MASSACHUSETTS INSTITUTE OF TECHNOLOGYPhysics DepartmentPhysics 8.01 Fall Term 2006Momentum DemonstrationPurpose of the Experiment:In this experiment you allow two carts to collide on a level track and run into a spring thatis attached to a force sensor. You will measure the position and velocity of the first cartand the force exerted by the spring while it is compressed. You can analyze your data todetermine the following things from this experiment:• An experimental test of the conservation of momentum in elastic and inelasticcollisions.• Determination of the maximum kinetic energy that is lost to non-conservative workin a completely inelastic collision.• You will make use of most of the ideas and computational tools that we need to analyzecollisions in one dimension.Because the track is level, we do not need to consider changes in the gravitational PE of thecarts and may take it to be zero. If we consider the two carts to be an isolated system (thisis a good approximation so long as the friction forces are small), the only mechanical energyis kinetic, K. A collision is inelastic if some of the initial K is lost to non-conservative work.A collision is elastic if no K is “lost.” A collision is completely inelastic if the maximumamount of K (consistent with conservation of momentum) is converted to non-conservativework; this happens when the two colliding objects stick together. Sometimes that is whatpeople mean when they ref er simply to inelastic collisions.Setting Up the Experiment:A Byx• At the the end of the track with the level adjustment screw attach a force sensor withthe hook replaced by the lighter of the two springs.• Clip the the motion sensor to the other end of the track.• Level your track as well as you can using the level adjustment screw. Test by makingsure an empty cart does not have a tendency to roll in either direction; the test ismore sensitive if you put two 250 gm weights in the cart.Momentum Demonstration 1 November 1/2, 2006The LabVIEW ProgramThe LabVIEW program for this experiment is Momentum.exe ; it isvery similar to the program you used last week for work/energy andthe harmonic oscillator. The main pull-down menu is slightly different,with “Analyze Data” being the command to fit data or calculate theintegral under a curve. Besides calculating the integral, the programcan fit the functions A, A + Bx or A + Bx + Cx2to the data. Theposition of cart A and the force on the spring are measured.Connect the motion sensor (yellow plug into jack 1) and the force sensor to the SW750interface. The force sensor should be plugged into channel A of the SW750. Be sure to tarethe force sensor before each measurement.For all of the measurements set the Run Time to 10 s, the Sample Rate to 100 Hz and theGain to 10X. When you choose Measure from the pull-down menu the RUN button changesto bright green. Clicking the button (or typing the Esc key) starts the measurement; thebutton will change to red and say STOP. Measurement will stop when you click the buttonor the Run Time has passed. While measuring the cart position and the force, the programwill not actually record the data until the position crosses a trigger value of 30 cm whileincreasing, and recording will stop at the same trigger value with x decreasing. The normalway to make a measurement is to begin with the cart from 16 to 20 cm in front of the motionsensor, click the RUN button, and push the cart. The cart will roll at least 10 cm beforedata are recorded; that gives the cart time to stabilize and roll smoothly after you pushit. The program will record measurements until the cart returns to the 30 cm point or theRun Time elapses.Completely Inelastic Collisions:You should study completely inelastic collisions first in this experiment. Place two emptycarts on the track with the the Velcro pads facing each other. One cart (which I call thetarget cart, with mass mB) should be placed on the track with the end with the Velcro padsabout 70 cm from the motion sensor; then the other end of the cart will be about 10 cm fromthe spring on the force sensor. The s econd cart (which I will call the incident cart, withmass mA) should be placed on the track between 16 cm and 20 cm from the motion sensor.You should push the incident cart just hard enough that it comes back to the starting pointafter colliding with the other cart and bouncing off the spring. If you push too hard a cartmay jump during the collision, and if you push too softly cart A will not come back farenough to stop the program f rom taking data.You should experiment to get this right before you start to make measurements. How hardyou need push cart A changes with the masses of the two carts and whether or not thecollision is inelastic, so you will have to find this out by trial and error for each of the sixmeasurements that you makeNotation: the subscripts A and B refer to the carts, and subscripts 1 and 2 are before andafter the carts collide, respectively. Make measurements with mA= mB= 250 gm (bothcarts empty), mA= 250 gm, mB= 500 gm, and mA= 500 gm, mB= 250 gm. Measure vA,1before the carts collide and v2= vA,2= vB,2after the collision when the two carts are stucktogether but have not yet hit the spring.Momentum Demonstration 2 November 1/2, 2006The raw data when mA= mB= 0.250 kg are shown in the plot below.The best way to determine vA,1is to plot Position (x vs. t) and do a Linear fit to x(t) beforethe collision. The data between the cursors will be included in the fit; there is some roundingof the x vs. t during the collision, so don’t go right up to the collision with your fit.Momentum Demonstration 3 November 1/2, 2006Find v2by a fit to data after the collision of the carts. Be careful not to include any datafrom the region where the carts are compressing the spring; a Force plot can show you thetime when this begins to happen.Repeat the inelastic collision measurements for mA= 0.25 kg with mB= 0.50 kg and formA= 0.50 kg with mB= 0.25 kg. Record the values of vA,1and v2for each collision in thetable below. Include the velocity σ values from the fits and calculate the kinetic energiesK1and K2.mAmBvA,1(m/s) v2(m/s) K1(J) K2(J)0.25 kg 0.25 kg0.25 kg 0.50 kg0.50 kg 0.25 kgAnalysis of Your Measurements:More data analysis will be carried out as the part of Problem Set 9 which is included as thelast three pages of these notes. You will need the data from the table above and from thetable on page 6 to do the homework problems. Make a
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