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62 Activity 8 In this activity, the cart will collide with a force sensor located near the bottom of an incline, and a motion sensor will record the cart's velocity during the collision. Therefore, the force sensor should have a collision pad mounted in place of the hook. Experimental Procedure 1. Collision of Cart with Force Sensor. Connect the force sensor and motion sensor to the computer interface. Calibrate the motion sensor and set its frequency to 100 Hz. Also, click on the force sensor's icon on the main screen and set the sensor's frequency to 2,000 Hz. These higher frequencies are necessary because of the extremely short collision time involved. 2. Set up the sensors on the track as shown in Figure 2. The track should be elevated slightly (about 2-3 cm). Motion Force = 507.78 9 Track Sensor Sensor Bracket todoubount Figure 2 (Courtesy PASCO scientific) Allow the cart to roll from rest down the inclined plane from a well-marked location. Select 'graph' as the recording medium to record force vs. time for the cart. Tare the force sensor just before rolling the cart and before each new data run. 4. On an F vs. t graph, expand the x-axis around the spike recorded. This will require several cycles of expansion and translation of axes since the width of the spike is quite narrow. Also, adjust the F axis if necessary. 5. With the mouse, drag a rectangle around the pulse. Make sure both the width and height of the pulse are included in the rectangle. 6. On the graph window, click the 'statistics' (down arrow) button and select 'area.' The area under the curve will be highlighted in grey. The resulting legend will give the area under the curve in units of N-s. You have now effectively integrated under the pulse and obtained the impulse. The area under the curve will be found in the legend box on the face of the graph. 7. Record the value of the impulse in Data Sheet 1. Print the pulse graph with the area-under-curve information. . Change in Momentum of the Cart. This change in momentum should equal the impulse measured above. To do this, drag 'velocity' from the data window to the graph of F vs. t to get a v vs. t plot. 9. Locate the appropriate portion of the v vs. t curve relating to the collision. Some axis expan- sion may be required. 10. With the 'smart tool,' determine the maximum velocity of the cart i.e. the velocity of the cart just at the time of collision with the force sensor. Record this value in Data Sheet 1.Impulse and Momentum 63 11. With the smart tool, determine the velocity of the cart immediately after collision. The cart will be traveling in the opposite direction at this time, and the maximum velocity should be a negative number below the axis. Record in Data Sheet 1. Print this velocity vs. time curve. You now have the velocity immediately before and immediately after the collision. 12. Using the lab balance, determine the mass of the car and record in Data Sheet 1. 13. Calculate the change in momentum of the cart using the velocities determined in steps 10 and 1 1 above. Record in Data Sheet 1. 14. Compare the change of momentum determined in step 13 to the impulse determined in step 6. Calculate the percent difference between the two values. Record in Data Sheet 1. 15. A Soft Collision. Remove the collision bumper from the force sensor and replace it with the clay holder cup (you will find it on the side of the bracket). Fill the holder cup with some modeling clay so that a "soft" collision will occur. Release the cart from the same position on the incline as you did previously. Measure the impulse as before and note the general shape of the collision curve. Measure the change in momentum as before. Include a printout of these new curves in the lab report. Normal -collision calculations I = Fit = 0.4 1 - DP = M ( VF - Vi ) = 0.50778 ( 26:32- 29.98 ) . = 1.81 toerror = 1: 81 - 0.4 * 100 Aug = 1.8 - 0.4 x 100 1.8 + 0.4 2 = 1.2727 x 100 = 127. 27 0 error64 Activity 8 Normal Soft Data Sheet 1 Impulse, as measured in Procedure 6 = 0.4 N.S 0 . 7 N.S Velocity immediately before collision = _29.9% m/s 28.70 M/s Velocity immediately after collision = = 26, 32 as -25. 99 re/s Mass of cart = 507.18 , 507,78 9 Change in momentum, as per Procedure 13 = 1, 8 N.S 1. 38 N.S Percent Difference, Ap and 1 = 127. 27 % 65, 3840 Calculations Soft collision calculation I = F. E = 0.7 N.S AP = M ( V F - vi ) = 0.5 0778 ( 25, 99 - 28. 70) = - 1. 37 6 = 1.38 %% error = ( 1.38 - 0.7 ) x100 Avg = 1. 38 + 0.7 - 1,04 2 Aug = ( 1,38 - 0.7 ) x/00 1.04 = 65. 38 0 errorNormal collision 'd" and 2.220 s. 29.98 m/s_ Run #1 . Velocity (m/s) O 2.250 s, -26.32 m/s -20 m 2.00 2.02 2.04 2.06 2.08 2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2.64 2.66 2.68 2.70 2.72 Time (s ) [Graph title here] Area: 0.4 N . S F Run # 1 4 oft Force (N) 2.430 2.435 2.440 2.445 2.450 2.455 2.460 2.465 2.470 2.475 2.480 2.485 2.490 2.495 Time (s ) [Graph title here]Soft Collision 2.870 s. 28.70 m/s Run #1 . (S/W) ATPODA 2.900 s. -25.99 mv's 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2 2.80 2.82 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98 3.00 3.02 3.04 Time ( S ) 3.08 3.10 3.12 3.14 Graph title here] Area : 0.7 N . S F Run #1 4 Force (N) NO 3.02 3.04 3.06 3.08 3.10 3.12 3.14 3.16 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34 Time (5) [Graph title here] imActivity 8 Impulse and Momentum Equipment and Supplies Required: Motion Sensor, Force Sensor, Dynamics Cart, Precision Track, Force Sensor Bracket and Collision Bumpers. Introduction When two objects interact through a collision they exert forces on each other. The objects may interact for a short period of time only, with the forces varying considerably over the time of inter- action. An example of a force vs. time plot is shown in Figure 1 below. This curve might be typical of the force distribution in time when a golf club strikes a ball, for example. F Figure 1 The area under this curve is defined as the impulse, or, I = F(tf - t;). The impulse of a force over a time interval from t; to t is a vector defined by I = Fat Using Newton's second law, F = dp/dt, we see that the impulse equals the change in momentum during the time interval. 1="Fat = d (pr dp * dt = Pf - Pi The software of Data Studio has a program that can determine the area under an irregular curve such as this F vs. t plot. The area under the curve is obviously the value of the integral of Fdt. 61