lab report 5 - PHY2053L

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Broward College *

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2053L

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Physics

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Dec 6, 2023

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Cristian Acuna Vasquez 02/17/2020 PHY2053L Title: Momentum, Energy and Collision Purpose: To test for conservation of momentum, measure energy changes during different types of collision and classify such collisions. Background Information: Energy and momentum both relate to forces that act on objects, but they are different concepts. The simplest difference between energy and momentum is that energy is a scalar quantity and momentum is a vector. The law of conservation of momentum states that in the collision of two objects such as billiard balls, the total momentum is conserved. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions. At this point we have to distinguish between two types of collisions: Elastic and Inelastic. Elastic collisions are defined as one win which there is no net conservation of kinetic energy into other forms of energy. For a brief moment, which the two objects are in contact, some ( of all ) energy is store momentarily in the form of elastic potential energy. In contrast, an inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Work and energy do not have a direction associated with their values (the definition of a scalar). In contrast, momentum has a direction as well as a value (the definition of a vector). In order to calculate momentum (p) the equation used is p=mv. M for mass and v for velocity. Kinetic energy ( KE) is calculated before and after collision.
Materials: Computer, Vernier Computer interface, Logger Pro, two Vernier Motion Detectors, Vernier Dynamics track, Vernier Dynamic carts with magnetic and hook and pile strip bumpers, scale. Procedure: After obtaining all of the equipment listed in the material list, two carts were labeled cart 1 and cart 2; The masses of the carts were measured and recorded. The track was placed on top of a horizontal leveled table. The motion detectors were place at each end of the track 0.15 m minimum distance between detector and cart. In logger Pro, 18 momentum Energy Coll was opened to start recording the data. The carts were tested to check that everything was working properly and data collection was accurate; The goal of the lab was to create a gentle collision by releasing cart 1 into a resting cart 2 located in the middle of the track and use the motion detector to find the velocity. For part I, carts were reposition so that the magnetic bumpers were facing one another and repeated the gentle collisions of cart 1 into resting cart 2. To make sure there was enough data to analyzes, another run was made. In part II of the experiment, there was a change in the cart bumpers into hook-and -pile setting facing one another so the carts should stick together after collision. One more attempt was made to record data. Finally in part III, the bumpers were changed again, this time one hook-and-pile was facing the magnetic bumper on the other, so that even though they will not stick together, they will not smoothly bounce apart; A total of 2 runs were made in order to get all the data for accurate calculations. Data: Table 1 Mass of cart 1 (kg) 0.272 Mass of cart 2 (kg) 0.263
Table 2 Bumper type Run Numbe r Velocity of cart 1 before collision (m/s) Velocity of cart 2 before collision (m/s) Velocity of cart 1 after collision (m/s) Velocity of cart 2 after collision (m/s) Part I: Magnetic 1 0.523 0 -0.427 -0.021 Magnetic 2 0.622 0 -0.453 -0.034 Part II: Hook-and-pile 3 0.441 0 0.249 -0.161 Hook-and-pile 4 0.490 0 0.207 -0.189 Part III: Both 5 0.606 0 0.042 -0.428 Both 6 0.500 0 -0.020 -0.395 Results / Calculation: 1. For each run, determine the momentum (mv) of each cart before the collision, after the collision and the total momentum before and after the collision. Calculate the ratio of the total momentum after the collision to the total momentum before the collision. Enter the values in table 3. Table 3 Run number Momentum of cart 1 before collision ( kg.m/s) Momentum of cart 2 before collision ( kg.m/s) Momentum of cart 1 after collision ( kg.m/s) Momentum of cart 2 after collision ( kg.m/s) Total momentum before collision ( kg.m/s) Total momentum after collision ( kg.m/s) Ratio of total momentum after/before 1 0.142 0 -0.116 -0.006 0.142 -0.122 0.86 2 0.169 0 -0.123 -0.009 0.169 -0.132 0.78 3 0.120 0 0.068 -0.042 0.120 0.11 0.97 4 0.133 0 0.056 -0.050 0.133 0.106 0.80 5 0.165 0 0.011 -0.113 0.165 -0.102 -0.6 6 0.136 0 -0.005 -0.104 0.136 -0.109 -0.8 2. For each run, determine the kinetic energy ( KE=1/2 mv 2 ) for each cart before and after the collision. Calculate the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision. Enter the values in Table 4. Table 4
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Run number KE of cart 1 before collision (J) KE of cart 2 before collision (J) KE of cart 1 after collision (J) KE of cart 2 after collision (J) Total KE before collision (J) Total KE after collision (J) Ratio of total KE after/before 1 0.037 0 0.025 0.00006 0.037 0.025 0.68 2 0.053 0 0.028 0.0002 0.053 0.028 0.53 3 0.026 0 0.008 0.0034 0.026 0.011 0.42 4 0.033 0 0.006 0.0047 0.033 0.011 0.33 5 0.050 0 0.0002 0.024 0.050 0.024 0.48 6 0.034 0 0.00005 0.021 0.034 0.021 0.62 3. If the total momentum for a system is the same before and after the collision, we say that momentum is conserved, If kinetic energy were conserved, what would be the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision? According to law of conservation of linear momentum, the total momentum of the system before collision is equal to the total momentum of the system after collision, thus the ratio of the total momentum after collision to the total momentum before collision is 1.0 4. If the total kinetic energy for a system is the same before and after the collision, we say that kinetic energy is conserved If the kinetic energy were conserved, what would be the ratio of the total kinetic energy after collision to the total kinetic energy before the collision? For the elastic collision, the kinetic energy of the system is conserved. Hence, the ratio of the total kinetic energy of the system before and after collision is 1.0. 5. Inspect the momentum ratios in table 3. Even if the momentum is conserved for a given collision, the measured values may not be exactly the same before and after due to measurement uncertainly. The ratio should be close to one, however. Is momentum conserved in your collision? Some of the momentum is conserved but not of the values are the actual ratio of 1.0. 6. Repeat the preceding question for the case of kinetic energy, using the kinetic energy ratios in Table 4. Is Kinetic energy conserved in the magnetic bumper collisions? How about the hook-
and-pile collision? Is kinetic energy consumed in the third type of collision studies? Classify the three collision types as elastic, inelastic or completely inelastic? Run 1 and 2, the magnetic bumper collision are examples of an elastic collision. The two carts bounce after the collision so that they move separately. Both momentum and the kinetic energy are conserves in this collision. In run 3 and 4, the hook-and-pile collision, the carts stuck together; This is an example of completely inelastic collision, thus momentum is conserved but kinetic energy is not. Runs 5 and 6 are examples of inelastic collision, as some energy is lost. Error Analysis The majority of the sources of error were due to frictional forces. The mass of the cars is pressing against the track. The friction that causes is static, if we increase the mass of the cars, it will affect the whole system by increasing the static friction. Also there were observers errors, as some teammates did not stop the program when each trial ended. Conclusion: In conclusion, the purpose of the experiment was met. It was verified through data and observation the three types of collisions: elastic, inelastic and completely inelastic collisions. A collision is an event where momentum or kinetic energy is transferred from one object to another. Only elastic collisions conserve both momentum and kinetic energy: Inelastic collisions converse only momentum alone.