Lab Report 2 PDF

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Lab Report 2...

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A’Ishah Trahan Lab Partners: Tommi McNamee and Jasmin Francis Experiment: Adding and Resolving Vectors—Determining the equilibrium force February 6, 2019 Section 008

Purpose: The purpose of this experiment was to compare two of the several methods for determining vectors to find the resultant to test which method was more accurate. Graphically is method one, and analytically is method two.

Theory:       

Vectors are a type of physical property that take direction into consideration. The resultant is known as the sum of the vectors; however, all of the vectors cannot be added up to calculate it. To find the resultant graphically, you graph the vectors on graph paper and connect the initial point to the final point. To find the resultant analytically, you resolve each vector into its x and y components and add the sums of each up. Equilibrium is when the net force is equal to zero newtons. Equilibrium force counter balances the other forces present and is found after the resultant. Equilibrium vector is a vector that is exactly 180 degrees from the original vector.

*X-Component

*Y-Component

*Percent Error

*Newton’s Second Law

*Conversion of kg to g

*Calculating the Resultant

*Calculating the Angle of the Resultant

Procedure: Part I 1. The given vectors were drawn on a piece of graph paper using a pencil, ruler, and protractor, and the x and y components were predicted based on the resulting drawing. (Graphically) 2. The same steps and supplies were followed to draw the equilibrium vector, and the x and y components were calculated using the sine and cosine functions. (Analytically) 3. A percent error analysis was performed using the equation for percent error. 4. An apparatus was then used to test the equilibrium. Apparatus Set-Up 1. Position and clamp the strings of the apparatus into place at the appropriate angles of the vectors determined in part I. 2. Add the appropriate amount of weight to each string (include the weight stand in the total weight). 3. Remove the pin in the center to test equilibrium. (strings will remain around the center if in equilibrium). 4. In this part of the experiment, I attached the stands to the end of some of the strings and added the weights to them.

Part II

1. The three given vectors were drawn on a piece of graph paper, using a pencil, protractor, and ruler, where the resultant and equilibrium vector were predicted based on the resulting drawing. (Graphically) 2. The x and y components, resultant, and equilibrium vector were then calculated analytically and recorded using the sine and cosine functions. 3. The same apparatus used in part one was used to test the equilibrium for part two by using the calculated values for part II.

Conclusion: After performing the experiment, the conclusion was reached that using the analytical method to add and resolve vectors to determine equilibrium force, is more accurate than the graphical method, thus, supporting the theory that calculated values are more accurate than values collected graphically by hand. The inability to take completely accurate and precise measurements by drawing them out by hand was random error. When the apparatus was used to test the values calculated analytically for part one, the equilibrium was slightly off, resulting in 6 total grams of weight having to be added. The error could be attributed to the floor and apparatus being unlevel, the weights being worn from being used constantly, and the acceleration used to calculate the mass needed being 10 m/ss instead of 9.80 m/ss. It could also be due to systematic error because the apparatus itself may have contained inaccurate tick marks for measuring the angle, therefore causing all the calculated data to be slightly off when placed on it. For part two of the experiment, it was learned that it is very important to place the weight at the appropriate angle because if not, the vectors will not be in equilibrium, and the weights will fly off of the apparatus. Using the analytical method proved to be more accurate than the graphical method because the analytical method provided exact numbers and calculations, making it the generally accepted value in terms of percent error; whereas, the graphical method was just a prediction based off of a drawing and counting, leaving it open to more sources of error....