Lab 2 One Dimensional Motion L2-1 $%&'(((((((((((((((((((((((()%*'(((((((((((((((+%,*-',.((((((((((((((((((((((((((((((((! L02-1 Name Date!

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1 ! "#!! Lab 2 One Dimensional Motion L2-1 $%&'(((((((((((((((((((((((()%*'(((((((((((((((+%,*-',.((((((((((((((((((((((((((((((((! L2-1 Name Date! Partners Name Date Partners "#$!%&! Lab LAB 22 -'()!*+,)(-+'(#"!,'.+'(! - One ONE DIMENSIONAL Dimensional MOTION Motion!"#$%&'(%)*+&(,%$-')%*.+%/&+<!! Slow and steady wins the race. Slow and steady wins the race. Aesop s fable: The Hare and the Tortoise!"#$%&'($)* OBJECTIVES Aesop s fable: The Hare and the Tortoise! D3!B'%,-!73>!*3!K.'!%!&3*3-!;'*'8*3,!%-;!6%-!4%&B%,*2!>*7!1&*&%!*2(-#3! To learn how to use a motion detector and gain more familiarity with Data Studio. OBJECTIVES! To D3! explore 'S9B3,'! how 73>! various 1%,3K.! motions &3*3-.! are %,'! represented,'9,'.'-*';! on a 3-! distance %! ;.*%-8'! (position) time N93.*3-PR*&'! graph 6,%97! To learn how to use a motion detector and gain more familiarity with Data Studio.! To D3!'S9B3,'!73>!1%,3K.!&3*3-.!%,'!,'9,'.'-*';!3-!%!1'B38*2R*&'!6,%97! explore how various motions are represented on a velocity time graph To explore discover howthe various relationship motionsbetween are represented position time on a distance and (position) time velocity time graph! D3!;.831',!*7'!,'B%*3-.79!L'*>''-!93.*3-R*&'!%-;!1'B38*2R*&'!6,%97.! graphs! To explore D3!L'6-!*3!'S9B3,'!%88'B',%*3-R*&'!6,%97.! begin to how explore variousacceleration time motions are represented graphs on a velocity time graph OVERVIEW! To discover the relationship between position time and velocity time graphs In this lab you will begin your examination of the motion of an object that moves along a line!($+('$,* To begin to explore acceleration time graphs and how it can be represented graphically. You will use a motion detector to plot distance time (position time) motion of your own body. You will examine two OVERVIEW O-!*7.!B%L!23K!>BB!L'6-!23K,!'S%&-%*3-!34!*7'!&3*3-!34!%-!3LT'8*!*7%*!&31'.!%B3-6!%! B-'! %-;! 73>! *! 8%-! L'!,'9,'.'-*';! 6,%978%BB2<! different F3K! ways >BB! that K.'! the %! &3*3-!;'*'8*3,! motion of an object *3! 9B3*! ;.*%-8'R*&'!N93.*3-R*&'P!&3*3-!34!23K,!3>-!L3;2<!F3K!>BB!'S%&-'!*>3!;44','-*! that moves along a line can be represented >%2.!*7%*!*7'!&3*3-!34!%-!3LT'8*!*7%*!&31'.!%B3-6!%!B-'!8%-!L'!,'9,'.'-*';!6,%978%BB2<! graphically. You will use a motion detector F3K! In this >BB! to lab plot you K.'! distance time will %! &3*3-! begin your ;'*'8*3,! (position examinationand of the velocity time motion of an object graphs that moves of the *3! 9B3*! time) ;.*%-8'R*&'!N93.*3-R*&'P!%-;!1'B38*2R motion *&'! alongof 6,%97.! a line your and own 34! how *7'! body it&3*3-! canand be represented a 34! cart. 23K,! The 3>-! study L3;2!%-;!%! graphically. of motion You 8%,*<!D7'!.*K;2!34!&3*3-!%-;! and will its use mathematical a motion detector to plot &%*7'&%*8%B! representation distance-time (position-time) is %-;! known 6,%978%B! as and graphical *.! kinematics.,'9,'.'-*%*3-!.!a-3>-!%.!4-'+5&*-)<! motion of your own body. You will examine two different ways that the motion INVESTIGATION 1: DISTANCE TIME GRAPHS! :%,A';! OF YOUR MOTION! of an object that moves along a line can The purpose of this investigation is to ;.*%-8'.! learn how! beto represented relate graphs graphically. of the You distance will use as a function! of time to the motions they represent. a motion detector to plot distance-time (position-time) and velocity-time graphs You! will need the following materials: of the motion of your own body and a cart. The /-1',.*2!34!5,6-%!+72.8.!)'9%,*&'-*! study motion of motion detector and its mathematical and graphical :3;4';!4,3&!+<!=%>.?!)<!@3A3B344?!C<!D73,-*3-! representation is known as kinematics. +EF@!"GHG?!I%BB!"GJ"! number line on floor in %-;!*7'!/<@<!)'9*<!34!M;K8%*3-!NIO+@MP?!JQQHR"GGG!!! PHYS University 1429, of Spring Virginia 211 Physics Department

2 L2-2 Lab 2 One Dimensional Motion INVESTIGATION 1: Distance Time Graphs of Your Motion The purpose of this investigation is to learn how to relate graphs of distance as a function of time to the motions they represent. You will need the following materials: motion detector masking tape marked on floor in meters Questions to consider: How does the distance -time graph look when you move slowly? Quickly? What happens when you move toward the motion detector? Away? After completing this investigation, you should be able to look at a distance-time graph and describe the motion of an object. You should also be able to look at the motion of an object and sketch a graph representing that motion. Comment: Distance is short for distance from the motion detector. The motion detector is the origin from which distances are measured. The motion detector detects the closest object directly in from of it (including your arms if you swing them as you walk) transfers information to the computer via the interface so that as you walk (or jump, or run), the graph on the computer screen displays your distance from the motion detector will not correctly measure anything much closer than about 2 cm. W hen making your graphs, don t go closer than 2 cm from the motion detector. Activity 1-1: Determining the Initial Speed Before we begin taking data for our experiments you will briefly learn how to set up new experiments using DataStudio software and ScienceWorkshop interface. For the majority of the future experiments all of the set-ups will be configured ahead of time. However it is important that you understand some basic operations before we proceed. 1. Be sure that the interface is connected to the computer. Open Data Studio. Click on Create Experiment on the opening page or under File, click on New Activity, which will go to the page where you can click on Create Experiment. 2. Click on Digital Channel Input 1 on far left. A list of sensors appears. Find the Motion Sensor line, double click on the Icon beside the Motion Sensor line, and the software will connect the Motion Sensor to the 75 Interface. You should physically have the Motion Detector plugged into the Interface in the same manner. Close the Setup by clicking on the X in the upper right. 3. On the left side of the screen under Data, click on Position and drag it down to the graph icon in the display window. A graph should appear on the right side of the screen displaying Position vs. Time.

3 Lab 2 One Dimensional Motion L Note that you can change the scale on both axes by moving the mouse to the numbers, click and drag them to decrease or increase the scale. Try this for both scales. 5. Check that the switch on the motion detector is set to broad beam. Mount the motion detector on the edge of the table; ask your TA for specific instructions. 6. To start the experiment, click on the Start button. Notice then that this button is replaced by a Stop button that allows you to stop the experiment. 7. You can erase data by clicking on Experiment on the top row and then clicking on Delete Last Data Run. Be careful of Deleting All Data if you don t mean to do so. Now you should be comfortable with DataStudio basic functions. Let s begin taking relevant data. 1. Begin graphing and make distance-time graphs for different walking speeds and directions. Lab 2 One Dimensional Motion L2-3 (a) Start at the 1/2 meter mark and make a distance-time graph, walking away from the detector (origin) slowly and steadily. Start the computer before walking and stop the 8. Begin graphing and make distance time graphs for different walking speeds and computer when finished. Do not erase the data. directions. (b) Make a distance-time graph, walking away from the detector (origin) medium fast a. Start andat steadily. the ½ meter Start computer mark and before make walking a distance-time and stop when graph, finished. walking away from the detector (origin) slowly and steadily. (c) Start at the 2 meter mark and make a distance-time graph, walking toward the detector (origin) a distance-time slowly andgraph, steadily. walking Start and away stopfrom computer the detector as before. (origin) medium fast b. Make (d) and Make steadily. a distance-time graph, walking toward the detector (origin) medium fast and c. Start steadily. at the Start 2 meter and stop mark computer and make as before. a distance-time graph, walking toward the (e) detector Click on (origin) Stop when slowly finished. and steadily. You should have all four graphs on computer. 2. d. Print Make one a setdistance-time of graphs for your graph, group. walking toward the detector (origin) medium fast and steadily. 9. Print Comment: one set Ifof you graphs do not for erase your thegroup. graph, it will remain stored in the computer so that it is persistently displayed on the screen. You can also go to the Data icon and click on and Comment: If you do not erase the graph, it will remain stored in the computer so that it is off this run so the data is or is not displayed. persistently displayed on the screen. You can also go to the Data icon and click on and off this Prediction run so the 1-1: data Predict is or is thenot position-time displayed. graph produced when a person starts at the 1 m mark, walks away from the detector slowly and steadily for 5 s, stops for 5 s, and then Prediction 1-1: Predict the position time graph produced when a person starts at the walks toward the detector twice as fast. Draw your prediction on the left axes below. Label 1 m mark, walks away from the detector slowly and steadily for 5 s, stops for 5 s, and the axes appropriately. Compare your predictions with those made by others in your group. then walks toward the detector twice as fast. Draw your prediction on the left axes Draw your group s prediction on the right-hand axes below. The individual prediction below. Label the axes appropriately. Compare your predictions with those made by should be done before coming to lab. others in your group. Draw your group s prediction on the right-hand axes below. Individual Prediction Group Prediction Position (m) Position (m) 1. Test your prediction by using the computer to graph your position over a range of 2 m for a time interval of 15 s. Move in the way described in Prediction 1-1, and graph your motion. 11. When you are satisfied with your graph, print one copy of the graph for your group.

4 L2-4 Lab 2 One Dimensional Motion 3. Test your prediction by using the computer to graph your position over a range of 2 m for a time interval of 15 s. Move in the way described in Prediction 1-1, and graph your motion. 4. When you are satisfied with your graph, print one copy of the graph for your group. Question 1-1: Is your prediction the same as the final result? If not, describe how you would move to make a graph that looks like your prediction. 5. Everyone should gather around the computer for the next few steps to make sure everyone learns how to do these manipulations with Data Studio. 6. Keep the previous graph of your motion on the screen. Change scales as desired or use the Autoscale (scale to fit) icon on the Graph window toolbar on far left. Click the Autoscale to see what happens. 7. Click on the Smart Tool and drag the crosshair to individual data points to read the data at that point. 8. To highlight regions of data, go to a beginning spot and click-and-drag a window around the region of interest. Data will be highlighted with yellow background. Highlight the first region of data when you walk away from the motion detector. 9. To fit data, click on the Fit icon and choose the function you desire, in this case Linear Fit. Note the parameters (slope and y-intercept) are immediately given on the screen. To remove them, go back and unclick Linear Fit. 1. Note that if you leave Linear Fit on, but choose a different highlighted region, the fit will be applied to the new region. 11. Let s now examine the region where the person was at rest. Highlight the second region of your data which should be level. Then click on the Statistics icon (which appears as a Σ). Click on Mean and the mean value over that region will be displayed. Note the varying functions that can be obtained with the Statistics functions. 12. If you have multiple runs on the screen, note that the various tools work on the run that is highlighted in the box in yellow. You can choose which data runs are displayed by clicking on the Data icon and clicking on and off the runs as you desire. 13. Now find the slopes of the two regions in which you were walking. Remember that the return path was supposed to be twice as fast as the initial path. Use the Fit to find the velocity (slope) and velocity uncertainty (error) of each path: First path slope: ± m/s Second path slope: ± m/s

5 Lab 2 One Dimensional Motion L2-5 Question 1-2: How did you do? Was the speed in the second path about twice that in the first? INVESTIGATION 2: Position-Time Graphs of Motion The purpose of this investigation is to learn how to relate graphs of position as a function of time to the motions they represent. You will need the following materials: motion detector number line on floor in meters Activity 2-1: Matching a Position-Time Graph Lab By2 now One you Dimensional should be Motion pretty good at predicting the shape of a position-time graph of your L2-5 movements. Can you do things the other way around: reading a position-time graph and figuring out how to move to reproduce it? In this activity you will move to match a position graph shown graph on theand computer figuring screen. out how to move to reproduce it? In this activity you will move to match a position graph shown on the computer screen. 4 Position (m) In Data Studio, select Open and navigate to the 142W folder. Do not try to save the 1. In previous Data Studio, activity select (you Open will be andprompted navigate to to the do 23 this). folder. Open the Do experiment not try to save file called the L2.1-2 previous Position activity (you Match. will bea prompted position to graph do this). like Open that shown the experiment above will file called appear on the L2.A2-1 screen. Position Clear any Match. other Adata position remaining graphfrom like that previous shownexperiments. above will appear on the screen. Clear any other data remaining from previous experiments. It is a good idea to Comment: always This clickgraph on the is Setup stored icon in the on the computer computer so screen that it tois see persistently if your cablesdisplayed are correctly on the screen. connected New todata the PASCO from the interface, motion nowdetector and in the can future. be collected without erasing the Position Match graph. 2. Try to move so as to duplicate the Position Match graph on the computer screen. Comment: This graph is stored in the computer so that it is persistently displayed on the You screen. may try New a number data from of the times. motion It helps detector to work can be in collected a team. without Each person erasing should the Position take a turn. Match graph. Question 1-3: What was different in the way you moved to produce the two differently sloped 2. parts Try toof move the graph so as to you duplicate just matched? the Position Match graph on the computer screen. You may try a number of times. It helps to work as a team. Each person should take a turn.

6 L2-6 Lab 2 One Dimensional Motion Question 2-1: What was different in the way you moved to produce the two differently sloped parts of the graph you just matched? INVESTIGATION 3: Velocity-Time Graphs of Motion You have already plotted your position along a line as a function of time. Another way to represent your motion during an interval of time is with a graph that describes how fast and in what direction you are moving. This is a velocity-time graph. Velocity is the rate of change of position with respect to time. It is a quantity that takes into account your speed (how fast you are moving) and also the direction you are moving. Thus, when you examine the motion of an object moving along a line, the direction the object is moving is indicated by the algebraic sign (positive or negative) of the velocity. Graphs of velocity vs. time are more challenging to create and interpret than those for position. A good way to learn to interpret them is to create and examine velocity-time graphs of your own body motions, as you will do in this investigation. You will need the following materials: motion detector number line on floor in meters Activity 3-1: Making Velocity Graphs 1. Open the experiment file called L2.A3-1 Velocity Graphs. This will allow you to graph velocity. Check that the switch on the motion detector is on the broad beam. 2. You will want to walk at different speeds to match the motion as described in (a)-(d) below. Each member of the group should try at least one of these. Ask your TA how to choose what data are displayed on the screen (and printed out). Basically you click on and off various runs under the DATA icon to show on the screen (a) Begin graphing and make a velocity graph by walking away from the detector slowly and steadily. Try again until you obtain a graph you re satisfied with. You may want to adjust the velocity scale so that the graph fills more of the screen and is clearer. (b) Make a velocity graph, walking away from the detector medium fast and steadily. STOP the data taking after each try. Then START for the next experiment. (c) Make a new velocity graph, walking toward the detector slowly and steadily. (d) Make a new velocity graph, walking toward the detector medium fast and steadily. 3. Print out one graph that includes all the data you decide to keep. Make sure you denote on your print out with letters a) d) to indicate what you were trying to do.

7 Lab 2 One Dimensional Motion L2-7 Question 3-1: What is the most important difference between the graph made by slowly walking away from the detector and the one made by walking away more quickly? Question 3-2: How are the velocity-time graphs different for motion away THAN FOR motion towards the detector? Lab 2 One Dimensional Motion L2-7 Prediction 3-1: Each person draw below in your own manual, using a dashed line, your prediction of the velocity-time graph produced if you, in succession, Prediction 2-1: Each person draw below in your own manual, using a dashed line, your prediction (a) walk of the away velocity time from the detector graph slowly produced and steadily if you, for in about succession, 5 s (b) walk thenaway standfrom still for the about detector 5 s slowly and steadily for about 5 s stand still for about 5 s (c) then walk toward the detector steadily about twice as fast as before. walk toward the detector steadily about twice as fast as before. Do the predictions before coming to lab. Label your predictions and compare with your Label your predictions and compare with your group to see if you can all agree. Use a group to see if you can all agree. Use a solid line to draw in your group prediction. solid line to draw in your group prediction. 1 Velocity (m/s) ! 4. Test your prediction. (Adjust the time scale to 15 s.) Be sure to think about your 4. starting Test your point! prediction. Begin Open graphing experimental and repeat file L2.A3-1 your motion Velocity until Graphs you think Two. it Be matches sure to the description. think about your starting point! Begin graphing and repeat your motion until you think it matches the description. 5. Print out one copy of the best graph for your group report. Activity 5. Print 2-2: out Matching one copy ofa the Velocity best graph Graph for your group report. In this activity, you will try to move to match a velocity time graph shown on the Activity 3-2: Matching a Velocity Graph computer screen. This is much harder than matching a position graph as you did in the previous investigation. Most people find it quite a challenge at first to move so as to Inmatch this activity, a velocity you will graph. try to In move fact, to some match velocity a velocity-time graphs that graphcan shown be invented on the computer cannot be screen. matched! This is much harder than matching a position graph as you did in the previous investigation so do not spend a lot of time on this activity. Most people find it quite a challenge to 1. Open the experiment file called L2.2-2 Velocity Match to display the velocity time graph shown below on the screen. 1 (m/s)

8 Activity 2-2: Matching a Velocity Graph L2-8 In this activity, you will try to move to match a velocity time Lab 2 One Dimensional graph shown Motion on the computer screen. This is much harder than matching a position graph as you did in the move previous so as investigation. to match a velocity Most graph. people In fact, find some it quite velocity a challenge graphs thatat canfirst be invented to move cannot so as to be match matched! a velocity graph. In fact, some velocity graphs that can be invented cannot be matched! Open the experiment file file called called L2.A3-2 L2.2-2 Velocity Match Match to display to display the velocity-time the velocity time graph graph shown shown below below on the on screen. the screen. Velocity (m/s) ! Prediction 3-2: Describe in words how you would move so that your velocity matched each part of this velocity-time graph. Do this before coming to lab. to 4 s: PHYS 41429, to 8 s: Spring to 12 s: 12 to 18 s: 18 to 2 s: 2. Begin graphing, and move so as to imitate this graph. Try to do this without looking at the computer screen. You may try a few times. Work as a team and plan your movements. Get the times right. Get the velocities right. It is quite difficult to obtain smooth velocities. We have smoothed the data electronically, but your results may still oscillate significantly. Looking at the screen for feedback can actually make things worse. 3. Draw in your group s best match on the velocity-time graph shown above. As we stated earlier, don t spend a lot of time trying to improve this. It is difficult!

9 Lab 2 One Dimensional Motion L2-9 Question 3-3: Is it possible for an object to move so that it produces an absolutely vertical line on a velocity-time graph? Explain. Question 3-4: Did you have to stop to avoid hitting the motion detector on your return trip? If so, why did this happen? How would you solve the problem? If you didn t have to stop, why not? Generally speaking does a velocity graph tell you where to start? Explain. INVESTIGATION 4: Relating Position and Velocity Graphs You have looked at position-time and velocity-time graphs separately. Since position-time and velocity-time graphs are different ways to represent the same motion, it is possible to figure out the velocity at which someone is moving by examining her/his position-time graph. Conversely, you can also figure out how far someone has traveled (change in position) from a velocity-time graph. To explore the relation between position-time and velocity-time graphs, you will need the following materials: motion detector number line on floor in meters Activity 4-1: Determining Velocity Graphs From Position Graphs 1. Open the experiment file called L2.A4-1 Velocity from Position to set up the axes shown that follow. Clear any previous graphs. Remember to check Setup! Prediction 4-1: Determine the velocity graph from a position graph. Carefully study the position-time graph that follows and predict the velocity-time graph that would result from the motion. Use a dashed line to sketch what you believe the corresponding velocity-time graph on the velocity axes will be. Do this before coming to lab.

10 Prediction 3-1: Determine the velocity graph from a position graph. Carefully study the position time graph that follows and predict the velocity time graph that would result L2-1 Lab 2 One Dimensional Motion from the motion. Use a dashed line to sketch what you believe the corresponding velocity time graph on the velocity axes will be. Position (m) Velocity (m/s) Prediction Results 1. Test your prediction. Open L2.3-1 Velocity from Position. 2. Test your prediction. Begin graphing, and do your group s best to make a position graph 2. like After the each one shown. person Walk has as sketched smoothly a as prediction, possible. begin graphing, and do your group s best to make a position graph like the one shown. Walk as smoothly as possible. 3. When you have made a decent duplicate of the position graph, sketch your actual graph University over the of Virginia existing Physics position-time Department graph. Use a solid Modified line to from draw P. the Laws, actual D. Sokoloff, velocity-time R. Thornton PHYS graph 1429, onspring the velocity 211 graph where you drew your prediction. Do not erase your prediction or your data the computer. Question 4-1: How would the position graph be different if you moved faster? Slower? Question 4-2: How would the velocity graph be different if you moved faster? Slower? Activity 4-2: Calculating Average Velocity In this activity, you will find an average velocity from your velocity-time graph in Activity 4-1 and then from your position-time graph. 1. Here you will find your average velocity from the velocity graph that you obtained in Activity 4-1. Choose a region where your velocity is relatively constant and pick 1 adjacent velocity values. Do not choose a region where the velocity is zero. Use the Smart Tool in Data Studio to read values of velocity and write them in the table below. Once the Smart Tool is focused on a curve you can use left- right- arrows on the keyboard to freely move along the chosen graph. Use these values to calculate the average (mean)

11 Lab 2 One Dimensional Motion L2-11 velocity and standard deviation using a calculator Excel spreadsheet. Remember the difference between standard deviation of a sample and standard deviation of the mean. For reference, note the time at the first and last points. You will need them later. Time at first point: s Time at last point: s Velocity values (m/s) Average (mean) value of the velocity: ± m/s This is method 1 of determining the average velocity. Comment: Average velocity during a particular time interval can also be calculated as the change in position divided by the change in time. (The change in position is often called displacement.) For motion with a constant velocity, this is also the slope of position time graph for that time period. As you have observed, the faster you move, the steeper your position time graph becomes. The slope of a position time graph is a quantitative measure of this incline. The size of this number tells you the speed, and the sign tells you the direction. 2. Calculate your average velocity from the slope of your position graph in Activity 4-1. Make sure you use the same time region here that you just used in step 1. Use the Smart Tool again to read the position and time coordinates corresponding to the two end points (of your ten-point velocity region). Point 1 Point 2 Position (m) 3. Calculate the change in position (displacement) between points 1 and 2. Also calculate the corresponding change in time (time interval). Divide the change in position by the change in time to calculate the average velocity. Show your calculations below. Change in position (m) Time interval (s) Value of the velocity: m/s This is method 2 of determining the average velocity.

12 L2-12 Lab 2 One Dimensional Motion Question 4-3: Does the average velocity you just calculated from the position graph agree with the average velocity you found from the velocity graph? Do you expect them to agree? How would you account for any differences? Activity 4-3: Using Statistics and Fit to Find the Average Velocity In Activity 4-2, you found the value of the average velocity for a steady motion in two ways: from the average of a number of values on a velocity-time graph and from the slope of the position-time graph. The statistics feature in Data Studio (look for the Σ icon) allows you to find the average (mean) value directly from the velocity-time graph. The fit routine should allow you to find the line that best fits your position-time graph from Activity 4-1. The equation of this line includes a value for the slope and the uncertainty of the slope.. 1. Using statistics: You must first select the portion of the velocity-time graph for which you want to find the mean value. Make sure you select the same region here that you used in step 1 of Activity 4-2. Next use the statistics feature Σ to read the mean value of velocity during this portion of the motion. The standard deviation of the sample and the number of counts can also be activated and read from the statistics feature. Average (mean) value of the velocity: ± m/s This is method 3. Question 4-4: Compare this method to the one in Activity 4-2 (step 1) where you determined the average by hand. Which method is easiest? Why? 2. Using fit: You must first select the portion of the position-time graph that you want to fit. Use the same 1-point region you have been using. Next, use the fit routine, select a linear fit, y = mx + b, and then find the equation of the line. Record the equation of the fit line below, and compare the value of the slope (m) including uncertainty to the velocity you found in Activity 4-2. Value of the velocity from slope: ± m/s This is method 4.

13 Lab 2 One Dimensional Motion L2-13 Question 4-5: What does b represent? Activity 4-4: Predicting Position Graphs From Velocity Graphs 1 Velocity (m/s) Prediction 4-2: Carefully study the velocity graph shown above. Using a dashed line, sketch your prediction of the corresponding position graph below. (Assume that you started at the 1 m mark.) Do this before coming to lab. Prediction and final result Position (m) Prediction Result Test your prediction. 1. First shut off the analysis features (fits and statistics), and adjust the time axis to to 5 s as needed before you start. 2. Each person has already made a prediction. Your group should try to duplicate the velocity-time graph by walking. Try to do it without looking at the computer monitor.

14 L2-14 Lab 2 One Dimensional Motion When you have made a good duplicate of the velocity-time graph, draw your actual result over the existing velocity-time graph. 3. Use a solid line to draw the actual position-time graph on the same axes with your prediction. (Do not erase your prediction.) Question 4-6: How can you tell from a velocity-time graph that the moving object has changed direction? What is the velocity at the moment the direction changes? Question 4-7: How can you tell from a position-time graph that your motion is steady (motion at a constant velocity)? Question 4-8: How can you tell from a velocity-time graph that your motion is steady (constant velocity)? INVESTIGATION 5: Introduction to Acceleration There is a third quantity besides position and velocity that is used to describe the motion of an object: acceleration. Acceleration is defined as the rate of change of velocity with respect to time (just like velocity is defined as the rate of change of position with respect to time). In this investigation you will begin to examine the acceleration of objects. Because of the jerky nature of the motion of your body, the acceleration graphs are erratic. It will be easier to examine the motion of a cart. In this investigation you will examine the cart moving with a constant (steady) velocity. Later, in Lab 3 you will examine the acceleration of more complex motions of the cart. You will need the following: motion cart without friction pad 2-m motion track Level motion detector Activity 5-1: Motion of a Cart at a Constant Velocity

15 Lab 2 One Dimensional Motion L2-15 To graph the motion of a cart at a constant velocity you can give the cart a quick push with your hand and then release it. 1. Clip the motion detector on the end of the ramp. Ask your TA for help if it is not clear how to do this. Set switch to narrow beam and aim the motion detector at the cart. Be sure that the track is level. 2. Open the experiment file called L2.A5-1 Constant Velocity. Prediction 5-1: Based on your observations of the motions of your body, how should the position and velocity graphs look if you move the cart at a constant velocity away from the motion detector starting at the.3-m mark? Sketch your predictions with dashed lines on the axes that follow. Do this before coming to lab Test your prediction. Give the cart a quick push and release it. Be sure that the cart is never closer than 2 cm from the motion detector and that your hand is not between the cart and motion detector. Begin graphing right after releasing the cart. Try several times until you get a fairly constant velocity. Sketch your results with solid lines on the axes. 4. Print out one copy for your group report. Question 5-1: Did your position-time and velocity-time graphs agree with your predictions? Discuss. What type of curve characterizes constant velocity on a position-time graph?

16 L2-16 Lab 2 One Dimensional Motion Activity 5-2: Acceleration of a Cart Moving at a Constant Velocity Prediction Activity 4-2: 5-2: Acceleration Sketch with a dashed of a Cart linemoving on the axes at a that Constant follow your Velocity prediction of the acceleration Prediction of4-2: the cart Sketch you with just observed a dashed moving line on at the a constant axes that velocity follow away your prediction from the of the motion acceleration detectorof inthe cart previous you just Activity observed 5-1. Base moving your at prediction a constant on velocity the definition away from of the acceleration. motion detector. Do not do Base this your before prediction coming to on lab. the definition of acceleration. Acceleration (m/s 2 ) 1-1 PREDICTION AND FINAL RESULTS You Display will the use real the data acceleration you tookgraph in theof previous the cart activity. by dragging Displayacceleration the real acceleration data from graph the left ofcolumn the cart by onto dragging existing acceleration graph. Ask data your fromta thefor left help column if needed. onto existing graph. 2. Sketch Print out the acceleration one copy of graph the graph usingfor a solid your line group on the report. axes above. Label Ask it. your TA for help if needed. 2. Print out one copy of the graph for your group report. Label it. Question 5-2: Does the acceleration-time graph you observed agree with your prediction? Discuss. PHYS 3. Find 1429, thespring average 211 acceleration of the car using one of the techniques that you used earlier to find the average velocity. Show your work. Please clean up your lab area