Lab 3: The Force Plate and Vertical Jump

Transcription

1 3 Lab 3: The Force Plate and Vertical Jump I. Introduction A. In this lab, you'll explore Newtonian mechanics of an extended, non-rigid object: your own body. Whenever your center of mass accelerates, it must be due to a net external force; conversely, any time there is a next external force on your body, it will result in motion of your center of mass. This motion can be extremely non-obvious, because your center of mass can move as a result of a shift in body position rather than an overall movement of your entire body. II. Lab goals A. Observe Newton's second law applied to your body B. Locate your center of mass C. See how much your center of mass moves when you change your body position D. Measure how high you can jump! III. Prelab Assignment A. Read through this handout in its entirety (this will help you answering the questions below). B. Do the Logger Pro tutorial: "11-1 Working with Movies." 1. Remember, the tutorials are all inside the sub-folder: Experiments/Tutorials. 2. This tutorial will teach you how to synchronize a video with data collected from a sensor. a. Note that, the sync button is the button below the movie window. 3. Print page 4 of the tutorial and bring it to lab. C. Download the LoggerPro file "Prelab-BallBounce.cmbl" from the lab website. 1. This is a tutorial that will teach you how to make calculations within Logger Pro. This will become handy during your in lab work. 2. Answer all the questions, print the graphs and turn them in with the rest of the prelab work. D. After reading through this handout, answer the following questions. You can print out this page and write your answers directly on this sheet. Be sure to write your name, your lab TF's name, and your lab section at the top of the page and hand it in at the start of lab. 1. Examine the following graph of the reading on a force plate as somebody executes a standing jump on it: The jumper starts out in a standing position at the point labeled a. He then bends his knees into a crouch, then springs up into his jump. His feet leave the ground at time t=0 and he spends some in the air before landing. a. Identify the point on the graph corresponding to each of the following. You can write in the letter next to the appropriate dot on the graph. (Hint: each part does in fact correspond with a dot.) (1) The start of the crouch preceding jump (this one has been labeled for you) (2) The highest point of the jump (3) The jumper's center of mass reaches its maximum downward velocity during the crouch (4) The jumper's center of mass reaches its maximum upward velocity 1

2 (5) The lowest point of the crouch (6) The jumper's feet touch the ground at the end of his jump b. Estimate the jumper's approximate mass from the graph. c. Estimate the height of the jump (the distance by which the jumper raised his center of mass) from the graph. Explain your reasoning. IV. Background A. Newtonian mechanics of an extended object 1. Recall Newton's second law for a particle or simple object: the sum of the forces on the object is equal to its mass multiplied by its acceleration. At this point in the course, you've used this fact many times to solve physics problems. Typically, we proceed by drawing the free-body diagram of an object and adding up all the forces on it, and then using Newton's second law to equate the total force to the object's mass times its acceleration. 2. But what about an extended object or system, which can have many moving parts? Which acceleration are we talking about? As you might remember from the early weeks of this course, the center of mass of an extended object does what we want here. Let's remind ourselves why this is: a. The sum of all the forces on an extended system can be broken into the sum of external forces (forces from something outside the system which act on objects inside the system), plus the sum of internal forces (forces between objects which are both inside the system). But by Newton's third law, the internal forces all come in matched pairs of equal and opposite forces, so they completely cancel when you add them up. Thus the sum of all the forces on the system is equal to just the sum of the external forces on the system. (The external forces all have 3rd-law partners, too, but they are not forces that act on the system, so we do not consider them when using the 2nd law.) b. By Newton's second law, the sum of all the forces on the system is equal to the rate of change of the system's total momentum. But we defined the center of mass so that the system's total momentum would be equal to its total mass multiplied by the velocity of the center of mass. So if the total mass of the system is constant, the rate of change of the total momentum is just equal to the total mass times the rate of change of the velocity of the center of mass. 3. The upshot of all of this is: the sum of all external forces on a system is equal to the total mass of the system multiplied by the acceleration of the system's center of mass. Or in equation form, We'll use this relation to study the mechanics of the human body, which will first require us to think about where the center of mass of a person is. It turns out to be pretty close to the person's belly button. B. Jumping 1. What is the physics of jumping? Whether you are standing or jumping, the only external forces acting on your body are the normal force from the ground, and gravity. So how can you jump? Raising your center of mass into the air seems like it would require gravity to diminish, or the normal force to grow. Why would either of these happen? 2. The one thing we know for sure is that gravity isn't changing. So it must be that the normal force from the ground increases as you jump, propelling you into the air. This occurs because you push off harder on the ground with your legs; by Newton's 3rd law, this must also mean that the ground is pressing harder on you. 3. If there were a way of measuring that normal force throughout your jump, we would know everything there is to know about the physics of your jump. Hey, that gives us a really good idea for a fun lab! If only there were a device that could measure normal forces... V. Materials A. Two force plates! 1. The force plate is simply a flat plate that can measure the normal force exerted on it: 2

3 2. Like the force sensor in lab2, the force plate connects to a computer via the LabPro interface, and data from it can be collected and analyzed using Logger Pro. Unlike the force sensor, the force plate can measure large forces up to and beyond the weight of a person. 3. There is a switch on the force plate that toggles between the two ranges. One setting is for measuring forces between -200 N and +800 N. (Negative forces correspond to pulls; positive forces correspond to pushes.) The other setting is for larger forces, between -800 N and N. On this setting, the force plate can be used to study a person standing or jumping on it. 4. The force plates are pretty sturdy, but they can be permanently damage if you apply very large forces to them (greater than 5000 N). In ordinary standing or jumping, the forces involved are quite a bit less than this, but if you intentionally stomp as hard as you can on it, or jump and land with your knees locked, you can exceed 5000 N and break the force plate. (Landing with your knees locked, in particular, is a bad idea on so many levels. Just don't.) B. Digital video camera 1. This is a video camera connected to the computer that can be used to capture video in Logger Pro. 2. It is the same as the one used in lab 2. C. Other miscellaneous tools 1. Meter stick, long wood board, 5 kg steel weight mass and fluorescent stickers. VI. Procedure A. This lab consists of three parts, all using the force plate as the main measuring device. 1. Locate your center of mass 2. Motion of a complex object: Arm motion 3. Jump analysis (requires the use of the video camera) B. Locate your center of mass! 1. Open Lab3-ForcePlate.cmbl in Logger Pro. Immediately save it with a new name using your group initials. Read the introduction on page one and then move on the the following pages. 2. Place the long board so that it is resting on both force plates, with one support on each force plate: 3. Click the button to zero the force plates reading, making sure to select both plates on the pop-up window. 4. Place a 5-kg mass on the board, near the middle. Move it back and forth until both force plates give the same reading (to within 1 or 2 N). 5. Mark the position of the mass on the board with a piece of tape. This is the center of the board as it stands on the force plates. 6. Remove the mass and zero both force plates again. 7. Take turns and lie down on the board with your arms straight by your sides, and do the same exercise you did for the 5- kg mass: slide towards one end of the board or the other until the force plates give the same reading (at least to within 5 N or so). Your lab partners will have to tell you which way to move. a. Make sure the board does not slide relative to the force plates. If it does, you will have to re-mark the center of the board. b. When the readings are equal, note the position on your body which is at the same location as the tape marking the center of the board. This is the location of your center of mass! Mark it with a label that provides the best contrast with the clothes you are wearing. c. Repeat the measurement for each member of your lab group. 8. In addition, at least one of you should repeat the exercise but with the arms extended perpendicular to your body and with 3

4 the arms straight above and parallel to your head. a. Does your center of mass change? If so, enter here the differences between the different arm positions and comment on the results. C. Move your arms! 1. We will now use only one force plate. Remove the long board and choose force plate Move to page 3 of your LoggerPro file and zero your force plate (with nothing on it). 3. Have one member of your group stand on the force plate with arms down at his/her sides. 4. Have another member of your group click the Collect button in Logger Pro. 5. The force plate will then collect data for 10 seconds; you'll see the trace appear on the graph. During this time, have the person who is standing on the force plate should quickly raise their arms so that they are pointing outwards, and then keep them there for the rest of the 10 seconds: If you need to do it over, just click on 6. Paste the graph of the normal force vs time here: Collect again and take another 10 seconds of data. 7. Explain the features of the graph. Why does it go both up and down? Is the reading at the end the same as at the beginning? Should it be? 8. Make a qualitative sketch of the height of the person's center of mass as a function of time during the 10 seconds. Take a picture of it using photobooth and include it here: a. Make sure the option "Auto Flip New Photos" under the edit menu is checked. 9. Your arms have a mass of about 5 kg (each). Using this information, estimate about how much you moved your body's center of mass when you raised up your arms. (Hint: the CM of your arm is pretty close to your elbow.) D. Jump! 1. In this part, you will analyze a jump using video and the force plate. All members of your group will do the jump and estimate their jump height. However, the video analysis of the jump only needs to be done for one jump. 2. Move to page 4 of your LoggerPro file. 3. Change the DV camera shutter speed: a. Look at the flip screen on your digital video camera. It looks something like this: 4

5 b. If your camera is in screen-saver mode, press the FUNC button to get it to stop. Press FUNC again to access the camera's settings. c. The camera's menu will now appear on the display screen. To navigate the menu, use the little joystick. To select an entry, click the joystick (press into the middle instead of in one of the four cardinal directions). Start by clicking to get the menu. d. Click again for CAMERA SETUP. e. To change the shutter speed, press and then click once. Press until the shutter speed is 1/500 of a second, and then click again. f. To exit the camera setup menu, press FUNC again. 4. Set up Logger Pro to take video captures: a. In Logger Pro, go to the Insert menu and select Video Capture. b. If it prompts you to select a camera, select DV Video. c. If they ask for a resolution select 800x600 or 720x480. d. If they ask for a sound source, it doesn't really matter; pick one. e. The video capture window will open. On the right side of this window, click the Options... button. (1) Video Capture Mode: Video Capture Synchronized with Data Collection (2) Duration: 10 seconds (3) Make sure "Time-Lapse Capture" is not checked. (4) Capture File Name Starts With: MovieCapture (5) Click on the Camera Settings button. (a) In the Compression tab, under Motion, Frames per Second: 60 (b) Click OK. (Don't worry if it tells you that the compression mode is not the default.) (6) Click OK. 5. We will use your force plate 1, so you should zero it again. 6. Have one of your group members stand on the force plate facing the camera. Make sure their CM label and their feet are clearly visible. Another group member should stand next to them holding a meter stick. You will record a standing vertical jump, using both the force plate and the video camera. 7. When you are ready to start filming, click Start Capture. Both the camera and the force plate will begin collecting and recording. The capture runs automatically for 10 seconds and then stops. 8. During the 10 seconds, jump up as high as you can, and land back on the force plate. You should see a force graph that looks something like this: 5

6 9. Synchronize the movie to the force data: a. The place where the reading on the force plate goes to zero is the moment of takeoff, i.e. when your feet lose contact with the force plate. You will use this moment to synchronize the video to the force data. (Although both are collected at the same time, they are on slightly different clocks so they are not really synchronized to begin with.) If you did the tutorial in the pre-lab, this will be a cinch. b. In the lower-right corner of the movie window, click the button. (1) A synchronization dialog box will open. First, click in the graph on the moment of takeoff. In the force graph above, this occurs at pretty much exactly t=3.0 seconds. You should see the time corresponding to your click appear in the dialog box. (You may need to click and drag the dialog box to somewhere where it won't cover up the graph you are looking at.) (2) Next, play through the video frame by frame until you find the very first frame where your feet leave the force plate. The time corresponding to this frame will also appear in the synchronization dialog box. (3) Now click OK in the dialog box to sync the movie c. Once the movie is synchronized with the force data, you can use the button in the graph and the movie will automatically show the frame corresponding to the time you are examining. You can also set up a replay control (Analyze Replay...) to watch the force plate trace and the movie at the same time, at whatever speed you like. It's pretty cool. 10. Analyzing your jump: a. Your name: b. Paste a copy of your force graph here: c. From the force graph, determine the time of flight, i.e. how long you were in the air. You will need to zoom in on the graph to measure it accurately. flight time = d. From the flight time, use kinematics to calculate the height of your jump: jump height (from flight time) = e. Now use Video Analysis to track the motion of your center of mass (conveniently marked with a label in the movie). Use the meter stick to set the scale. You don't have to mark every frame in the video; begin just before you start to go down into your crouch and stop when you touch down at the end of the jump. f. After you have added the video analysis points, double-click on the force graph and go to the Axes Options tab. Check the box for Right Y-Axis and have it display the column "VideoAnalysis Y"; then click OK. Now your graph will display both 6

7 the force and the CM position simultaneously, and the g. Paste a copy of your graph (showing both Force and Y vs Time) here: feature will also show the corresponding frame in the movie. h. From the video analysis, how much did you raise your center of mass from its initial position (when you were just standing there) to the top of your jump? jump height (from video) = i. Compare the results of the two methods of measuring the jump height. If they are way off, see if you can figure out why. (Hint: do the two methods measure the same thing?) j. The video analysis gives a simpler, more direct, and more reliable measurement. Can you think of a method to correct the time-of-flight measurement to make it comparable to the video measurement? (Talk to your TF about this.) jump height (from time-of-flight, corrected) = k. VERY IMPORTANT. When you have finished analyzing your jump, go to File Save As... and name the file with your name, e.g. "Lab3-joon.cmbl". Put it in the Lab3 folder on the Desktop. You will need it later. l. Go to the blackboard and write your jump height there in centimeters. (Use the one from the movie.) 11. Now repeat the jump analysis for another jumper. a. Your name: b. Paste a copy of your force graph here: c. From the force graph, determine the time of flight: flight time = d. From the flight time, calculate the height of your jump jump height (from flight time) = e. You don't have to do the video analysis for every jumper; once is sufficient. However, recall that the time-of-flight measurement does not measure the jump height using the same definition of jump height. If you "correct" your time-offlight measurement the same way you did with the first jump, what would the result be? jump height (from time-of-flight, corrected) = f. When you have finished analyzing your jump, go to File Save As... and name the file with your name. g. Attach the Logger Pro file here (by dragging it from the Finder into the space below): h. Go to the blackboard and write your (corrected) jump height there in centimeters. 12. Repeat the jump analysis for the last jumper. a. Your name: b. Paste a copy of your force graph here: c. From the force graph, determine the time of flight: flight time = d. From the flight time, calculate the height of your jump jump height (from flight time) = e. You don't have to do the video analysis for every jumper; once is sufficient. However, recall that the time-of-flight measurement does not measure the jump height using the same definition of jump height. If you "correct" your time-offlight measurement the same way you did with the first jump, what would the result be? jump height (from time-of-flight, corrected) = f. When you have finished analyzing your jump, go to File Save As... and name the file with your name. g. Go to the blackboard and write your (corrected) jump height there in centimeters. 13. After everybody in the group has jumped, you can move on to the next part. 14. Check of Newton's 2nd Law a. Open the file you saved with the video analysis of your jump. (You do not have to do this part for every member of the 7

8 group.) b. In the Latest data set, create a new calculated column called "Net Force" which contains the net force on you (in the y- direction). Remember, the force plate only reads the normal force. (1) Follow the tutorial from the prelab to create calculated columns. c. In the Video Analysis data set, create a new calculated column called "ma" which contains your mass times the y- acceleration of your CM. (You'll have to take the second derivative of Y, or the first derivative of your y-velocity.) d. Create a new graph which has both "Net Force" and "ma" on the y-axis, and Time on the x-axis. Paste a copy of it here: e. Zoom in on the region where both Net Force and ma are visible. (It will only calculate ma for the times when you put a dot in the video analysis.) How well do the two curves track each other? f. Save your LoggerPro file one last time and attach it here. E. Challenge lab exercise: 1. Did you ever wonder what is the acceleration in an elevator? You can try it with the force plate. You can also measure the distance between the floors in the science center. 2. Take one force plate, the LoggerPro interface and the laptop to the science center elevator. a. Start recording the force data when the elevator is stopped. Travel up and down and record the floors you are visiting (one or two floors are enough) b. Enter the graph of "force versus time" here and try to interpret it. c. Can you estimate the velocity and the distance between the science center floors from the graph. Hint: you will likely need to integrate the graph using calculated columns. It is as easy as doing the derivative. VII. Conclusion A. Make sure that you saved your lab report with your own name, i.e. the updated version of this file. B. In addition, make sure to submit your lab report to the class website. Upload the file to the "Lab3 - Force Plate" Dropbox in the lab website; ask the TF for help. If your lab report isn't submitted, you won't get credit for doing the lab. Also, make sure that if you scroll down in the lab report, your attached Logger Pro files are there. 8