a higher velocity theoretically traveled a further distance by the time they collided. In reality, this was true, as each time the two collided, the faster vehicle travelled significantly farther. On the catch up problem, the faster one did travel a further distance, shown in the graph, equation and diagram, as the faster vehicle started 100 cm. behind the slower one. Also, the table shows the same.

In both set-ups, there were many opportunities for error. First of all, it took two people to flip the switch on the vehicles, so human error contributed to the results, as there was a reaction time between the two. To counter this, a mechanism that could simultaneously flip the switches at the exact time would be necessary. Furthermore, the vehicles were not always perfectly lined up, so they could have possibly travelled an extra distance. Lines could have been used. Finally, due to a malfunction in our faster vehicle, it tailed off to the side, so we had to use a meter stick to keep it on the correct course. Thus, it travelled a little further than was necessary. good

This lab has many real-life implications. For example, if a car is traveling behind another, slower vehicle, it can determine what point it will pass the vehicle. Also, in track, relay runners often receive the baton far away from other competitors, and if the runner knows how much faster he is than his competitors, he will know roughly where he will pass them. In the collision situation, two friends deciding where to meet up could take into account the speed they would be traveling in order to decide a fair location. Also, in baseball, a batter must determine when to swing in order to make contact with the ball. Without thinking, he is actually calculating the speed of his bat versus the speed of the ball and determining at what millisecond the two will collide.

Lab: What is the Acceleration of a Falling Body? Ross and Chris 9/28/10

Hypothesis: The weight will fall with negative constant acceleration, and will increase velocity.

Discussion Questions-


 * 1) Does the shape of your graph agree with the expected graph? Why or why not?

Yes, it is originally curved, then becomes more sloped towards the end. It agrees with the expected graph since it is originally sloped as it is accelerating. However, once it becomes linear, it is obvious that the object has reached constant velocity. However, the initial velocity should be zero, thus making it only the squaring of the acceleration.


 * 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?

Yes, it maintained a curved line before eventually becoming a line once free fall was reached.


 * 1) What should the velocity-time graph of this object look like?

At first, it would start at zero, and keep on increasing with a slope of 980 cm/s 2. Then, after it reaches the constant velocity it would even out as it would have a slope of 0.

y=916.3x
 * 1) Write down the expected equation of the line from this v-t graph (use specific information from your x-t graph).


 * 1) What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?

The air pressure pushing down, weight of the object, and a subtle, unintentional "push" on the object could be reasons for it being higher. However, if the weight did not have enough time to reach free fall it would be lower than it should be.



Conculsion:

The results from this freefall experiment supported our hypothesis. We expected the weight to fall with constant acceleration, thus increasing velocity. However, towards the end of the graph, we noticed that the trendline started to straighten out, thus the velocity began to become constant. This implies that there must be a speed at which an object falling due to gravity cannot increase its velocity past. That speed is 9.8 m/s. we did not get 980 cm/s as we expected, however there are numerous factors that can account for this. First, friction. the friction between the sparker and the spark tape may have created drag that would have caused the velocity not to reach its maximum potential. Second, human error. When measuring the distances between the dots on the spark tape, there is a possibility we may have made a mistake in judgement.