Ch2_MalleyJ

Ch2_MalleyJe toc

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


 * __ Hypothesis __** : Based on how fast we saw the CMV move in class, it will move about 40 cm/s. Distance can be measured fairly precisely, depending on how it’s measured, but no measurement will ever be an exact number. A position-time graph can tell you the position of something at a particular time.

**Graph:**
 * Position Time Data for CMV**:
 * Time (s) || Position (cm) ||
 * 0 || 0 ||
 * 0.1 || 1.71 ||
 * 0.2 || 3.49 ||
 * 0.3 || 5.25 ||
 * 0.4 || 7.27 ||
 * 0.5 || 8.99 ||
 * 0.6 || 10.67 ||
 * 0.7 || 12.44 ||
 * 0.8 || 14.01 ||
 * 0.9 || 15.78 ||
 * 1.0 || 17.52 ||

**Analysis** : My hypothesis was partially accurate. Because we tested a slower CMV, we got a slower time than what we witnessed in class. To test my hypothesis, I would have to test the witnessed CMV. We discovered, however, that a CMV does move constantly, no matter the speed.


 * Discussion Questions **
 * 1) Why is the slope of the position-time graph equivalent to average velocity?
 * 2) The slope of the line in the case of a position-time graph is equal to the change in position divided by the change in time. This is equivalent to the average velocity because the slope is the equation for velocity.
 * 3) Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * 4) If we were only looking for instantaneous velocity, we’d be looking for the velocity at a set time, which wouldn’t be a s accurate in this case as the average velocity. We are making that assumption that the CMV is moving at a constant speed.
 * 5) Why was it okay to set the y-intercept equal to zero?
 * 6) The y-axis could be set to zero because we started with zero seconds at point zero.
 * 7) What is the meaning of the R2 value?
 * 8) The R2 value shows the trendline’s ability to pass through all of the points on the graph. By doing this, the value shows us the accuracy of the trendline.
 * 9) 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?
 * 10) I would expect the new line to have a lower slope than my line, so it would lie below it and not be parallel.

I hypothesized that the cart would be moving around 40 cm/s, however, our cart move around 17.633 cm/s. There’s no evidence from our cart to support my hypothesis, as the cart we witnessed was a fast cart with two batteries, as opposed to the one we had that was slower with one battery. However, this does not necessarily mean my hypothesis was wrong. Some inaccuracies in our data may be due to estimations with the ruler. Additionally, the ruler may have shifted and made the data slightly inaccurate. It’s also possible that the spark timer was read before it became consistent. More accurate tools could have been used to minimize inaccuracies. We could have used a flat ruler or tape measure that would provide for only one point of view when looking at the ruler. Additionally, using a fresh battery will ensure that the results are more accurate and consistent with other people's in the class.
 * Conclusion **

Lesson 1: Describing Motion with Words

 * Introduction to the Language of Kinetics
 * Key Words:
 * __mechanics__: the study of the motion of objects
 * __kinematics__: the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations
 * 1.) To be successful at physics, you can't memorize; rather, you should examine the information and determine how it's useful.
 * 2.) It's important to study kinematics to discover how things move.
 * 3.) The introduction was pretty clear.
 * 4.) The concept of motion was covered in class.
 * Scalars and Vectors
 * Key Words:
 * __scalars__: quantities that are fully described by a magnitude (or numerical value) alone
 * __vectors__: quantities that are fully described by both a magnitude and a direction
 * 1.) Physics is based on mathematics. Physics is used in everyday life.
 * 2.) This section helped to clarify what a scalar and vector was.
 * 3.) The section is pretty clear.
 * 4.) The concept of scalars and vectors was only briefly covered in class, but this helped me to understand it.
 * Distance and Displacement
 * Key Words:
 * __distance__: a scalar quantity that refers to "how much ground an object has covered" durings its motion
 * __displacement__: a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position
 * 1.) Displacement is based on the idea of how far you are from you're starting point while distance is based on the idea of how much of an area you've covered.
 * 2.) This section helped to clarify the difference between distance and displacement. It also cleared up the fact that going the opposite direction of which way you already went cancels out whatever displacement there once was.
 * 3.) The section was pretty clear.
 * 4.) The concept of displacement and distance was covered in class, but this helped me to be more certain of what it was.
 * Speed and Velocity
 * Key Words:
 * __speed__: a scalar quantity that refers to "how fast an object is moving"; can be though of as the rate at which an object covers distance
 * __velocity__: a vector quantity that refers to "the rate at which an object changes its position"; the rate at which the position changes
 * __instantaneous speed__: the speed at any given instant in time
 * __average speed__: the average of all instantaneous speeds; found simply by a distance/time ratio
 * Equations:
 * This one shows how to calculate the average speed of an object:
 * [[image:average_speed]]
 * This one shows how to calculate the average velocity of an object:
 * [[image:average_velocity]]
 * 1.) Speed and velocity, although they both involve rates, are actually very different. Speed refers to the rate at which an object is moving, while velocity refers to the rate at which an object changes its position.
 * 2.) This section helped to clarify what to do when calculating velocity. You must keep track of the direction an object is going in to know where it is at the end of a problem.
 * 3.) Does the rate at which an object moves matter when dealing with velocity, or just the direction?
 * 4.) The concept of instantaneous speed and average speed were much more clear in the reading, although they were covered in class.

Class Notes on Lesson 1: At Rest and Constant Speed
Page One: Page Two:

Lesson 2: Describing Motion with Diagrams
Introduction to Diagrams Ticker Tape Diagrams Vector Diagrams Questions after Reading (Notes):
 * Notes:
 * physics is a largely visual class, and so the diagrams help us to see what's happening in the physical world
 * all the vocabulary that you learn should have some relation to something physical
 * Key Words:
 * __ticker tape analysis__: a long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time, as the object moves, it drags the tape through the 'ticker,' thus leaving a trail of dots; the trail provides a history of the object's motion and therefore a representation of the object's motion
 * Notes:
 * the distance between the dots on the tape represents the object's position change during that time interval
 * a large distance shows that the object was moving quickly, while slower they'll be closer together, as shown in the below diagram
 * [[image:ticker_tape_fast_slow]]
 * you can also use the ticker tape to see the change in motion between: constant speed or accelerating
 * if the distance between the dots change, there's a change in acceleration; a constant distance between dots represents a constant velocity and therefore no acceleration, more examples are show in the diagram below
 * [[image:ticker_tape_speeds]]
 * Key Words:
 * __vector diagrams__: diagrams that depict the direction and relative magnitude of a vector quantity by a vector arrow; can be used to describe the velocity of a moving object during its motion
 * Notes:
 * the magnitude of a vector quantity is represented by the size of the vector arrow
 * the first diagram depicts an object in constant motion, while the other one shows it speeding up (you can tell because the arrows get larger)
 * [[image:vector_diagram_velocity]]
 * vector diagrams are more useful when dealing with physical things, like force, acceleration, and momentum
 * arrows can point other ways to show that they're going different directions
 * What did you read that you already understood well from our class discussion?
 * Today in class we learned about how to tell whether a ticker tape diagram is slowing down or speeding up. I understood this very well because it makes sense that the space in between the dots would get smaller as the object slowed down, and vice versa. The reading also covered it well. Additionally, the reading also made sense about how to tell if something is accelerating in a vector diagram, as there will be larger/smaller arrows.
 * What did you read that you were a little confused about from class, but the reading helped to clarify?
 * I wasn't all that confused about anything, but the reading was very clear in explaining, if only in less depth.
 * What did you read that you still don't understand?
 * Everything was pretty clear.
 * What did you read that was not gone over during class today?
 * Everything was covered, and more, in class.

Graphical Representation of Equilibrium Lab

 * Objectives:**
 * What is the difference between static and dynamic equilibrium?
 * How is “at rest” represented on a position vs. time graph? On a velocity vs. time graph? On an acceleration vs. time graph?
 * How is constant speed represented on a position vs. time graph? On a velocity vs. time graph? On an acceleration vs. time graph?
 * How are changes in direction represented on a position vs. time graph? On a velocity vs. time graph? On an acceleration vs. time graph?

Rest (No Motion):
 * Graphs**:

Constant:

Slow:

Fast:

Change Direction:


 * Discussion** **Questions**:
 * 1) How can you tell that there is no motion on a…
 * 2) position vs. time graph: There’s a straight line with a slope of 0.
 * 3) velocity vs. time graph: There’s a straight line with a slope of 0.
 * 4) acceleration vs. time graph: There’s a straight line with a slope of 0.
 * 5) How can you tell that your motion is steady on a…
 * 6) position vs. time graph: T here will be a linear line going diagonally up.
 * 7) velocity vs. time graph: A linear line will be on the graph with a slope of 0. It will be slightly above the x axis.
 * 8) acceleration vs. time graph: There should be a straight line with a slope of 0 on the x axis.


 * 1) How can you tell that your motion is fast vs. slow on a…
 * 2) position vs. time graph : If it’s fast, the diagonal line will have a steeper slope, while if it’s slow, it’ll have a less steep slope.
 * 3) velocity vs. time graph: You can’t really tell as long as the velocity is constant.
 * 4) acceleration vs. time graph: You can’t really tell as long as the motion is constant.


 * 1) How can you tell that you changed direction on a…
 * 2) position vs. time graph: T he linear line will curve as you turn, and then come back down (with the same slope, except negative), as you walk back.
 * 3) velocity vs. time graph: You can't really tell.
 * 4) acceleration vs. time graph: You can't really tell.


 * 1) What are the advantages of representing motion using a…
 * 2) position vs. time graph : A position time graph is useful because it shows where exactly you are at a particular time and is fairly easy to read. It also shows if you speed up or slow down and some change in direction.
 * 3) velocity vs. time graph: This can tell you the approximate velocity at a certain time of an object.
 * 4) acceleration vs. time graph: This is helpful in seeing when there's a change in velocity.


 * 1) What are the disadvantages of representing motion using a…
 * 2) position vs. time graph : This isn’t all that accurate in demonstrating changes in speed.
 * 3) velocity vs. time graph: This can only tell you when the velocity changes, otherwise it's just a straight line.
 * 4) acceleration vs. time graph: This graph is useful in showing a change in speed.


 * 1) Define the following:
 * 2) No motion: when there is no motion, nothing is moving and there is only a straight line on the graph, no matter which graph it is
 * 3) Constant speed: when something is at constant speed, it is moving with a continual motion; velocity and acceleration of 0, but still a speed and position that will show up on a position vs time graph

Class Notes on Important Equations (The Big 5)
Page One: Page Two:

Class Notes on Increasing and Decreasing Speed Graphs

 * *mistakes you shouldn't make: confusing the three different graphs, labeling the graphs incorrectly
 * "Where are you located?" is the question that can be answered by the __position time graph__.
 * when you're moving away from the origin, it's positive; away, it's negative
 * slope = speed
 * "How fast are you going?" is what's being asked by the __velocity time graph__.
 * negative velocities don't mean you're going slow, they may be fast, just going in a different direction
 * slope = acceleration
 * if you get the area of the graph, you get the displacement (area = displacement)
 * Acceleration time graphs provide a bit less information
 * change in velocity = area "under" graph

Graph Examples (refer to worksheet):

Lab: Acceleration on an Incline

 * 9/14/11 with Nicole Kloorfain**


 * Objectives**:
 * What does a position-time graph for increasing speeds look like?
 * What information can be found from the graph?
 * Hypothesis**: On the position time graph, this will be a positive graph that curves to show acceleration. The slope will get steeper as the acceleration increases. From this graph, we will be able to find the position of the object at any recorded time and its increasing acceleration and velocity. (Kinda like a J-graph).


 * Materials**: spark tape, spark timer, tape, dynamics cart, meter stick, textbook, track
 * Procedure**:
 * 1) Gather all of the necessary materials.
 * 2) Lay the textbook on top of a flat surface and place the edge of the track on top of it. The track should now be at an angle.
 * 3) Set up the spark timer and attach the spark tape to the dynamics cart.
 * 4) Place the dynamics cart at the top of the slope that you formed with the track.
 * 5) Turn the spark timer on 10 Hz and let go of the dynamics cart.
 * 6) When the dynamics cart is at the bottom, turn off the spark timer and remove the spark tape from the dynamics cart.
 * 7) Tape the ticker tape to a flat surface and record the distance between each dot. Record the time as well.
 * 8) Make a position vs. time graph with the data.

Acceleration Deceleration Combined Acceleration Deceleration Combined
 * Data**:
 * Graph**:

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.
 * Analysis**:
 * 1) The R2 value is .999603, which shows that our polynomial graph is fairly accurately following the equation. The line’s equation is y=Ax2+Bx. In this case, A represents half of the velocity and B represents the initial velocity. So, for our graph the acceleration is 18.43 cm/s, and the initial velocity is 1.29 cm.
 * 1) instantaneous speed = 17.95 cm/s
 * 2) [[image:Photo_on_2011-09-14_at_16.06_#2.jpg]]
 * 1) [[image:Screen_shot_2011-09-14_at_9.30.37_AM.png]]
 * Discussion Questions**:
 * 1) What would your graph look like if the incline had been steeper?
 * 2) If the incline had been steeper, the graph itself would have been steeper. The curve would have been more noticeable, and the acceleration would have been greater.
 * 3) What would your graph look like if the cart had been decreasing up the incline?
 * 4) If the cart had been decreasing up the incline, it would look a bit like the acceleration graph, accept flipped over. The graph, because it’s positive, still goes away from the origin, however, it’s very steep to begin with and then curves up and begins to flatten out.
 * 5) Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
 * 6) The average speed is 19.56 cm/s, while the instantaneous speed is 17.95 cm/s. The reason that these are similar but not the same is because the average speed is the median speed of the entire trip, while the instantaneous speed is the speed at one point of the trip.The reason that the instantaneous speed, in this case, is lower than the average speed is because it's in the middle of the data, so it's going to be lower than the average speed, but it's still higher than the initial speed because of the increasing velocity.
 * 7) Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
 * 8) This makes sense because instantaneous speed means that you’re taking the speed of one point. Because the tangent line only runs through one point on the graph, the speed you’re going to get will be of the point.
 * 9) Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
 * 10) [[image:Screen_shot_2011-09-14_at_5.53.31_PM.png]]

From this lab, we were able to realize what a position vs. time graph looks like when something is accelerating and when something is decelerating. Additionally, by examining the graphs, we realized that an equation for a deceleration would show a negative acceleration, even though it's still a positive graph because it's direction didn't change. My hypothesis was fairly accurate in terms of the predicted description of the graph of acceleration: it did get steeper as it continued to accelerate. Some inaccuracies can be contributed to the uncertainty of the last digit when using a meter stick. Additionally, by only running one trial, there's no way to say we would get the same results again, despite the certainty of our measurements that the graph provided for us. Next time, to minimize the inaccuracies, we could make sure we're measuring extremely precisely and we could run the trial multiple times to see if the graphs sync up.
 * Conclusion**:

Lesson 1e: Acceleration

 * Key Words:
 * __Acceleration__: a vector quantity that is defined as the rate at which an object changes its velocity; an object is accelerating if it's changing it's velocity
 * __Constant Acceleration__: changes acceleration in constant intervals
 * __Free-Falling Object__: usually accelerates as it falls
 * __Positive Acceleration__: the acceleration is in the same direction as the velocity (when an object is speeding up)
 * [[image:positive]]
 * __Negative Acceleration__: the acceleration is in the opposite direction of the velocity (when an object is slowing down)
 * [[image:negative]]
 * Notes:
 * acceleration just means the speed is changing, not necessarily that a person's going fast
 * accelerating objects are changing their velocity
 * an object that is accelerating at a constant rate (like a free falling object) will cover different distances in each second
 * Equation for Average Acceleration:
 * [[image:average_acceleration]]
 * can be used to calculate acceleration of the object whose motion is depicted by the velocity-time data table
 * This is the calculation of an example problem:
 * [[image:calculation]]
 * The units later become:
 * [[image:units]]
 * which is m/s^2
 * the direction of acceleration vector depends on two things: whether the object is speeding up or slowing down and whether the object is in the + or - direction
 * RULE OF THUMB: If an object is slowing down, then its acceleration is in the opposite direction of its motion.
 * positive and negative, in these cases, has a physical meaning
 * Summarizing
 * 1) What did you read that you already understood well from class?
 * 2) In class, I understood the concept of average acceleration very well. It's the change in velocity over the change in time.
 * 3) What did you read that you were a little confused about from class, but the reading helped to clarify?
 * 4) The reading helped to further clarify the units when dealing with average velocity. Additionally, it helped to clarify the negatives and positives on the graph, and their meaning.
 * 5) What are you still unsure about?
 * 6) The reading was pretty clear.
 * 7) What did you read that wasn't covered in class?
 * 8) We touched only briefly on the concept of free-falling objects in the discussion of the egg drop project, but it was well explained in the text.

Lesson 3: Describing Motion with Position vs. Time Graphs

 * The Meaning of Shape for a p-t Graph**:
 * Key Words:
 * __Position vs. Time Graphs__: in this graph, the specific features of the motion of objects are demonstrated by the shape and the slope of the lines
 * __Constant, Rightward (+) Velocity__: velocity of an object that is constantly going away from the origin
 * Example when Drawn:
 * [[image:drawn_constant_rightward]]
 * Example when Graphed:
 * [[image:constant_rightward_velocity]]
 * __Rightward (+), Changing Velocity__: the object is moving rightward but is accelerating
 * Example when Drawn:
 * [[image:drawn_changing_right_velocity]]
 * Example when Graphed:
 * [[image:graph_changing_right_velocity]]
 * Notes:
 * words, diagrams, numbers, and equations are all useful when representing motion
 * the slope of the line on a p-t graph reveals useful information
 * whatever characteristics the velocity has, the slope will exhibit the same (and vice versa)
 * if velocity is negative, so is slope; if velocity's constant, so is slope
 * the principle of slope can be used to extract relevant motion characteristics from a position vs. time graph
 * observe the two examples below: the only difference is that the slope of the second is steeper and hence a faster velocity; however, the velocity's still constant in both
 * Slow, Rightward (+) slope = constant velocity
 * Graphed Example:
 * [[image:slow]]
 * Fast, Rightward (+) slope = constant velocity
 * [[image:fast]]
 * the next two graphs below display the same concept, except that they're negative
 * Slow, Leftward (-), Constant Velocity
 * [[image:slow_left]]
 * Fast, Leftward (-), Constant Velocity
 * [[image:fast_left]]
 * the concept of slope = velocity still applies when the acceleration changes - it uses a curve. however, all the other same rules apply (slope's steeper if it's faster, etc)
 * Negative (-) Velocity, Slow to Fast (__Negative Acceleration__: moving in the negative direction and speeding up)
 * [[image:neg_accel]]
 * Leftward (-) Velocity, Fast to Slow (__Positive Acceleration__: moving in the negative direction and slowing down)
 * [[image:pos_accel]]
 * The Meaning of Slope for a p-t Graph**:
 * Notes:
 * graph of constant speed to rest
 * [[image:U1L3b2.gif]]
 * that graph occurs because the slope of the line is equal to the velocity on a p-t graph
 * Determining the Slope on a p-t Graph**:
 * Notes:
 * slope equation is: [[image:U1L3c2.gif]]
 * that equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points (same as we've learned in math class)
 * example of using equation:
 * [[image:U1L3c3.gif]]
 * this: [[image:U1L3c5.gif]] would have a negative slop of -3 m/s because its speed/velocity is decreasing
 * Summary**:
 * 1) What did you read that you already understood well from class?
 * 2) In class, we learned about the difference between negative and positive graphs. I understood this fairly well because of the concept of slopes.
 * 3) What did you read that you were a little confused about from class, but the reading helped to clarify?
 * 4) The reading helped to clarify the difference between positive acceleration and negative acceleration.
 * 5) What are you still unsure about?
 * 6) I'm still slightly confused about graphing negative velocity and positive acceleration together. Does this just mean that the object is moving back toward the origin but speeding up?
 * 7) How can you tell certainly on a graph the difference between positive acceleration and negative acceleration?
 * 8) What did you read that wasn't covered in class?
 * 9) As far as I know, the entire reading was covered in class.

Lesson 4: Describing Motion with Velocity vs. Time Graphs

 * The Meaning of Shape for a v-t Graph**:
 * Key Words:
 * __Velocity vs. Time Graphs__: used to describe motion; the specific features of the motion of objects are demonstrated by the shape and the slope of the lines on this graph
 * __Constant, Rightward (+) Velocity__: 0 acceleration moving rightward
 * [[image:U1L4a4.gif]]
 * __Rightward (+), Changing Velocity__: moving rightward but speeding up (accelerating) - has positive acceleration
 * [[image:U1L4a5.gif]]
 * Notes:
 * a constant velocity graph of a car going +10 m/s looks like:
 * [[image:U1L4a1.gif]]
 * a changing velocity (positive acceleration) graph:
 * [[image:U1L4a2.gif]]
 * //The slope of the line on a velocity-time graph reveals useful information about the acceleration of the object//.
 * reading a velocity vs. time graph can give you a lot of useful information
 * a positive velocity means the object is moving in the positive direction, and a negative velocity means the object is moving in the negative direction
 * graphs that are useful in understanding the above concept:
 * [[image:U1L4a7.gif]]
 * speeding up means that the numerical value of the velocity is getting larger and vice versa
 * graphs that are useful in explaining the above concept:
 * [[image:U1L4a6.gif]]
 * The Meaning of Slope for a v-t Graph**:
 * Notes:
 * if you had a car like this: [[image:U1L3a1.gif]] with constant motion, it's graph would look like this: [[image:U1L4b2.gif]] because of the data you've been given
 * however, if the car was moving like this: [[image:U1L4b3.gif]], the graph would look more like this: [[image:U1L4b6.gif]] because the speed is increasing and so is the velocity - this is constant acceleration
 * if the car were to go from constant speed to constant acceleration, it would look like this:
 * [[image:U1L4b4.gif]] because your slope is changing
 * the slope of the line on a velocity-time graph is equal to the acceleration of the object
 * this idea can be used for all velocity-time in order to determine the numerical value of the acceleration
 * Relating the Shape to the Motion**:
 * Notes (useful graphs and explanations):
 * [[image:U1L4c1.gif]]
 * [[image:U1L4c2.gif]]
 * [[image:U1L4c3.gif]]
 * [[image:U1L4c4.gif]]
 * [[image:U1L4c5.gif]]
 * [[image:U1L4c6.gif]]
 * Determining the Slope on a v-t Graph**:
 * Notes:
 * equation for slope:
 * [[image:U1L3c2.gif]]
 * use of the equation:
 * [[image:YES]]
 * Determining the Area on a v-t Graph**:
 * Notes:
 * for v-t graphs, the area bound by the line and the axes represents the displacement
 * example:
 * the shaded area is representative of the displacement during from 0 secs to 6 secs: this area takes the shape of a rectangle and can be calculated using the appropriate equation
 * [[image:rectangle]]
 * the shaded area is representative of the displacement during from 0 secs to 4 secs: this area takes on the shape of a triangle and can be calculated using the appropriate equation
 * [[image:triangle]]
 * the shaded area is representative of the displacement during from 2 seconds to 5 seconds: this area takes on the shape of a trapezoid and can be calculated using the appropriate equation
 * [[image:U1L4e8.gif]]
 * area formulas:
 * [[image:U1L4e2.gif]]
 * the area bounded by the line and the axes of a v-t graph is equal to the displacement of an object during that particular time period
 * the area represents the displacement of the object
 * Summary**:
 * 1) What did you read that you already understood well from class?
 * 2) I understood the concept of slope equaling velocity very well, and the reading only further helped to expand my knowledge on the topic.
 * 3) What did you read that you were a little confused about from class, but the reading helped to clarify?
 * 4) In class, we briefly covered the concept of the area of a shape in a v-t graph equaling the total displacement, but I didn't understand it that well. The reading helped to further explain it.
 * 5) What are you still unsure about?
 * 6) I'm still a little confused about interpreting a v-t graph that's not at constant speed.
 * 7) What did you read that wasn't covered in class?
 * 8) I think everything was covered in class.

Lab: Crash Course

 * Date**: 9/21/11 **Names**: Jenna Malley, Nicole Kloorfain, Ryan Hall, and Sarah Malley


 * Original Data**: (blue is slow, green is fast)


 * Calculations**:

media type="file" key="Movie on 2011-09-21 at 08.57.mov" width="300" height="300" media type="file" key="Movie on 2011-09-21 at 09.06.mov" width="300" height="300"
 * Procedure/Data**:


 * Data Collected**:


 * Discussion Questions**:
 * 1) Where would the cars meet if their speeds were exactly equal?
 * 2) If the cars had equal speeds, they would meet at exactly the halfway point if they were facing each other. This is because it would take them the same amount of time to travel equal distances, and the half way point would be equal distances for both of them. The same reasoning applies if one car started ahead of the other. If one starts 100 m in front of the other, and they're both traveling in the same direction, it will remain 100 m in front for the entire trip.
 * 3) 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.
 * 4) [[image:Screen_shot_2011-09-21_at_10.23.40_AM.png width="704" height="357"]]
 * 5) The two cars crash at about 9.35 seconds at around 160 cm.
 * 6) Catching up CMVs
 * 7) Position (cm) [[image:Screen_shot_2011-09-21_at_2.13.40_PM.png]]
 * 8) Time (s)
 * 9) ^^^ These intersect at about 3 seconds at 159 cm.
 * 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?
 * 11) [[image:Screen_shot_2011-09-21_at_2.20.02_PM.png]]
 * 12) There is no way to find out when they're at the same place at the same time because using a velocity time graph, you don't know their position.

Crashing Catching Up
 * Conclusion**:

According to my calculations done before the experiment, the two carts should have collided at approximately 164.21 cm. This was fairly accurate, according to the data that my group collected. Our percent error was 2.34%, which means that we were that close to being exactly in line with our theoretical conclusion, which was actually based off of experimental data. Additionally, our precision was fairly on target, as the smallest number was within 1.3% of our average position, and the largest was within 1.08%. This experiment could have been more accurate if the CMVs were on a flat surface (not curved, like the school floor) and didn't curve. Additionally, some inaccuracies may be contributed to our estimations with the ruler, as there was no real accurate way of saying exactly where they collided, other than eye balling both carts and the ruler at the same time. However, doing multiple trials assured as that our data was at least fairly accurate and precise. If I had to change the lab to address the errors, I would have used a more accurate measuring device to track the cars. Additionally, I would perform it on a flatter surface, as the floor of the school would sometimes make the cars veer in a certain direction. This made it more difficult to gather data.

Example Word Problems
A car is behind a truck going 30 m/s on the highway. The car’s driver looks for an opportunity to pass, guessing that his car can accelerate at 2 m/s2. He gauges that he has to cover the 15-m length of the truck, plus 10 m clear room at the rear of the truck and 10-m more at the front of it. In the oncoming lane, he sees a car approaching, probably traveling at 20 m/s. He estimates that the car is about 450-m away. Should he attempt the pass? //(requires a minimum of 330.9 m, so yes)//

A runner hopes to complete a 6-km run in less than 16.0 minutes. After exactly 13.0 min, there are still 1500 m to go. The runner must then accelerate at 0.25 m/s2 for how many seconds in order to achieve the desired time? //(10.6 s)//

From Packet:

Egg Drop Lab

 * Partner**: Sarah Malley

**Analysis of Project** :


 * Picture of final**:


 * Brief description of result**: To create the egg drop, we had to do a lot of tests to see which designs and materials worked the best. We started with researching possible designs, but quickly realized that the material restrictions rendered all of the good egg drop designs that we found invalid. Next, we decided to just test a few designs with basic shapes: a rectangular prism and a pyramid. These worked sometimes, but not always. Finally, we did more research and realized that a larger surface area would lead to less acceleration, meaning less speed to stop when the object finally hit the ground. We made a base for the egg drop, put a square on top of that padded with straws and made a pyramid to hold the egg in. The only problem was that the egg fell out. To solve this, we made the pyramid tighter and added walls and tin foil.


 * Calculation for acceleration**: The acceleration of our egg drop was _. This makes sense because it can't be larger than 9.81 m/s^2, which is g.


 * Brief analysis of why it worked or didn't work**: Our egg drop worked. I think this is because there was a large enough surface area to slow down the acceleration a little bit and enough padding so that the egg had something to bounce off of. Additionally, the middle part of the project had straws that were higher off the ground as opposed to the sides on the bottom, so the sides hit the ground first and absorbed some of the stopping impact before the egg did.


 * What would you do differently?** Next time, I would try to make it weigh less. Our egg drop weighed only slightly less than the egg itself, but it probably could have been lighter if we had removed a few pieces of tape of took off possibly unnecessary straws. However, it worked, so it wasn't too bad.

Lesson 5: Free Fall and the Acceleration of Gravity

 * Introduction to Free Fall**
 * Key Words:
 * __free fall__: an object that is falling under the sole influence of gravity
 * Notes:
 * IMPORTANT:
 * 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
 * Diagrams of this would show acceleration as the item fell
 * The Acceleration of Gravity**
 * Key Words:
 * __acceleration of gravity__: the acceleration for any object moving under the sole influence of gravity, //g//
 * //g// = 9.8 m/s/s, downward
 * how we got this acceleration: [[image:gravity]]
 * Notes:
 * example depiction of a free fall:
 * [[image:example_2184]]
 * Representing Free Fall by Graphs**
 * position vs time graph for a free falling object (notice that it's curved because the velocity changes, ending with a larger one)
 * [[image:pt_graph]]
 * velocity vs time graph for a free falling object: (notice that it's a straight diagonal line that has an increasing velocity as it moves in the negative direction while speeding up) - negative vt graph (slope analysis reveals that this object is moving with a constant acceleration of 9.8 m/s/s in the downward direction)
 * [[image:vt_graphh]]
 * How Fast? and How Far?**
 * free falling objects are constantly accelerating, specifically at the rate of gravity (9.8 m/s/s)
 * 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
 * this can be used to calculate the velocity of the object after any given amount of time when dropped from rest
 * 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
 * The Big Misconception**
 * Doesn't a more massive object accelerate at a greater rate than a less massive object? //Absolutely not//!
 * However, the above information only applies when we're considering free falling objects (refer to part one of these notes)
 * the acceleration of an object is directly proportional to force and inversely proportional to mass
 * increasing force tends to increase acceleration while increasing mass tends to decrease acceleration
 * cute little depicting image:
 * [[image:funny_hahaaaa]]
 * Summarizing**
 * Using method one to summarize this: it's mostly notes, etc. I deleted everything that seems trivial to make it more understandable to me (the cross outs confuse me, as I tend to think it's false information). Additionally, I didn't add repetitive information in my notes. I tried to generalize to keep them concise.
 * Topic Sentence: Free falling objects depend on the acceleration of gravity.

Free Falling Object Lab
This graph shows that the velocity is increasing over time, because the slope is increasing. This graph shows that the acceleration is constant because it's a linear graph of velocity, so the slope is equal to acceleration.
 * Purpose**: What results do you think your experiment will produce? What do you think the v-t graph will look like? How will you find 'g' from this graph?
 * Hypothesis**: The acceleration due to gravity of a free-falling object is about -9.81 m/s/s, and the results of the experiment should show us this. If this is true, the v-t graph should be a linear line with a slope of 9.81 m/s/s. This being the acceleration should equal 'g.'
 * Weight**: 50 g
 * Nicole and Jenna's Data**:
 * Class Data**:
 * Graphs**:
 * These graphs are //negative// not //positive// because they were falling. (Even though they look positive, they're actually negative).


 * Discussion Questions**:
 * 1) Does the shape of your vt graph agree with the expected graph? Why or why not?
 * 2) The shape of the free fall graph does not agree with what I expected because I put in positive values for the velocity. However, the general concept of it does agree with what I believed it would look like, which is a linear line that shows constant acceleration. It did not, however, have the slope of 981 cm/s/s like I predicted that it would.
 * 3) Does the shape of your xt graph agree with the expected graph? Why or why not?
 * 4) Again, the shape of the position time graph doesn't look like I thought it would solely because I put in positive values for the position. Other than that however, it is accurate in what I predicted. The slope constantly increases, showing a linear change in velocity.
 * 5) How do you results compare to that of the class? (Use percent difference to discuss quantitatively).
 * 6) [[image:Screen_shot_2011-10-05_at_2.48.57_PM.png]]
 * 7) Our results aren't totally accurate, but they're precise according to the graph. According to our data, the difference was 21.45% different from the class data.
 * 8) Did the object acceleration uniformly? How do you know?
 * 9) The object accelerated constantly. I found this out by looking at the graph for velocity vs. time, which shows a linear line. Because the slope of a vt graph shows acceleration, it's evident from the graph that the acceleration is constant.
 * 10) What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?
 * 11) The acceleration due to gravity would be lower if the tape was being dragged, whether it the spark timer was held horizontally instead of vertically, or simply because a hand was in the way of its constant flow. It could be higher than normal if the data was incorrectly gathered, or if the measuring tape was read at the wrong starting or ending point.
 * Conclusion**: Although our results did not exactly match my hypothesis, which was that an object would free fall at an acceleration of -981 cm/s/s, part of this is because negative measurements were not included in our Excel graph. Additionally, Nicole and I ended up with a lower acceleration than what it should've been. This may be due to a myriad of factors, most notably the way the spark timer was held, and if there was anything in the way of the tape. Additionally, it's extremely likely that the tape may have shifted slightly when we were measuring it, therefore altering our gathered results slightly. Also, some of the ticker tape points weren't totally in one spot (the dots were a little crooked) and this made it a bit more difficult to get a completely accurate reading. If I were to redo this lab, I would make sure that the spark timer was vertically fixed when the object was being dropped, and that there was nothing in the way of the ticker tape as it moved. Additionally, I would find a more accurate way to measure the data.