AH-22 COLLISION AND IMPULSE (SMART CART SAMPLE DATA AND CALCULATIONS: With Rubber Bumper: Time of Peak Initial Final Change in Percent Average Percent Trial Velocity Velocity Momentum Impulse, J Difference Collision Force Force (N) Loss of (m/s) (m/s) Ap (N-5) between Ap (S (N) Kinetic (kg-m/s) and J Energy 17 0.435 -0.162 0.149 0.16 7.1 0.018 8.89 20.27 86.1 Sample Calculations: Ap = m Av = (0.250 kg)*(-0.162 - 0.435) = 0.14925 kg.m/s Impulse = Area under the curve (blue shaded part) = 0.16 N.s % difference = 10.149 - 0.161 [9-149 + 0.16] x100 = 7.12 = 7.1 Time of collision = 1.258 - 1.240 s = 0.018 s Average Force = Impulse / AT = 0.16/0.018 = 8.888 N Percent Loss of Kinetic Energy = 100x,m(v; - v?)/=mv? = 100x(0.1622 - 0.4352)/0.4352 = 86.13 - Un led.cap" Page #1 Page #2 Page =] Displays IT at 0. 20 1246 s, 20.27 N F. Blue v. Blue Run # 17 + 0.3 1.240 s, 0.435 m/'s 0.2 0.1 Velocity, Blue (mi's) 1.258 s, -0.162 m/'s 0.0 rex: 0. 16 N-s NONAGO -0.1 -0.2 03 1230 1 235 1 240 124 1250 1255 1.260 1.265 1 270 Time (s Graph title here 1 Controls X 00:02.51 Smart Cart Farce Sensor. Blue - 303.10 13 : | Fecal's. Type here to search 6 PASCO / 013-XXXXXAH-22 COLLISION AND IMPULSE (SMART CART) DATA Table 1: Impulse and momentum of a cart undergoing a collision with Rubber Bumper Time of Average Peak Force Percent Loss Initial Final Change in Percent Momentum Impulse, J Difference collision force in during of Kinetic Trial Velocity Velocity Ap (N'S) between Ap collision collision (m/s) (s) Energy (m/s) (kg.m/s) and J 2 Table 2: Impulse and momentum of a cart undergoing a collision with Magnetic Bumpers. Change in Percent Time of Average Peak Force Percent Loss Initial Final Momentum Impulse, J Difference collision force in during of Kinetic Trial Velocity Velocity Ap (N.S) between Ap collision collision Energy (m/s) (m/s) (s) kg-m/s) and J 2 In your report, discuss the effect of magnetic bumper versus the rubber bumper on the collision time, average force, peak force and loss of kinetic energy. 5 PASCO / 013-XXXXXAH-22 COLLISION AND IMPULSE (SMART CART) GRADING: Grading for this report will be based on: Title Page, Table of Contents, Procedure copied from Manual = -5 Objective, Theory, Procedure = 15 Wrong page numbers = -2 Wrong Course Titleumber= -1 Data Tables = 10 No Units = - Capstone Graphs = 5 each (max =10) Graphs should show Vi, Vf, Area Sample calculation = 5 Calculation errors = -3 Conclusion = 10 PASCO / 013-XXXXXAH-22 COLLISION AND IMPULSE (SMART CART) 3. Open Capstone, and then power-on the Smart Cart and connect it wirelessly to Capstone. Select the Smart Cart's Force Sensor and Position Sensor. 4. Set up a graph with Force on Y-axis and time on X-axis. Open another Y-axis by using the tool: Set the second Y-axis as Velocity. Change its color from that of the Force to make it easier to differentiate the two curves. 5. Increase the Data sampling rate for both position sensor and force sensor to 500 Hz. 6. Set the cart at the left end of the track with its rubber bumper facing the right side end stop. COLLECT DATA 7. Begin recording data, and then gently push the cart toward the end stop. 8. Stop recording after the cart collides with the end stop and reverses its direction. 9. Repeat the same data collection steps four more times, pushing the cart at different velocities and or masses in the cart. NOTE: Do not push the cart very fast. Do not use both 250 g masses on the cart. Support the End Stop with your hand as the cart bumps into it. If this is not done, the force curve shows a dip in the middle of the collision, likely due to the backward motion of the End Stop. Data Analysis Mass of cart (kg) = 10. Use the coordinates tool in your software to determine the velocity of the cart just before collision (initial velocity v, ) and just after collision (final velocity v, ) for each trial, and then record each value in Table 1. See Fig 1, and also the figures in Sample Data. NOTE: Make sure the signs of the velocities are correct 11. On the Force vs. Time graph, use the Area tool to measure the area under the curve. This is the impulse that the Smart Cart experienced. Select the same range of data for both velocity and force measurements. 12. Calculate the percent loss in kinetic energy during the collision. 13. Repeat with the Magnetic Bumper on the cart. NOTE: You will have to spread out the time axis to be able to see the collision properly. Figure 2 shows how and why the velocity of the cart and the force change during the experiment. Figure 1; Force Vs Time, and Velocity Vs Time graphs. 0.2- Force IN) Velocity [m/s) 0.875 s. -0.242 m/s Area: -0.20 N . s PASCO / 013-XXXXXAH-22 COLLISION AND IMPULSE (SMART CART) With Magnetic Bumpers: Change in Percent Time of Average Peak Percent Initial Final Momentum Impulse, J Difference Collision Force Force (N) loss of Trial Velocity Velocity Ap (N.S) between Ap (S) (m/s) (N) Kinetic m/s) kg.m/s) and J Energy 0.34 0.529 2.29 5.42 0.364 -0.354 0.1795 0.18 0.3 Sample Calculations: Ap = m Av = (0.250 kg)*(-0.354 -0.364) = 0.01795 kg.m/s Impulse = Area under the curve (blue shaded part) = 0.18 N.s 10.1795 - 0.181 % difference = [9.1795 + 0.18] x100 = 0.278 = 0.3 Time of collision = 2.300 s - 1.960 s = 0.34 s Average Force = Impulse / AT = 0.18 / 0.34 = 0.529 N Percent Loss of Kinetic Energy = 100x,m(v} - v?)/ amv? = 100x(0.3542 - 0.3642)/0.3642 = 5.419 -Untitled cap' Page v3 Taale ITat 3.5 O. 3.0 T. Blue , Blue 2.130 s, 2.29 N 1.960 s, 0.364 mis Run # 19 I 2.5 0.1 2.0 Ca leras en 0.0 Velocity. Blue im/s 1 5 0.1 16 10 1.960 5, 0.03 N 2.300 s, 0.03 N -0.2 Area: 0.18 N - s -0.3 D.0 -0.4 0.5 2 300 s.-0.354 m/'s 1.90 1.95 2.00 2.05 2.10 2.15 2.20 225 2.30 2.35 2.40 Time is) [Gmph title here ] aarrals M 00:04.38 Smart Fart Farte Sarwar. Al.my 309 93 19 Fasty Type here to search PASCO / 013-XXXXXAH-22 COLLISION AND IMPULSE (SMART CART) Rev 4-0?-2021 from Passe Manuals Objective To verify the Impulse-Momentum Theorem i.e. J = 1'th = A3) Materials and Equipment 0 PASCO Smart Cart II PASCO Rubber Bumper o PASCO Track with feet II PASCO Magnetic Bumper 0 PASCO Track End Stops Background Vehicle airbags and the large yellow barrels full of sand called Fitch barriers near highway exits are credited with saving thousands of lives and reducing injuries to car occupants. Two important physics phenomena that occur during a collision are the change in momentum and the impulse imparted on the vehicle and its occupants. In a collision, even though the change in momentum and Impulse remain the same. an increase in the collision time reduces the average force on the occupants of the vehicles. The change in momentum of an object experiencing a collision can be calculated by subtracting the momentum before the collision from the momentum after the collision: Ab = Wit me (I) where Ab is the object's change in momentum. in is its mus. k is its nal velocity. and it. is its initial velocity. I For constant forces, impulse j is dened as the product of the force PL acting on an object (the force responsible for changing the object's momentum) and the time interval At over which the force is acting: J'l = l;At (2) For variable forcesi impulse is dened as the area under a force versus time curve during the time in which the collision occurred. 1" = Area Underli' versus t Curve (3) J = Ith = 11;) (4) Equation (4) is the Impulse-Momentum Theorem. In collisions. e.g. automobile collisions. the dip is usually xed by the initial speed of the cars. In order to reduce the average force on the occupants of the car, we try to increase the dr during which the change in momentum is taking place. i.e. the time in which the collision is completed. Usually this time is very short, but can be increased by the use of plastic bumpers (instead of steel bumpers). crushable bonnet (instead of a strong bonnet), padded dashboards, seat belts and air bags. The yellow barrels mentioned above also have the effect of increasing the time in which the car stops when it hits them. A thing to be carei] about while calculating the Ap is that the sign of the velocity usually changes in a collision, and the proper sign is to be used in the calculations [see sample calculations near the end of this manual). Procedure SETUP l. Assemble the Track and level it. You may use only one half of the track if you like. Attach the end stops at each end with their magnets facing towards the track. 2. Screw on the Rubber Bumper to the Force Sensor on the front of the Smart Cart. PASCOI Dis-meet ERRO Rl BOOKMARK NOT DEFINED