vector quantities lab

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University of New Orleans *

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1033

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Physics

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Apr 3, 2024

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Lab 1 Vector Quantities Caylee Fields Brandon Howe PHYS-1033-P001 General Physics Laboratory 22 January 2024
Abstract In this experiment, the main goal was to be able to successfully add vectors, graphically, analytically, and experimentally. Although not in person for this lab, the goal for this lab was achieved at home, with the use of a protractor and a ruler to correctly display the vectors. Theory Give me the background to understand the results. Remember your lab on vectors. You went over Analytical and Graphical methods of adding vectors. What are these and how are they done? This is pretty much a condense and summarized version of the theory section of your lab manual Vectors can be defined as a quantity that obtains both magnitude and direction, but is more formally, a useful description for things such as acceleration, velocity, speed, etc. The use of graphically adding when talking about vectors allows for the visualization of the direction and allows for a comfortable understanding of direction. Adding graphically as the first step is essential to grasp an understanding of the concept, and also a way to double-check as you go. Adding vectors analytically involves the use of trigonometric functions to evaluate and determine the resultant. To add vectors, we take A, the magnitude of the vector, and plug it into the following equation: A x = Acos ( θ ) A y = Asin ( θ )
Where θ (theta) is the angle the vector creates. We then would repeat the same steps with vector B. B x = B cos ( θ ) B y = B sin ( θ ) After achieving the values for both A and B, and so on dependent on the amount of vectors given, the results from all equations are plugged into the following equation to solve for R, the resultant of the two vectors. R x = A x + B x R y = A y + B y R = ¿¿ tan 1 ( R y R x ) Where tan 1 is the tangent inverse of R y R x . Results Table 1 - Graphical, Analytical, and Experimental Addition Data
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Graphical Analytical Experimental Vector addition 1 75° R = 2.8 N 74.9° R = 2.8 N 255° 250 g Vector addition 2 49° R = 2.8 N 45° R = 3.0 N 225° R = 300 g Vector addition 3 173° R = 1 N 163° R = 1.3 N 340° R = 150 g Discussion 1. What possible sources of error can you identify for the graphical method of vector addition? A few possible sources of error for the graphical method are incorrectly using the protractor, and or not going back to check your work. 2. What possible sources of error can you identify for the analytical method of vector addition? Some sources of error for the analytical method can include not double-checking your work, or incorrectly plugging in values. 3. What possible sources of error can you identify for the experimental method of vector addition?
A few sources of error for the experimental method would be not placing the weights in the right position, and or not following the experimental procedure plan. 4. Of the graphical and analytic methods, which one do you consider to be more accurate? Why? I would say the analytical method is definitely more accurate, because human error can easily come into play with using the graphical method, while there is shown work to always look back on using the analytical method. 5. Why is it not possible to experimentally determine the resultant vector directly from the force table? It is impossible to determine results from the force table alone, because you would be unsure of the amount of weight to add as well as the angle calculated. Conclusion Overall, I would say that the methods were quite accurate when it comes to experimental error. After completing a full data analysis, and going back to look over my work, the data lines up to where it is needed every time. Although my graphs aren’t completely accurate, given human error, everything amounted to about where they needed to be.