PRELAB IMPULSE AND MOMENTUM

Transcription

1 Impulse Momentum and Jump PRELAB IMPULSE AND MOMENTUM. In a car collision, the driver s body must change speed from a high value to zero. This is true whether or not an airbag is used, so why use an airbag? How does it reduce injuries?. You want to close an open door by throwing either a 400 g lump of clay or a 400 g rubber ball toward it. You can throw either object with the same speed, but they are different in that the rubber ball bounces off the door while the clay just sticks to the door. Which projectile will apply the larger impulse to the door and be more likely to close it? 3. Ranking Task: In the figures below, six identical shape and size balls are dropped from rest at heights indicated. Each ball s mass is indicated. The balls fall onto a horizontal plate attached to a force probe that is zeroed. Each ball stops in the same time after it hits the horizontal plate. Rank, from greatest to least, the impulse registered by the force probe for each case. Greatest Least Or, all of the impulses will be the same. Please carefully explain your reasoning. 4. Ranking Task: Each figure below shows an individual who has jumped vertically off a force plate. Information is given on the individual s mass and the maximum height that she reaches. Rank, from greatest to least, the impulse registered by the force plate for her in each case. Greatest Least Or, all of the impulses will be the same. Please carefully explain your reasoning.

2 Impulse Momentum and Jump Part I: Impulse and Momentum The impulse-momentum theorem relates impulse, the average force applied to an object times the length of time the force is applied, and the change in momentum of the object: F t = mv f mv i Here we will only consider motion and forces along a single line. The average force, F, is the net force on the object, but in the case where one force dominates all others it is sufficient to use only the large force in calculations and analysis. For this experiment, a dynamics cart will roll along a level track. Its momentum will change as it reaches the end of an initially slack elastic tether cord, much like a horizontal bungee jump. The tether will stretch and apply an increasing force until the cart stops. The cart then changes direction and the tether will soon go slack. The force applied by the cord is measured by a Force Sensor. The cart velocity throughout the motion is measured with a Motion Detector. Using Logger Pro to find the average force during a time interval, you can test the impulse-momentum theorem. Force Sensor Motion Detector Elastic cord OBJECTIVES Measure a cart s momentum change and compare to the impulse it receives. Compare average and peak forces in impulses. MATERIALS computer Vernier computer interface Logger Pro Vernier Motion Detector Vernier Force Sensor dynamics cart and track clamp elastic cord string 500 g mass PROCEDURE. Measure the mass of your dynamics cart and record the value in the data table.. Connect the Motion Detector and the Force Sensor. Check with your Instructor if you are not sure.

3 Impulse Momentum and Jump 3 3. Open the file Impulse and Momentum in the Physics with Vernier folder. Logger Pro will plot the cart s position and velocity vs. time, as well as the force applied by the Force Sensor vs. time. 4. Optional: Calibrate the Force Sensor. a. Choose Calibrate Dual Range Force from the Experiment menu. Click. b. Remove all force from the Force Sensor. Enter a 0 (zero) in the Reading field. Hold the sensor vertically with the hook downward and wait for the reading shown for CH to stabilize. Click. This defines the zero force condition. c. Hang the 500 g mass from the sensor. This applies a force of 4.9 N. Enter 4.9 in the Reading field, and after the reading shown for CH is stable, click. Click to close the calibration dialog. 5. Place the track on a level surface. Confirm that the track is level by placing the low-friction cart on the track and releasing it from rest. It should not roll. If necessary, adjust the track. 6. Attach the elastic cord to the cart and then the cord to the string. Tie the string to the Force Sensor a short distance away. Choose a string length so that the cart can roll freely with the cord slack for most of the track length, but be stopped by the cord before it reaches the end of the track. Clamp the Force Sensor so that the string and cord, when taut, are horizontal and in line with the cart s motion. 7. Place the Motion Detector beyond the other end of the track so that the detector has a clear view of the cart s motion along the entire track length. When the cord is stretched to maximum extension the cart should not be closer than 0.4 m to the detector. 8. Click, select Force Sensor from the list, and click to zero the Force Sensor. 9. Practice releasing the cart so it rolls toward the Motion Detector, bounces gently, and returns to your hand. The Force Sensor must not shift and the cart must stay on the track. Arrange the cord and string so that when they are slack they do not interfere with the cart motion. You may need to guide the string by hand, but be sure that you do not apply any force to the cart or Force Sensor. Keep your hands away from between the cart and the Motion Detector. 0. Click to take data; roll the cart and confirm that the Motion Detector detects the cart throughout its travel. Inspect the force data. If the peak exceeds 0 N, then the applied force is too large. Roll the cart with a lower initial speed. If the velocity graph has a flat area when it crosses the time-axis, the Motion Detector was too close and the run should be repeated.. Once you have made a run with good position, velocity, and force graphs, analyze your data. To test the impulse-momentum theorem, you need the velocity before and after the impulse. Choose an interval corresponding to a time when the elastic was initially relaxed, and the cart was moving at approximately constant speed away from the Force Sensor. Drag the mouse pointer across this interval. Click the Statistics button,, and read the average velocity. Record the value for the initial velocity in your data table. In the same manner, choose an interval corresponding to a time when the elastic was again relaxed, and the cart was moving at approximately constant speed toward the Force Sensor. Drag the mouse pointer across this interval. Click the statistics button and read the average velocity. Record the value for the final velocity in your data table.. Now record the time interval of the impulse. There are two ways to do this. Use the first method if you have studied calculus and the second if you have not. Method : Calculus tells us that the expression for the impulse is equivalent to the integral of the force vs. time graph, or

4 Impulse Momentum and Jump 4 t final F t = F( t) dt tinitial On the force vs. time graph, drag across the impulse, capturing the entire period when the force was non-zero. Find the area under the force vs. time graph by clicking the integral button,. Record the value of the integral in the impulse column of your data table. Method : On the force vs. time graph, drag across the impulse, capturing the entire period when the force was non-zero. Find the average value of the force by clicking the Statistics button,, and also read the length of the time interval over which your average force is calculated. The number of points used in the average divided by the data rate of 50 Hz gives the time interval t. Record the values in your data table. 3. Perform a second trial by repeating Steps 0, record the information in your data table. 4. Change the elastic material attached to the cart. Use a new material, or attach two elastic bands side by side. 5. Repeat Steps 0 3, record the information in your data table. DATA TABLE Mass of cart kg Trial Final Velocity v f Initial Velocity v i Average Force F Duration of Impulse t Impulse Elastic (m/s) (m/s) (N) (s) (N s) Trial Elastic Impulse F t Change in momentum % difference between Impulse and Change in momentum Elastic (N s) (kg m /s) or (N s) (N s) Elastic

5 Impulse Momentum and Jump 5 ANALYSIS. From the mass of the cart and change in velocity, determine the change in momentum as a result of the impulse. Make this calculation for each trial and enter the values in the second data table.. If you used the average force (non-calculus) method, determine the impulse for each trial from the average force and time interval values. Record these values in your data table. 3. If the impulse-momentum theorem is correct, the change in momentum will equal the impulse for each trial. Experimental measurement errors, along with friction and shifting of the track or Force Sensor, will keep the two from being exactly the same. One way to compare the two is to find their percentage difference. Divide the difference between the two values by the average of the two, then multiply by 00%. How close are your values, percentage-wise? Do your data support the impulse-momentum theorem? 4. Look at the shape of the last force vs. time graph. Is the peak value of the force significantly different from the average force? Is there a way you could deliver the same impulse with a much smaller force? 5. Revisit your answers to the Prelab Questions in light of your work with the impulsemomentum theorem. 6. When you use different elastic materials, what changes occurred in the shapes of the graphs? Is there a correlation between the type of material and the shape? 7. When you used a stiffer or tighter elastic material, what effect did this have on the duration of the impulse? What affect did this have on the maximum size of the force? Can you develop a general rule from these observations?

6 Impulse Momentum and Jump 6 Part II: Physics of the Vertical Jump We will use the Impulse-Momentum theorem from part I of the lab to model the physics of the vertical jump. To simplify the physics, we will assume that you are a point mass, where your entire mass is located at the center of your body. OBJECTIVES: Use a High Speed Camera and Logger Pro to analyze the jump video, and determine the jump height and the jump velocity. Use a force plate to measure the jump force and the impulse of the jump. Use the velocity information from the Impulse-Momentum theorem to predict how high a person can jump. MATERIALS: computer Vernier computer interface Logger Pro Vernier Force Plate Sony High Speed Camera PROCEDURE ) Draw a free-body diagram for the jumper standing on the force plate. ) If the jumper just stands on the plate, what is the total force acting the jumper? How do you know? 3) Of the forces acting on the jumper, which, if any, could easily change? How could you test your idea? 4) Now prepare your equipment to take data via the force plate (nothing more than a high tech bathroom scale). While just standing on the force plate, what does the data represent? Which force in your force diagram does the value on the force plate reading correspond to? 5) Move around on the force plate while taking data and watch what happens to the readings. Feel free to bounce on your toes, go fast, go slow, move from foot to foot, just don t leave the scale while doing so. Explain what is happening to the data and why those changes are taking place.

7 Impulse Momentum and Jump 7 6) Think back to when the jumper was just standing on the plate: how did the upward force on compare to the downward force on the jumper? Does the weight force of the jumper remain the same or change? Look at your free-body diagram above. 7) Predict what you think the data would look like if the jumper crouched a little and then jumped off the force plate. Force 0 time 8) [Make sure the jumper has stretched and has no leg health issues]. Now use the force plate to test your prediction. [Make sure to video tape the jump. Place a piece of blue tape around where you think the center of mass of the jumper is located. The bluet tape will be used to track the jumper s motion on the video analysis.] How does the actual data differ from your prediction? 8) Thinking about the graph you created with the jump, what units would the area under the graph have in terms of kg, m and s? 9) Does the area under a graph tell you about you about the quantity or the change in quantity? 0) Based on your experiences, what quantities would need to be multiplied together to get the units that match the area under the curve? Which of the quantities is the more likely to change? ) Each figure below shows an individual who has jumped off a force plate. Information is given on the individual s mass and the maximum height that she reaches. Rank, from greatest to least, the impulse registered by the force plate for her in each case. Greatest Least Or, all of the forces will be the same. Please carefully explain your reasoning.

8 Impulse Momentum and Jump 8 ) Next you will need to collect numerical data for the jump. Use this data to help you determine how high the person jumped. Determine the Final velocity during the jump from the video analysis of the jump. Recall how you did this during the Video Analysis lab. What do you think the Initial velocity should be? Obtain the Average Force, Duration of Impulse, and the Impulse from the force plate data. Mass of Jumper kg Trial Final Velocity v f Initial Velocity v i Average Force F Duration of Impulse t Impulse (m/s) (m/s) (N) (s) (N s) Trial Impulse F t Change in momentum % difference between Impulse and Change in momentum (N s) (kg m /s) or (N s) (N s) 4) Use the velocity of the jumper, just as the jumper s feet leave the force plate and a Kinematics equation to calculate how high h that the jumper jumped. Then compare calculated height to the actual height obtained by the video analysis data. Trail Velocity when jumper s feet just leave the force plate (m/s) Calculated center of mass jump height h (m) Actual center of mass jump height h (m) % difference between calculated and actual jump height. 5) Use the Kinematics equation to calculate the hang time ( t that the jumper s feet were off of the ground) for the jumper. Then compare calculated hang time to the actual hang time obtained by the video analysis data. Trail Calculated hang time t (s) Actual hang time t (s) % difference between calculated and actual hang time

9 Impulse Momentum and Jump 9 Scenario: Assume the jumper in your group wants to become basketball player. He or she has come to you for guidance and wants you to determine how to jump high enough in order to slam dunk a basketball on a 0 foot high rim. Make the following recommendations:. Determine the jump velocity that the jumper would need to slam dunk a basketball.. Determine what impulse the jumper would need to slam dunk a basketball. 3. Determine what average force the jumper would need to slam dunk a basketball. 4. Recommend how the jumper could increase his or her impulse. 5. Recommend any technique the jumper could use to improve upon the jump height. [look at the force vs. time graph for someone who is able to jump high in our lab, and then compare that graph to your jumper s graph.] 6. Now it s time to show the instructor that by following the recommendation, the jumper is able to jump higher than the height obtained during the lab.