The purpose of this lab if for students to observe impulse through elastic and inelastic collision.
Apparatus:
There are two parts to this lab experiment. The first part is to find impulse through elastic collision, and to do that, we need the help of spring collision. We place the track on a level surface, with a cart at one end and a motion detector at the other end. The cart held in place at one end of the track has a spring connected to the cart, and is released in order for the collision to happen. Then, we place a force sensor on another cart, that is placed anywhere on the track. The second part is where we add mass to the cart in motion. The impulse should be larger since there is more mass. The third part is where we take the spring cart away and replace it with a wooden stock that has clay pasted on the wooden stock. Also, the force sensor needs a nail in place of the rubber stopper. With these equipments, we should produce an inelastic collision.
Explanation:
For Part 1 of this lab, we first calibrated the force sensor to read zero, and set Logger Pro to record force and distance. Giving the cart, on the track with a mass of 440g, a light push, the cart ran across the track and into the spring. With the proper data collected, we graphed force vs time and velocity vs time. Using the force vs time graph, we integrated the curve created by the change in force throughout a period of time, and came out with an impulse of 0.3136 N*s. Using the velocity vs time graph, we searched for the initial velocity, right before the collision, and the final velocity, right after the collision, and used the impulse equation to find the momentum of this system, which came out to be 0.292 N*s. The percent error was 6.89%, which is acceptable. The error was due to which instantaneous velocity we picked on Logger Pro. If we were to pick two different velocity, we may be able to decrease the percent error, but Logger Pro can only count to a certain decimal point. Also, the collision was not perfectly elastic, so there could have been some energy lost during the collision.
For Part 2 of this lab, we added mass to the cart, and the total mass came out to be 940g. With the same procedures as Part 1, the force vs time graph gave us a impulse of 0.7786N*s. Using the velocity vs time graph, we came up with an momentum of 0.8366N*s. The percent error was 7.45%, which is acceptable. The cause of the error was the same as Part 1, but only more heavily, due to the increase in mass. With the extra 500g, there were more energy lost during the collision.
For Part 3 of this lab, we replaced the cart with spring with the wooden stock and clay and the rubber stopper with a nail. Same as Part 1, we pushed the cart lightly, and the cart ran across the track and into the clay, stopping the cart completely. Graphing the force vs time , we can integrate it to find the impulse, which came out to be 0.1869N*s. Graphing the velocity vs time, we were able to find the initial velocity and final velocity. The mass of the cart was 0.44kg, so we calculated the momentum of the system to be 0.1892N*s. The percent error was 1.23%, which is almost zero, and considerable acceptable. This trial had less error because the purpose was to exert all the energy out of the cart and into the clay, so the only error came from Logger Pro.
Conclusion:
In order to find impulse and momentum, we had plot force vs time graph and velocity vs time graph. The impulse was found by integrating the force vs time graph, and the momentum was found by finding the initial velocity and final velocity and using the momentum equation. The impulse and momentum were almost equal to each other, which means that this system follows true with the impulse-momentum theorem. The error we found in this lab was due to Logger Pro's accuracy and the lost in energy in the collision. Other than that, the system was accurate.
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