Dynamics Track Magnetic Force Impulse and Momentum An object subjected to unbalanced forces undergoes acceleration, which changes the velocity of the object in question. This change in motion can be further described and quantified in terms of impulse and momentum. Multiplying the applied force by the time over which the force was applied gives us the quantity called impulse: Impulse= Ft Multiplying the velocity of the moving object by its mass gives us the quantity called momentum: Momentum = mv Each of these quantities, impulse and momentum, incorporates more information than just the force or the velocity alone. Force and velocity are both subject to changes over time. Both impulse and momentum represent cumulative effects, or running totals, so to speak, of the overall effects of changes that occur over some period of time. The measurements for this lab include force, time, mass, velocity, and changes in these quantities. Consider, briefly, the units of measurement for impulse and momentum: Impulse = Ft, using Newtons (1N = 1 kg m/s 2 ) and seconds (s) yields Ns = kg m/s Momentum = mv, using kilograms (kg) and meters per second (m/s) yields kg m/s Note that the common units, kg m/s, suggest a similarity between impulse and momentum. In fact, the abbreviated symbols for impulse and momentum generally use the same letter; p for example: impulse: Δp = Ft momentum: p = mv The Greek letter delta (Δ) preceding the p for impulse signifies a change, as usual in the notation of Physics: Δp = p - p, where p and p 2 signify the momentum of an object before and after it has been 1 1 2 affected by the force, F, over the time interval, t (often written as Δt). This summarizes the relationship between impulse and momentum, and further explains why they are measured in equivalent units: impulse represents the change in momentum due to an applied force. So the momentum you end up with equals whatever momentum you started with plus the applied impulse. Purpose: This lab activity is designed to demonstrate and investigate the relationships among force, time, speed, and mass as summarized by impulse and momentum. Cautions: This equipment is delicate. Everything should go together easily. Do not force anything! Dynamics carts roll very easily, so they must be placed upside down when they are off the track. Having a cart roll off the table and onto your foot could cause injury, and worse, damage the cart! Equipment: Dual-Range Force Sensor with Cart mounting bracket Dynamics Track Adapter (Vernier product for PASCO track) Ring stand with mounting clamp and crossbar Logger Pro data collection software Collision Cart Balance, scale, OR a second Dual-Range Force Sensor ibook Motion Detector Track end stop PASCO Dynamics Track LabPro Interface TOPS Dynamics Track Magnetic Impulse and Momentum.doc Page 1
Procedure to set up the Dynamics track and instrumentation interface 1. Confirm that the Dynamics Track has been set up with three support feet at approximately 20 cm, 115 cm, and 210 cm in the mounting groove along the edge of the track, below the centimeter distance scale. 2. Confirm that the track is level, using a level. Place the level in the middle of the lane over each support foot. If the bubble appears off center over any of the three supports, check with your instructor regarding adjustment. 3. Confirm that the Motion Detector is on the track with the threaded brass-mounting hole down (no screw attachment is necessary for this lab), and the hinged segment opened 90 degrees so that the ultrasonic transducer (circular screen on hinged segment) faces along the length of the track. This should place the transducer surface around 200 cm along the distance scale. 4. Install the Track Adapter accessory, which holds a set of magnets that will be used to push the cart in this lab. Insert the nylon thumb screws through the holes in the lower edge of the mounting plate so that they go into the square nuts in the mounting groove along the edge of the track, below the centimeter distance scale. Thread the screws cautiously into their corresponding nuts, being careful not to cross thread them or otherwise damage them with too much force. The raised flange holding the magnets should be oriented toward the motion detector. Slide the Track Adapter along the track to position the edge nearest the Cart at the 40 cm mark, and tighten the thumbscrews to secure the Adapter in place temporarily. 5. Confirm that the Dynamics Cart has a Dual-Range Force Sensor mounted on the top of the cart, with the force measurement post (on the end nearest the brand name Vernier ) on the opposite end from the cart plunger. The Force Sensor measurement post should already be attached to a bar holding two magnets, and the bar should be attached horizontally, above the top deck of the cart. Note that the pair of magnets on this bar may affect any memory media (floppy disks, hard drives, memory sticks, ATM cards, etc.) placed or passed too close to the magnetic surfaces. 6. The cart will be started on each test run from the position where the magnetic end of the cart is aligned with the 80 cm mark. Confirm that the Dual-Range Force Sensor selector switch is set to the 10 N range, where it should remain for the entire experiment. 7. The Force Sensor and Motion Detector plugs are mechanically different to prevent making the following connections incorrectly. Be careful not to force a plug into an incompatible socket! 8. Confirm that the Dual Range Force Sensor cable is connected to the LabPro interface socket CH1. 9. Confirm that the Motion Sensor cable is connected to the Lab Pro interface socket DIG/SONIC 2. 10. Confirm that the LabPro interface cable is connected to ibook laptop computer USB port (1 or 2, either is OK), and that the LabPro interface is plugged into wall or lab bench power socket using its transformer cord. 11. The ibook laptop computer may be operated on battery power, or through the Apple Portable Power Adapter plugged into a wall or lab bench power socket, as determined by the instructor. 12. Be sure that the ibook laptop computer is turned on at this time. (The power switch is near the right hand speaker, above keyboard, if you find the power off.) 13. To LOGIN, click student, the password is student. 14. Open the Student tab and click once on the icon labeled FtmVlog to activate the data collection software. (If a box appears announcing that LabPro Has Data, select the bottom button in the box to Ignore/Erase the leftover data.) 15. The data log screen should include graph axes for Distance vs. Time (-0.2 m to 0.0 m), Velocity vs. Time (-0.3 m/s to 0.10 m/s), and Force vs. Time (-10 N to +0.5 N), all over a 0.0 s to 3.5 s time span. Scales may be adjusted later in the lab to magnify specific graph areas of interest. 16. Make certain that the end of the cart that is facing the force sensor is positioned exactly at the 80cm mark and make sure that the cart sits at rest without rolling or moving due to a tilted track, tangled sensor cables, etc. Click on Zero, and click on Zero All Sensors and wait while the Motion Sensor clicks quietly, measuring the starting distance. This procedure also sets the unloaded Force Sensor measurement to zero. (Note: If the computer does not recognize the interface connection, consult with the instructor.) TOPS Dynamics Track Magnetic Impulse and Momentum.doc Page 2
17. Move the Cart gently 10 to 20 cm towards the Motion Detector and leave the cart there while you move the Track Adapter accessory so that its edge is at the 77cm mark (edge closest to motion detector). Tighten the thumbscrews to secure the Adapter in place. 18. Roll the cart gently back toward the Adapter, close enough to confirm that the Adapter magnets are mounted one or two millimeters higher than the Cart magnets. This helps to keep the cart safely on the track. Collecting and storing data: When doing the following steps, divide the work up among your group members. One person should operate the computer and the other launch the cart. If there are three or more members in the group, rotate jobs so everyone contributes. 1. Move the cursor on the computer screen to the Collect button pictured near the middle of the top of the screen. Hold the Cart gently at the starting position (sensor end at 80 cm). With the edge of the Adapter at 77 cm, and the edge of the Cart at 80 cm, the 3.0 cm space between them provides a 2.5 cm starting distance between the magnets. You should be able to feel a slight repulsion force between the magnets here. When you are ready to release the cart and collect data, click the Collect button on the computer, then quickly but smoothly release the cart when you here the motion detector start clicking. You will be identifying the actual release time by examining the graphs later. Be sure that the cart stops before it reaches the Motion Detector. Friction should slow and stop the cart satisfactorily in this lab, but assign one lab team member to protect the Motion Detector on each run anyway, just to be safe. Notice that the Distance and Velocity measurements for motion toward the Motion Detector, and the Force pushing the Force Sensor are all recorded as negative numbers. This is normal, and the minus sign in each case only indicates the direction of the displacement, velocity, and force vector, respectively. 2. Store this data set using the File menu, Save As using the following scheme: P#G#R#; whereas the P is period followed by the appropriate number, G is for the group (look at the left-front-edge of the computer), and R is for run (make sure you keep track of the conditions). If your instructor wishes, all of these data files will be downloaded to external storage media later for future analysis on other computers. 3. Reposition the Adapter to 78 cm. Reposition the cart to 80 cm and hold it carefully against the magnetic repulsion at this 1.5 cm starting distance (2.0 cm between Cart and Adapter, 1.5 cm between magnets). Initiate the computer data collection and release the Cart carefully, as before. 4. Store this data set as Run #2, using the scheme described before. 5. Repeat the data collection and storage for 1.0 cm starting distance, with the Adapter set at 78.5 cm, and starting the cart from 80 cm, as before (1.5 cm between Cart and Adapter, 1.0 cm between magnets). Save this file as Run #3. 6. Weigh the Cart and Dual-Range Force Sensor, with mounting hardware, to determine the moving mass. This may be accomplished with a simple two-pan or triple beam balance, an electronic scale with a capacity up to a kilogram, or by simply using the force sensor. To use the force sensor, use the Zero button and Zero All Sensors to set the unloaded zero point, activate the Collect button on the computer screen once more. Gently pick the cart up by the sensor s magnet bar. Ignore the Distance and Velocity measurements (they should both be basically zero), and read the weight of the cart in the Force column of the data table. Record the weight of the cart here: Divide this weight (in Newtons of force: 1 N = 1 kg m/s 2 ) by the Earth surface gravitational field strength (9.8 m/s 2 ) to calculate the mass of the Cart assembly (in kilograms: e.g. (9.56 N) / (9.8 m/s 2 ) = (9.56 kg m/s 2 ) / (9.8 m/s 2 ) = 0.98 kg, note: this is NOT the mass of the cart). N Record the mass of the cart and the sensor here: kg 7. Loosen the Track adapter and slide it back down the track away from the cart and motion detector. TOPS Dynamics Track Magnetic Impulse and Momentum.doc Page 3
Data analysis: Data analysis should begin with the Third Run data, since it offers the most dramatic and obvious changes in conditions for ease of data point identification. The analysis of Third Run data may proceed immediately, once the data have been captured by the computer and stored, or later by retrieving the stored data file. 1. Open the Third Run LabPro data file, if it is not already open. You will need to identify the release point by examining the Force data. The ending point for purposes of analysis will be identified based upon Velocity data. The Distance data have been included for reference, because the Velocity data are really conversions of the Distance and Time data, which the Motion Sensor and software calculate automatically. 2. Identifying the Release Point: Examine the Force graph. Notice that the force remains constant, as long as the magnets are held at a constant separation, so the Release Point is indicated where the force begins to change. Estimate the Time of the Release Point from the graph, and then find the corresponding time in the data table. Line numbers for the data table are in the gray column at the far left of the data table. Click on the line number of the time you have selected in the table to highlight that line, and to mark reference lines on all three graphs. If the graph mark does not quite match the point you had in mind, select another line in the table to try to find a closer match. Also, consider the patterns of change which may be apparent in the data table to choose a point which best represents the moment of release. The force should be nearly as strong as possible, but on the verge of getting weaker. The distance and velocity should both be nearly zero, on the verge of starting to change. 3. Record the Line Number, Time, Force, and Velocity for the Release Point here No. Time Force Velocity 4. Identifying the End Point: The force value should drop as the cart accelerated to a point where it was very close to zero. This is the End Point. Estimate the Time of the End Point from the graph, and then find the corresponding time in the data table. Line numbers for the data table are in the gray column at the far left of the data table. Click on the line number of the time you have selected in the table to highlight that line, and to mark reference lines on all three graphs. If the graph mark does not quite match the point you had in mind, select another line in the table to try to find a closer match. 5. Record the Line Number, Time, Force, and Velocity for the End Point. No. Time Force Velocity 6. Determine the area of the Force vs. Time graph from the Release Point to the End Point. As a product of Force multiplied by Time, this area represents impulse. Determination of the area of the graph may be done manually, using printouts, or digitally, using the integration function in the Logger Pro software or other software on hand at the time of data analysis (which may not be the same day as data collection). 7. Repeat the identification of Release Point and End Point for the Second Run and First Run data, and determine the impulse for each of these runs as above. The graphs may be rescaled manually to improve viewing for the points of interest. Click on one of the numbers at the middle of the x or y axis to bring up a scaling box. Select Manual Scaling and specify upper and lower limits as needed. Note that clicking on numbers at the end of an axis allows you to reset the value of that end (max or min) only. 8. Use the Velocity of the End Point and the moving mass of the Cart with Force Sensor (Data Collection step 6) to calculate the momentum at the End Point for each of the three runs. TOPS Dynamics Track Magnetic Impulse and Momentum.doc Page 4
9. Record the mass of the Cart Assembly and tabulate Time, Force, and Velocity for the Release Point and End Point in each of the three runs. Also tabulate Momentum (at End Point) and Impulse (up to End Point) for each of the three runs. Cart Mass = kg Line No. Time (s) Force (N) Velocity (m/s) Impulse (Ns) Momentum (kg m/s) Release 1 End 1 Release 2 End 2 Release 3 End 3 10. Graph one point for each run to show the absolute value of impulse vs. the absolute value of momentum on conventional equal interval coordinate axes. TOPS Dynamics Track Magnetic Impulse and Momentum.doc Page 5
Examine the tabulated and graphed data. TOPS Physics A. What is evident about the relationship between the impulse applied and the resulting momentum in this lab? B. What relationship is expected to exist between impulse and momentum under ideal conditions? C. Describe how the lab conditions are likely to have resulted in any observed deviations from the ideal case. TOPS Dynamics Track Magnetic Impulse and Momentum.doc Page 6