Understanding 1D Motion

Transcription

1 Understanding 1D Motion OBJECTIVE Analyze the motion of a student walking across the room. Predict, sketch, and test position vs. time kinematics graphs. Predict, sketch, and test velocity vs. time kinematics graphs. INTRODUCTION One of the most effective methods of describing motion is to plot graphs of position, velocity, and acceleration vs. time. From such a graphical representation, it is possible to determine in what direction an object is going, how fast it is moving, how far it traveled, and whether it is speeding up or slowing down. In this experiment, you will use a Motion Detector to determine this information by plotting a real time graph of your motion as you move across the classroom. The Motion Detector measures the time it takes for a high frequency sound pulse to travel from the detector to an object and back. Using this round-trip time and the speed of sound, you can determine the position of the object. Logger Pro will perform this calculation for you. It can then use the change in position to calculate the object s velocity and acceleration. All of this information can be displayed either as a table or a graph. A qualitative analysis of the graphs of your motion will help you develop an understanding of the concepts of kinematics. walk back and forth in front of Motion Detector APPARATUS Computer Vernier computer interface (Lab Pro) Logger Pro Colored Pencils Vernier Motion Detector Meter stick Masking tape Reflecting Surface Understanding 1D Motion Page 1

2 THEORY Distance and Displacement Distance and displacement are two quantities which may seem to mean the same thing, yet have distinctly different definitions and meanings. Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position. Speed and Velocity Just as distance and displacement have distinctly different meanings (despite their similarities), so do speed and velocity. Speed is a scalar quantity which refers to "how fast an object is moving." A fastmoving object has a high speed while a slow-moving object has a low speed. An object with no movement at all has a zero speed. Velocity is a vector quantity which refers to "the rate at which an object changes its position." Velocity can be expressed by the following equation: v x t Where, v [m/s] is the average velocity, Δx [m] is the change in the position of the object and Δt [s] is the time it took the object to travel Δx. If a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. Every step must go into moving that person further from where he/she started. For certain, the person should never change directions and begin to return to where he/she started from. Velocity is a vector quantity. As such, velocity is "direction-aware." When evaluating the velocity of an object, one must keep track of direction. It would not be enough to say that an object has a velocity of 30 m/s. One must include direction information in order to fully describe the velocity of the object. For instance, you must describe an object's velocity as being 30 m/s, east. This is one of the essential differences between speed and velocity. Speed is a scalar and does not keep track of direction; velocity is a vector and is direction-aware. Understanding 1D Motion Page 2

3 The Position vs. Time Graph The shapes of the position vs. time graphs for these two basic types of motion - constant velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle. The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. It's often said, "As the slope goes, so goes the velocity." Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right). This very principle can be extended to any motion conceivable. Constant Velocity Positive Velocity Positive Velocity Changing Velocity (acceleration) Acceleration Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity. This is expresses by the equation: a v t Where, a [m/s 2 ] is the average acceleration, Δv [m/s] is the change in the velocity of the object and Δt [s] is the time it took the object to change its velocity Δv. Since acceleration is a vector quantity, it will always have a direction associated with it. The direction of the acceleration vector depends on two things: whether the object is speeding up or slowing down whether the object is moving in the + or - direction Sometimes an accelerating object will change its velocity by the same amount each second. As mentioned in the above paragraph, the data above show an object changing its velocity by 10 m/s in each consecutive second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second. Understanding 1D Motion Page 3

4 An object with a constant acceleration should not be confused with an object with a constant velocity. Don't be fooled! If an object is changing its velocity -whether by a constant amount or a varying amount - then it is an accelerating object. And an object with a constant velocity is not accelerating. The Velocity vs. Time Graph The shapes of the velocity vs. time graphs for these two basic types of motion - constant velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle. The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line). If the acceleration is negative, then the slope is negative (i.e., a downward sloping line). As before, this very principle can be extended to any conceivable motion. Positive Velocity Zero Acceleration Positive Velocity Positive Acceleration During this lab you will want to consider the position vs. time graph and the velocity vs. time graph for each of the following situations: An object at rest An object moving in the positive direction with a constant speed An object moving in the negative direction with a constant speed An object that is accelerating in the positive direction, starting from rest Understanding 1D Motion Page 4

5 PROCEDURE Part l Preliminary Experiments 1. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. 2. Place the Motion Detector so that it points toward an open space at least 4 m long. Use short strips of masking tape on the floor to mark the 1 m, 2 m, 3 m, and 4 m positions from the Motion Detector. The motion detector is programmed in such a way as to recognize motion away from it as positive and motion towards it as negative. 3. Start the Logger Pro program. 4. Open the file 01a Graph Matching from the _Physics with Vernier folder. This will display a large position vs. time graph 5. Using Logger Pro, produce a position vs. time graph of your motion when you walk away from the detector with medium constant velocity. To do this, stand about 1 m from the Motion Detector and have your lab partner click the Motion Detector when you hear it begin to click.. Walk slowly away from There is a delay between when you click and when the Motion Detector actually stars collecting data; just be aware of this. Once satisfied with the graph, go to the Experiment menu option and select Store Latest Run (Ctrl+L will also work). This will lock the graph you just made onto the screen and allow you to make an additional run while keeping that previous data. Having done that, using Logger Pro, produce an additional position vs. time graph of your motion when you walk away from the detector with slow constant velocity (non-zero). Store this latest run on the screen as well. o There is a Clear Latest Run option under the Experiment menu option as well if you need it. Having now saved these two trials to the screen, using Logger Pro, produce a final position vs. time graph of your motion when you walk away from the detector with fast constant velocity. o Print a copy of this combined position graph for comparison and inclusion in your laboratory report. {GRAPH #1} For this, and each of the printouts for this lab, use ONLY the print graph printing option. This will NOT print the data tables; which we do not need anyway. Again, DO NOT print the data tables we do not need them and it just wastes paper to do so! o Additionally, Click on the position graph label, located on the vertical axis, to and change the graph axis to velocity. This will be the corresponding velocity vs. time graphs to the position vs. time graphs you just created. o Print a copy of this combined velocity graph for comparison and inclusion in your laboratory report. {GRAPH #2} Understanding 1D Motion Page 5

6 6. Starting from a blank graph, using Logger Pro, produce a position vs. time graph of your motion when you walk toward the detector with constant velocity and print a copy of this graph for comparison and inclusion in your laboratory report. {GRAPH #3} Click on the position graph label, located on the vertical axis, to and change the graph axis to velocity. This will be the corresponding velocity vs. time graph to the position vs. time graph you just created. o Your data may be off the screen...but it is there! The "autoscale" feature of Logger Pro will help here. Print a copy of this graph for comparison and inclusion in your laboratory report. {GRAPH #4} 7. Starting from a blank graph, using Logger Pro, produce a position vs. time graph of your motion when you walk away from the detector with constant positive acceleration and print a copy of this graph for comparison and inclusion in your laboratory report. {GRAPH #5} Click on the position graph label, located on the vertical axis, to and change the graph axis to velocity. This will be the corresponding velocity vs. time graph to the position vs. time graph you just created. Print a copy of this graph for comparison and inclusion in your laboratory report. {GRAPH #6} Part Il Position vs. Time Graph Matching 1. Open the experiment file 01b Graph Matching. A position vs. time graph will appear. 2. Print a copy of this graph {GRAPH #7} and on it write out a prediction describing how you would walk to produce this target graph; detailing each section's motion. Do this BEFORE moving on to Part 3! 3. To test your prediction, choose a starting position and stand at that point. Start data collection by clicking. When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the computer screen. 4. If you were not successful, repeat the process until your motion closely matches the graph on the screen. Print the graph with your best attempt for comparison and inclusion in your laboratory report. {GRAPH #8} Understanding 1D Motion Page 6

7 Part III Velocity vs. Time Graph Matching 1. Open the experiment file 01d Graph Matching. A velocity vs. time graph will appear. 2. Print a copy of this graph {GRAPH #9} and on it write out a prediction describing how you would walk to produce this target graph; detailing each section's motion. Do this BEFORE moving on to Part 3! 3. To test your prediction, choose a starting position and stand at that point. Start by clicking. When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the screen. It will be more difficult to match the velocity graph than it was for the position graph. Print the graph of your best attempt for comparison and inclusion in your laboratory report. 4. If you were not successful, repeat the process until your motion closely matches the graph on the screen. Print the graph with your best attempt for comparison and inclusion in your laboratory report. {GRAPH #10} 5. Remove the masking tape strips from the floor. COVER PAGE REPORT ITEMS (To be submitted and stapled in the order indicated below) (-5 points if this is not done properly) Lab Title Each lab group member s first and last name printed clearly Color Group Date DATA (worth up to 15 points) The EIGHT graphs that were to be printed as indicated within the Experimental Procedure. The TWO description graphs {GRAPH #7 & #9} that go along with GRAPH #8 & #10; these go on top of their respective graphs. Understanding 1D Motion Page 7

8 DATA ANALYSIS (worth up to 40 points) Part l Preliminary Experiments (For Graphs #1 - #6) For each of the six graphs printed, it is necessary that you explain, in detail, what the graph indicates at each point (beginning, middle, end). You will write this explanation on the graph itself (front or back). Additionally, be sure that you have clearly indicated what part of the graph you are talking about at each step. It may be best to break the graph into segments that have different meanings. For example, referencing the sample graph below, labeling different intervals (a to b, b to c, etc.) or transition points (a, b, c, etc.). The colored pencils will be useful in this step!! Your descriptions here, aside from the general description indicated above, should highlight "WHY" the graph indicates what it does. It is not merely sufficient to say a graph "clearly shows a object speeding up from rest." You must describe why that particular graph indicates that type of motion (for example) based on the line's format and/or shape. Part II Position vs. Time Graph Matching (For Graph #8) AND Part III Velocity vs. Time Graph Matching (For Graph #10) These graphs have a prediction/expectation of what the motion should have been. As such, if your trial differed in ANY way (small though it may be) from the absolute line the was to be matched, you are responsible for detailing WHY there was a difference. In particular, indicate whether it is possible to have achieved an exact match and why or why not. Do not simply say that we "needed to walk faster"...explain why that would have had to be the case. GRAPHS (worth up to 0 points) None Required Understanding 1D Motion Page 8

9 GRAPH ANALYSIS (worth up to 0 points) None Required CONCLUSION (worth up to 20 points) See the Physics Laboratory Report Expectations document for detailed information related to each of the four questions indicated below. 1. What was the lab designed to show? 2. What were your results? 3. How do the results support (or not support) what the lab was supposed to show? 4. What are some reasons that the results were not perfect? QUESTIONS (worth up to 15 points) DO NOT forget to include the answers to any questions that were asked within the experimental procedure 1. Explain the significance of the slope of a position vs. time graph. Include a discussion of positive and negative slope. 2. What type of motion is occurring when the slope of a position vs. time graph is zero? When the slope of a velocity vs. time graph is zero? 3. What type of motion is occurring when the slope of a position vs. time graph is constant, diagonal (straight line)? 4. What type of motion is occurring when the slope of a position vs. time graph is changing (curved line)? 5. What type of motion is occurring when the slope of a velocity vs. time graph is not zero? 6. What information, if any, can you get from a position vs. time graph that you can't from a velocity vs. time graph? What information, if any, can you get from a velocity vs. time graph that you can't from a position vs. time graph? Understanding 1D Motion Page 9