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# 13f impulse momentum-wireless 3-3-09

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### 13f impulse momentum-wireless 3-3-09

1. 1. Impulse-Momentum TheoremIntroductionDuring a collision, the contact force between the objects participating in the collision is notconstant, but varies with time. Thus the accelerations experienced by the objects will alsobe functions of the time. Since the accelerations are not constant we will not be able to usethe kinematics equations of motion to analyze this situation. Instead, we will rely upon theconcept of impulse and its relationship to the change in momentum through the Impulse-Momentum Theorem. The purpose of this lab is to determine the validity of the Impulse-Momentum Theorem.EquipmentComputer with Logger Pro SW Glider Ringstands (2)Vernier Lab Pro Interface Wireless Force SensorAir Track & Air Supply Vernier PhotogateAir Track Accessory Kit (Bumpers) ScaleFigure 1. Overhead view of the glider as it is about to impact the bumper attached to theforce sensor.13f Impulse-Momentum-Wireless 3-3-09 -1- Revised 10-11-07
2. 2. TerminologyImpulse: (Area under the F-vs-t graph) J = F ∆tNet Impulse: (Area under the Fnet-vs-t graph) J net = Fnet ∆tMomentum: p = mvChange in Momentum: ∆p = mv − mv0TheoryThe easiest way to analyze this collision situation is to make a graph of the force versustime. The impulse of this force over a given time interval is the area under the curve overthe same time interval. The time interval will usually be the interval during which theforce acts. If the force were constant, then the graph of the force versus time would be ahorizontal line and the area under the curve would be the value of the constant forcemultiplied by the time interval. However, since the force varies with time, we need to usethe average force, over the time interval. The net impulse acting on an object is the vector sum of all of the impulses that acton the object, or alternatively it is the area under the curve of the graph of the net forceacting on the object versus time. The Impulse-Momentum Theorem states that the netimpulse acting on the object is also equal to the change in the momentum of the object. J net = Fnet ∆t = ∆p p = mv & ∆p = mv − mv0 In this lab we will produce a one-dimensional elastic collision between a glider,riding on an air track, and a stationary force sensor. The photogate timer will record theinitial and final velocities and the force sensor will record the force as a function of time.We will then use this data to determine the validity of the Impulse-Momentum Theorem.13f Impulse-Momentum-Wireless 3-3-09 -2- Revised 10-11-07
4. 4. Glider Procedure –For a cylindrical “flag” its diameter is the length to be used.There is no orientation problem with the cylindrical flag. The “length of the flag” will bedetermined by measuring it with the calipers. You should enter this value of the length intothe computer To Enter the Flag Length into the computer: Click on the Experiment menu andclick on the Set Up Sensors menu item. Then select Show All Interfaces. Click on thePhotogate icon and select “Set Distance or Length.” Then enter the “Flag Length” andclick OK. Bumpers – The bumpers are mounted on each end of the glider (for balance) and onthe end of the force sensor. If there are only two (2) bumpers available then another objectequal in mass to the bumper needs to be mounter on the other end of the glider. Photogate Placement Procedure - We will use a photogate to measure the initialvelocity of the glider prior to the collision as well as the final velocity of the glider after thecollision. Place the photogate as close to the force sensor as possible so that the glidercompletely clears the photogate before it comes into contact with the force sensor. Checkto make sure that the bumper on the glider does not come into contact with the photogate. Wireless Force Sensor Procedure – To ensure the integrity of your data you willneed to make sure that the force sensor does not move during the collision. Do not send theglider into the force sensor too hard, if the bumper bracket on the glider and the one on theforce sensor touch each other the data will not be accurate and the run will have to berepeated. Final Alignment Check - You will be using one of the cylindrical objects as theflag. Orientation is not a problem, but if the upper portion of the cylinder is a bladestructure make sure the photogate height is adjusted so that the beam is broken by theCYLINDRICAL portion and NOT the BLADE portion. The glider bumper should notstrike anything as it passes through the photogate and it should hit the bumper on the forcesensor dead center. The photogate should be centered over the air track and the beam pathaligned perpendicular to the length of the track. The photogate should be located farenough from the force sensor so that the glider clears the gate prior to hitting the forcesensor.13f Impulse-Momentum-Wireless 3-3-09 -4- Revised 10-11-07
5. 5. Experimental ProcedurePrecision - All observations should be recorded to 3 significant figures. You should carry3 significant figures in all of your calculations as well.1. To begin a run first zero the force sensor by clicking the Zero button and then click the Collect button to start the data collection. Gently push the glider to launch it toward the force sensor. You should have finished pushing the glider well before it enters the photogate. The brackets for the bumpers should not touch one another. Let the measurement run all the way out until the end of the collection time and the Stop button disappears and the Collect button returns.2. TURN OFF the sensor between runs to conserve battery power.3. On the Force versus Time graph locate the non-zero region of the graph and highlight it by clicking and dragging the cursor across the region. Click the Integral button and record the value of the integral, which is simply the area under the curve, as the Net Impulse in the Data Table.4. Locate and record the initial and final velocities that occurred before and after the collision. Don’t forget to include the directions for these vector quantities.5. Record the time interval for the collision as well as the maximum value of the force. Determine these by using the inspection function with the Force versus Time graph.6. Repeat this process five (5) more times with the first bumper. Print a representative graph for one of these runs. Measure the mass of your glider using the scale.Data Analysis• Calculate the following quantities for each run: ∆p and compare it through a percent difference with the Jnet.• Then calculate the average net force for each run by Fnet = J net ÷ ∆t• Plot a graph (X-Y Scatter) of Jnet (y-axis) versus ∆p (x-axis). Determine the slope, y- intercept and correlation coefficient of the trendline. Use the LINEST Excel function to determine the uncertainties in these quantities.13f Impulse-Momentum-Wireless 3-3-09 -5- Revised 10-11-07
6. 6. Questions1. In this lab we neglected friction because we have significantly reduced its affect by the use of an air track. If friction were present what would be its affect on the values of the velocities? How would this affect the momentum values? What would this do to the value of the momentum change as it compares to the net impulse?2. In general, how do the average force and the maximum force for each run compare to one another?3. In general what were the differences that you observed between the two bumpers that were used? Your description should involve things like the differences in the graphs, the amount of time of the collisions, as well as the average and maximum force involved in the collision.4. Within reasonable limits for experimental uncertainty were you able to verify the Impulse-Momentum Theorem?Lab ReportFollow the instructions in the document “ Format for Formal Lab Reports.”13f Impulse-Momentum-Wireless 3-3-09 -6- Revised 10-11-07
7. 7. Data Tables Diameter of cylindrical flag = _______________(m)Bumper #1 – Data Table Mass of glider = ________________(kg)Run Jnet ∆t Fmax V0 p0 V p (Ns) (s) (N) (m/s) (kg*m/s) (m/s) (kg*m/s) 1 2 3 4 5 6Bumper #1 – Analysis TableRun p0 p ∆p Favg (kg*m/s) (kg*m/s) (kg*m/s) (N) 1 2 3 4 5 613f Impulse-Momentum-Wireless 3-3-09 -7- Revised 10-11-07