Lab 2: Position, Velocity, and Acceleration (Physics 1AL)

2. POSITION, VELOCITY, AND ACCELERATION INTRODUCTION Today’s lab serves two general purposes. One purpose of this lab is to explore the concepts of position, velocity, and acceleration and understand the relationships between these three descriptions of motion. We will utilize a rolling cart on...

2. POSITION, VELOCITY, AND ACCELERATION INTRODUCTION Today’s lab serves two general purposes. One purpose of this lab is to explore the concepts of position, velocity, and acceleration and understand the relationships between these three descriptions of motion. We will utilize a rolling cart on a long, straight metal track for our exploration of these kinematic quantities. The second purpose of today’s lab is to help you become familiar with the use of computer-based data acquisition systems allow us to digitally collect and analyze physical data. In today’s lab we will utilize a position sensor, but in later labs, you will be exposed to a variety of other digital sensors that measure acceleration, force, temperature, etc. In this lab sequence, we will be using LabPro™ or LabQuest™ sensor hardware to acquire physical data and the LoggerPro™ software to digitally record, display, and analyze that data. The position sensor that we will use in today’s lab is based on ultrasound technology. The position sensor works by measuring the time for an ultrasonic pulse emitted by the sensor to travel to a target, reflect off of it, and travel back to an ultrasound detector in the sensor. The computer is programmed with the speed of ultrasound waves in air, and from the measured time and the known speed, it calculates the distance to the object. PRE-LAB PREPARATION It is vitally important that you take the time and effort to properly prepare yourself before you arrive at your lab session. This includes : (1) Doing the required Pre-Reading to familiarize yourself with the physics concepts involved in the lab, (2) Carefully reading every section and every step of the lab manual to familiarize yourself with the in-lab procedures, and (3) Performing the Pre-Lab Assignment questions and activities to ensure that you have the necessary knowledge and skills required for taking the Pre-Lab Quiz, performing the experiment, and completing your post-lab conclusion writeup. I. REQUIRED PRE-LAB READING Kudu: Chapter A2.10 and Chapters A3.2 - 3.13 The short primer on friction given at the bottom of this section, below. Pay special attention to vectors and the definitions of displacement, instantaneous velocity, and acceleration. Physics 1AL pg. 25 Primer on Friction A quick note about friction: Although you may not have yet studied the concepts of forces and friction in your lecture course, the force of friction will affect your measurements in this lab exercise. If friction were absent or negligible, then an object (e.g., a cart on a truly frictionless track) would continue to move indefinitely with constant velocity once it is set in motion. However, in the presence of frictional forces (e.g., the rubbing/rolling action between the cart and the track, or the air resistance between the cart and the surrounding air), the object will gradually slow down (i.e., decelerate) to a stop. The forces of friction on a moving object always act in the direction that is directly opposite to the object’s motion. We will study the quantitative details of friction later this quarter, but this basic qualitative understanding of friction will be sufficient for interpreting the results of this lab. II. PRE-LAB LEARNING OBJECTIVES As you perform the pre-reading and pre-lab questions assigned for this lab, keep in mind the following learning objectives. By the time you enter the lab to take the pre-lab quiz and perform the experiment, you should be able to comfortably do all of the following: Describe conceptually the relationship between position, velocity, and acceleration. Describe and identify the important features of a graph (e.g., axes, intercepts, slope, maxima, minima, “area under the curve”) using ordinary language. Interpret a motion diagram and describe an object's behavior based on its motion diagram. Describe mathematically (using the language of calculus) the relationships between position, velocity, and acceleration. Write out the four kinematic equations that relate position, velocity, and acceleration. Choose the appropriate kinematic equation(s) and use them to solve calculations involving moving objects with displacements, initial and/or final velocities, and constant acceleration. Explain how to determine: o velocity at a particular instant from a position-vs-time graph. o acceleration at a particular instant from a velocity-vs-time graph. o displacement up to at particular instant from a velocity-vs-time graph. o change in velocity to a particular instant from an acceleration-vs-time graph. Given a graph of one of the kinematic quantities of an object (position, velocity, or acceleration) as a function of time, be able to generate a graph of the other two kinematic quantities versus time, e.g.: o Given position-vs-time, generate graphs of velocity-vs-time and acceleration-vs-time. o Given velocity-vs-time, generate graphs of position-vs-time and acceleration-vs-time. o Given acceleration-vs-time, generate graphs of position-vs-time and velocity-vs-time. Describe the value and direction of the acceleration due to Earth's gravity at locations that are at or near the surface of the Earth. Explain how the position, velocity, and acceleration of an object change when an object is thrown straight up, is thrown downward, or dropped from rest. Physics 1AL pg. 26 III. MOTIVATION AND REAL - WORLD CONTEXT We live in a world in motion – objects and people move around, speed up, slow down, and change direction. Many serious injuries are a result of large accelerations (or decelerations) of the human body or specific body parts. Traumatic Brain Injury (TBI), whiplash, concussion, and muscle strains can all result from a large acceleration (i.e., a sudden, large increase or decrease in velocity) of one part of the body relative to another (e.g., the motion of the brain relative to the skull in the case of TBI or concussion). Understanding the biomechanics of such injuries requires a firm foundation in kinematics - the quantitative description of how things move in terms of object’s position, velocity, and acceleration. Additionally, application of kinematics is central to the field of biomechanics: kinematic data from body parts in routine activities (e.g., sitting, standing, walking, running, or eating) have led to and continue to drive important advances in prosthetic limbs and joints. IV. PRE-LABORATORY ASSIGNMENT The pre-lab questions are meant to help you prepare for the weekly quiz, and they are ungraded. You should try to do as many of them as you can. 1. The figure shows a position vs. time graph for a moving object. At which exact lettered point(s) is the object... (please do not include ranges such as “from A to B”) a) … slowing down? b) … turning around? c) … speeding up? d) … momentarily stationary? e) … moving to the left (i.e. negative x)? f) … moving to the right (i.e. positive x)? g) … moving the fastest? Physics 1AL pg. 27  2. The four motion diagrams below show an initial point 0 and a final point 1. A B C D Assume that initial & final positions, x0 or y0 velocities and (constant) accelerations are: x0, x1, vox, v1x, and a for horizontal x1 or y1 X motion, and equivalent symbols with y v0x or v0y (or subscript y) for vertical motion. Determine whether each of the v1x or v1y quantities is positive, negative or zero. aX or aY Give your answer by writing +, –, or 0 in the table. Copy the table into your lab book. 3. A sprinter starts from rest and accelerates at 3.3 m/s2 until reaching her top speed of 15 m/s, she then continues to run at top speed. Use one or more of the kinematic equations, answer the following questions: a. How long does it take for her to reach top speed? b. How long does it take her to run the entire 100 m dash? Physics 1AL pg. 28  4. For these velocity vs. time graphs, draw the acceleration vs. time graphs (to scale, with numbers on the vertical axis). 5. For these acceleration vs. time graphs, draw to scale with correctly numbered axes the velocity vs. time graphs, assuming vo = 0 m/s. Physics 1AL pg. 29 LAB EQUIPMENT [a] Rail [b] Wheeled cart [c] Motion Detector (Position Sensor) [d] LabQuest Mini™ computer interface [e] Lab jack [f] Meter stick [g] Protractor IN-LAB ACTIVITIES A. TUTORIAL: MOTION DETECTION WITH LOGGER PRO In part A, we will familiarize ourselves with our digital position sensor (a device that uses ultrasound technology to measure an object's position) and the LoggerPro software that we will be using throughout this lab course series to record, display, and analyze our data. We will learn how to zero our detectors, set the direction of our position sensor, start a collection run, display statistics for our data, selectively hide or display data runs, and save our data to a file. THE MOTION DETECTOR The motion detector is used to measure the distance from itself to a target object. It emits ultrasonic pulses and detects the echo from the target. The usable range of the detector is between 0.5 and 6 meters. Lab Pro / LabQuest: The LabPro (or LabQuest) device is an interface that converts signals from the motion detector or other sensor) to a form that the computer can read. Logger Pro: Logger Pro is the software which controls the interface and displays the results of the motion detector measurements. Set up the Motion Detector: These instructions should help you get good data. Place the motion detector at one end of the track with the gold disc pointing towards the other end. The ultrasound emitter and receiver are behind the gold disc. Be sure that there are no obstructions in the path of the motion detector. The motion detector emits ultrasound in a cone about 30 degrees wide. Anything within the cone of ultrasound can cause a reflection and possibly an accidental measurement. A common problem in using motion detectors is getting unintentional reflections from a desk, chair, the ceiling, or computer in the room. The detector will measure the closest object in its viewing angle. If you set it exactly horizontal it will see the track when the cart exceeds something around 1m distance. You can tilt the detector up a little to avoid this. Physics 1AL pg. 30 TUTORIAL PROCEDURE A1. Start Logger Pro. To open the Logger Pro application, double click on the UCSD Macintosh drive from the desktop. Then double click on the Applications folder. Next, double click on the folder entitled Logger Pro 3. Finally, double click on the Logger Pro application. A2. Check the detector. Make sure the motion detector is connected to DIG/SONIC 2 of the LabPro interface. A3. Check the hardware. Be sure to have a bumper at the other end of the track so that the cart does not overrun the track. Please don’t make a habit of letting the cart slam into the bumper or the sensor; try to catch the cart before that happens. A4. Zero your detector. Before starting each lab, you will need to zero your detector(s). To do this, go to the menu bar and click on “Experiment.” Note that there will be a drop-down menu with “Zero” near the bottom. Place a piece of paper in front of your detector covering the gold disc. After the paper is in place, scroll down to click “Zero.” This will zero your detector. A5. Try acquiring data with your hand. To take data, click and place your hand at various positions in front of the motion detector along the track. Check to make sure you can detect your hand and that its position as shown on the graph looks reasonable. Physics 1AL pg. 31 A6. Try acquiring data with the cart. Hold the cart from the side away from the sensor, so the cart’s position (and not your hand) is measured. Be sure that you can measure the cart’s position over the entire length of track. If the graph seems to be reading a constant displacement even though you are moving the cart, it may be seeing the track instead of the cart. Try adjusting the angle of the motion detector to fix this issue. In addition, keep your arms, shoulders, backpacks, etc. out of the sensor’s range (unless you want to measure their position). A7. Learn to Reverse Directions on the Detector. In some instances, you will need to reverse the direction of the detectors. This can be done by going to the menu bar and clicking on “Experiment.” Scroll down to “Set Up Sensors” and then to “Show All Interfaces.” A dialog box will appear. Click on the detector icon under DIG/SONIC 2 and scroll down to click on “Reverse Direction.” This will reverse the direction of your motion detector. Now that you have reversed the direction, you must re-zero your detector. Move the cart again along the track. Does the graph look different than it did before? After you have done this, go back and unclick the “Reverse Direction”. Re-zero your detector with the paper in front of the gold disc once more. Now, let’s begin taking data with the cart. Position the cart close to the motion detector where it is in the working range (it cannot be closer than 0.15m to the sensor *). A8. Acquire your first dataset (cart moving away). Click to begin data collection. When the motion detector starts making a repetitive clicking sound, data recording has started. You can give the cart a short pull** away from the motion sensor and let go after giving it that little tug. As data are gathered, the graph line extends to the right in real time. Data collection will stop after 10 seconds of data collection, or sooner if you click on the stop button. Repeat this until you are sure you are really measuring the position of the cart as it moves away from the sensor. A9. View Data Statistics. After you have obtained a reading that appears correct, click the button in the toolbar that has “STAT” and a “1” and “2” on it. This brings up a box that shows the statistics of your run. This box will be handy later on. * This can vary from sensor to sensor. You should test your own sensor in case it has a “dead zone” that is larger than the standard 15 cm. Gradually move the cart from 100 cm to 5 cm away from the detector while collecting data and see where the graph ceases to accurately report the cart’s position. ** Pull from the side of the cart that is away from the sensor to avoid measuring the position of your hand. Physics 1AL pg. 32 A10. Store your data. When you are ready, store a dataset by choosing Experiment from the menu bar, and then clicking on “Store Latest Run”. You should now see the data on the graph in a lighter color. A11. Acquire a second dataset. Make another trial. Compare the first graph to the second. Notice the similarities and differences. A12. Hide the first dataset. Under the Data menu, select “Hide Data Set” and choose to hide Run 1. Now you should only see your second trial. Again, store this run, and then hide it, so that no data is showing, but two trials are stored. A13. Acquire a third dataset. Do one more trial. Now look at all three runs, and keep the one that seems to represent the motion best (i.e. no “artifacts” like other objects getting in the way, and a fairly smooth line with low noise levels). To see all of the runs, go to the Data menu and click “Show Data Set” and show Run 1. Repeat this with Run 2. A14. Rescale your data. When plotting your data, it might look like a straight line on the screen. This might be because the scale is too large. You will need to be able to view your data at a useful scale. The quickest way to do this is to click the Autoscale button*. This will rescale your plot’s axes to fit all your data. You can also manually set the maximum and minimum values of your axes. Make sure you always autoscale your data (or manually set reasonable scale limits) before you draw / record any displayed data. Note: a poorly scaled graph will go off the top or bottom of the graph (scale is too small) or will look like a nearly horizontal line (scale is too large). A15. Hide the second dataset. Now, under the Data menu, select “Hide Data Set” and hide Run 1 and Run 2. Now you should only see your latest trial. Again, store this run, and then hide it, so that no data is showing, but three trials are stored. A16. Make a sketch of the data (cart moving away from detector). Sketch in your notebook a typical graph for motion away from the sensor. Label axes and include numerical scales. A17. Acquire data with cart moving towards detector. Repeat the process but start the cart at the far end of the track – now giving it a push toward the sensor. Get several graphs of the cart moving towards the sensor. Keep the best graph of the set. A18. Make a sketch of the data (cart moving towards detector). Sketch in your notebook a typical graph for motion towards the sensor. Label axes and include numerical scales. * The autoscale button is found on the toolbar, as indicated in the figure. Physics 1AL pg. 33 B. DESCRIBING AND DUPLICATING A MOTION In part B, we will split our lab group in half and play a “game” where one half of the group is allowed to see a motion graph and must try to describe (in words) the motion that produced that graph to the other half of the group. Working only off of that description of motion, the second half must then try to generate a similar graph on the computer by manually manipulating the cart in front of the position sensor. We'll then reverse roles with a different motion graph so that everyone gets a chance to both describe and to reproduce the motion. The default experiment screen on LoggerPro should already include a Position-vs-Time graph as well as a Velocity-vs-Time graph. If either of these graphs are missing, add* them back to your LoggerPro screen or ask your TA for help*. GAME OVERVIEW Split your lab group into two teams (or individuals for groups smaller than four) : the “talkers” and the “movers”. Your TA will give one of the pairs (the talkers) a plot of position vs. time. DO NOT SHOW THIS PLOT TO THE OTHER PAIR OF YOUR TEAM. The talkers will describe the motion needed to generate a similar plot, and the movers will try to follow those instructions by moving the cart in front of the detector appropriately. The talkers will judge whether the graph of the cart motion matches the paper plot well enough, or if the movers should try again (perhaps with refined instructions from the talkers). B1. Talkers obtain a type “A” plot from the TA. The talker team should obtain an “A” type plot from the TA. Make sure only the talker team sees the plot! You will see that part of the plot from the TA is dotted, and part is solid. You will be trying to get the mover team to reproduce the solid part well -- getting the same shape in the dotted sections in not necessary. B2. Talkers interpret the plot. The talker team should study the plot and (just amongst themselves) interpret the physical motion of the cart that would produce such a plot. Think about how to describe that motion. Consider using words like “starting position, ending position, turning around point, positive speed, negative speed, constant speed”, etc. whenever they are applicable. Do NOT describe the graph itself. Describe the motion needed to generate the graph. B3. Talkers describe the plot to the movers. Using only words, the talker team now describes how to move the cart to the movers. No graphs, or written material are allowed. The talkers should sit on their hands while talking (i.e., don’t point at the screen or use your hands to mime the plot). B4. Movers try to reproduce the plot with the cart. The movers try to reproduce the plot from the verbal description, working as a team with the talkers. All team members can see both the cart and the computer screen. If the talkers judge that the first attempt is not good enough, try again. Work continues until the talkers consider the plot made by the movers to be a good copy of the original. A “good copy” means that the relative slopes are about right, and that the division of time spent in each part of the motion is about right. You do not need to reproduce the exact numbers on the graph you were provided. There is no way to make an identical copy. A few “oopsies” where you may get data drop out because the sensor picked up a hand instead of the cart is OK as long as the major parts of the motion are correct. * Procedure for adding the velocity graph back to your screen if it is not present: In the top menu bar, click on “Insert” and then select “Graph” (the first option in the drop-down menu). To change the type of graph, click on the property being displayed on the y-axis (e.g., Position, Velocity, etc.) and then select the type of graph you want. To properly arrange the multiple graphs, click on “Page” in the top menu bar and then select “Auto Arrange” Physics 1AL pg. 34 TA CHECKPOINT #1. Call the TA to show off your skills. You should be ready to make the motion, describe the motion with words using the standard vocabulary of physics, and explain both the velocity vs. time and the position vs. time plots.. B5. Record your results. Record 3 pieces of information. (i) Make a sketch of the “A” type plot that you’ve been working with in your lab notebook. (ii) Summarize the instructions given by the talkers to the movers. (iii) Take a photograph or screenshot of the resulting LoggerPro screen capturing the motion generated by the movers. B6. Swap roles and repeat with a type “C” plot. Exchange talker and mover roles and finish with a “C” type. Store the final “C” type motion (hit “Experiment” then “Store latest run”). TA CHECKPOINT #2. Call the TA to show off your skills. (same as Checkpoint #1, but for the “C” plot.). C. MOTION WITH CONSTANT ACCELERATION In Part C, we will look at the acceleration associated with the motion of the cart on the track. We will start by predicting and then displaying the acceleration for the motion data captured in part B. We will then incline the track at an angle and attempt to generate/reproduce one of the graphs by utilizing gravity instead of manually manipulating the cart, and we will record the quantitative acceleration data from this attempt. C1. Predict the acceleration for type “C” plot. For the last motion (the “type C” graph used above), predict what an acceleration vs. time plot of the motion would look like. Discuss how to do this as a group and draw your plot on your whiteboard. When you are all in agreement, you should use the program to check your plots (it is best to show all three graphs, x, v, and acceleration vs. time on the same screen). To add an acceleration graph, click “Insert” and scroll down to “Graph”. To arrange all graphs, click “Page” and then “Auto Arrange”. C2. Replicate motion for a type “D” plot by hand. Get one of the type “D” plots from your TA. Move the cart with your hand so the acceleration vs. time measured by LoggerPro matches that plot. (Pay attention to the instructions for the initial speed.) Store one of your best efforts and discard any other stored plots. C3. Use gravity to replicate the motion. If you raise one end of the track about 5 cm (or 2 inches) and place the cart near the top, the cart will accelerate to the downhill end. Keep the track at this angle for the remainder of part C. Have a discussion and come to agreement about which end of the track should be raised, where to start the cart and which way to push it. Record your decisions and note which were correct. Now try to reproduce the motion in from step C2 by raising one end of the track. Can you make the right type of motion with this technique? Store this motion in LoggerPro. Display the data using all three graphs on the same screen. Physics 1AL pg. 35 C4. Let gravity reverse the cart’s motion. Now, place the cart at the lowered end of the track. Give it a quick, sharp push to launch it up the track so that it runs first uphill and then back downhill on its own (remove your hand immediately after the initial, sharp push). Record the entire motion with LoggerPro. How do the three graphs compare to the graphs from C3? C5. Measure the angle of the track. Using the provided protractor, measure the angle of your track relative to the horizontal tabletop and record this value in your logbook. Be sure to take all data for the previous step (C4) with the track at the same inclination angle. As always, be sure to evaluate the precision of this measurement tool and the uncertainty of your measurement. C6. Analyze the uphill motion. Select the section of the acceleration graph that corresponds to the cart’s uphill motion. Record the average acceleration and its uncertainty in this part of the graph. (You may find the statistics tool useful) C7. Analyze the downhill motion. Repeat step C6 for the downhill motion of the cart and record all these values in your notebook. C8. Graph the data in your notebook. Draw the graphs of position, velocity and acceleration vs. time for step C4 to scale in your notebook. Label on your plots where you gave the cart a push at the start, where it turned around, and where you caught it. What is the speed at the turn-around point? What is the acceleration: as the cart goes up? As the cart comes down? When the cart is at the turn around point? Record your answers to these questions in your notebook. TA CHECKPOINTS #3 & #4 (END). Show all three graphs from C8 to your TA. What is the speed at the turn-around point? What is the acceleration and its uncertainty as the cart goes up the track? What about as it goes down the track. Clean up your table, have your TA check you off when you are done, and obtain their signature.. Physics 1AL pg. 36  1AL Lab 2 Conclusion: Position and Velocity Logistical [Deductions will apply if the items listed in Q1 are not included in your report] Q1. Submit and tag all raw data pages from your lab logbook. Your TA’s signature should appear at the end of these raw data pages. Your name and the names of your lab partners who were present should appear clearly on these raw data pages (ideally at the top). These are all required for you to receive credit for your submission. Conceptual Q2. [1.00 pt] Describe (in words) the graphical relationship between position, velocity, and acceleration (i.e., give your description in terms of the position, velocity, and acceleration vs. time graphs that you looked at in Parts B and C of the lab manual). Part B Q3. [1.25 pts] Report your results for the type “A” plot that you recorded in Step B6. i. [0.25 pts] Sketch the type “A” plot that you used in your experiment. ii. [0.50 pts] Summarize the instructions given by the talkers to the movers that led to a successful recreation of the plot. iii. [0.50 pts] Include a photograph/screenshot of your group’s LoggerPro plot of position-vs-time for your “movers” recreation of the type “A” plot. Part C Q4. [1.00 pt] Consider the motion of the cart moving down the inclined track in part C of the lab manual. i. [0.50 pts] What is the physical reason that lifting one end of the track leads to constant acceleration? ii. [0.50 pts] What experimental aspect(s) in the lab dictate the actual value of acceleration that you obtain. Q5. [2.25 pts] Plot/Sketch each of the plots listed below from Part C8 of the lab manual. On each plot, clearly indicate when you pushed the cart, when it turned around, and when you stopped the cart. As always, remember to include a title and labels (with units!) for each axis. These plots/sketches must be generated either by hand on graph paper or in a drawing program or in a spreadsheet or plotting program (do not simply attach the screenshot or photo of LoggerPro for this question). i. [0.75 pts] Plot of position vs. time ii. [0.75 pts] Plot of velocity vs. time iii. [0.75 pts] Plot of acceleration vs. time (continued on next page) Physics 1AL pg. 37  1AL Lab 2 Conclusion : Position and Velocity (page 2) Q6. [1.00 pt] Report the average uphill acceleration (aup) and the average downhill acceleration (adown) you measured in Step C6 & C7, both with uncertainties (as always). Explain how you arrived at those uncertainty values. Q7. [1.50 pts] For this question, use the values for aup and adown that you reported in question Q6. i. [1.00 pt] Compare aup and adown. Are the two accelerations consistent with each other? How did you use your data and uncertainties to conclude this? ii. [0.50 pts] What is the physical reason that the two accelerations are or are not consistent with each other? Q8. [2.00 pts] For this question, use the values for aup and adown that you reported in question Q6. As always, remember to include uncertainties in all your calculations. i. [0.25 pts] Calculate the average acceleration along the track. ii. [1.00 pt] Use your average value of acceleration and your measured value for the inclination angle of the track to calculate the downward acceleration due to gravity, g. iii. [0.50 pts] Is your calculated value of g consistent with the generally-accepted value of g = 9.80 m/s2 ? Justify your answer in terms of your measured value and uncertainties. Iv. [0.25 pts] Assume that the effects of friction have the same magnitude for both the uphill and downhill portions of the experiment. Do you expect the effect of friction to bias (i.e., offset) your calculated value of g? If so, do you expect friction to contribute a positive or negative bias to your calculated value; if not, explain why not. Additional Submission Requirements: In Gradescope, be sure you tag all of the relevant pages of your submission for each conclusion question. Gradescope tagging for Q1 should include all of your raw data pages. Physics 1AL pg. 38