Impulse+Provided+by+a+Variable+Force


 * Lab Title:** Impulse Provided by a Variable Force


 * Primary Authors:** Megan


 * Contributing Authors:** Peter


 * Abstract:** The goal of the first part of the lab is to experimentally confirm the relationship between impulse on an object and the objects resulting change in momentum. It was found that the value of impulse is the same as the value of the change in momentum. Therefore, change in momentum=impulse. The goal of the second part of the lab is to compare the impulses experienced by two different objects when they pull on each other.


 * Introduction:** The lab, part one and part two, was designed in order to find the connection between impulse and the change in momentum. Theoretically, change in momentum and impulse should be the same. Through algebra, impulse (F x t) and change in momentum (m x v-v) are found to have equal equations and therefore they are the same value. For example, if the impulse of an object is 14.7, the change in momentum would also be 14.7. Most of the collected impulses and momentums are very similar, but not exactly the same. For one trial, the impulse was .7991 and the change in momentum was .7287. As is seen by this example, the lab purely experimental and bound to have flaws. However, this lab was based upon the theory that change in momentum is equal to impulse.In the second part of the lab, only impulses were compared. Since they pull on each other and the force is the same along with the time, the impulses should be equal. The second part of the lab demonstrates that F x t is equal to impulse.


 * Methods:** The program Logger Pro, a cart, a spring, and a track are used in this lab. The spring is used to apply force to the cart that is moving on the track. Data is then recorded on graphs in Logger Pro. The area below the selected part of the graph is called impulse (F x t). Also, the stat button is used for the velocity-time graph to find the minimum and maximum velocities. The maximum, or final, velocity is subtracted from the minimum, or inital, velocity. That number is then multiplied by the car mass (in kg). The car mass was found to be .649 kg. For the second part of the lab, a spring is also used to provide force between the two carts. The impulse and change in momentum are calculated the same way as in part one of the lab.

Part one results: Although there is some error because it is experimental, it is proven that impulse and change in momentum are the same value.
 * Results:**
 * ~ Vi ||~ Vf ||~ Impulse ||~ Change in Momentum ||
 * = -.557 || .5659 ||= .7991 ||= .728762 ||
 * = -.5414 || .6012 ||= .7547 ||= .741547 ||
 * = -.5553 || .6039 ||= .7622 ||= .752321 ||

Part two results: No weights were added to the carts in these three trials:

**Impulse** The error is visible in this part of the lab as well, but the impulse values of both cars are proven to be the same.
 * Trails || Car 1 || Car 2 ||
 * 1 || **.**7491 || **.**7684 ||
 * 2 || **.**6483 || **.**6492 ||
 * 3 || **.**6665 || **.**6729 ||


 * Conclusion:** This lab helped to demonstrate the ideas of impulse and change in momentum. In the first part of the lab, the relationship between impulse and the change in momentum was confirmed, that relationship being that the two are the same value. In all three trials the values were very close, trial three being the most accurate with an impulse value of 0.7622 and a momentum value of 0.752321. In the second part it was found that when two objects pull on each other they have equal impulse values. The most accurate trial in this experiment was trial two with an impulse value of 0.6483 for car one and and impulse value of 0.6492 for car two.