Lab 4

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School

Arizona State University *

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112

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Mechanical Engineering

Date

Dec 6, 2023

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pdf

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Uploaded by karen4546

Lab 4: Vector Addition 1. Testable Question: ➢ Can following a series of vector-based directions lead to a comparable value for total displacement, instead of a direct route from the initial position to the endpoint? ➢ How do the individual 2-dimensional displacement vectors relate to their resultant vector? 2. Hypothesis: Following vector-based directions and then adding them will create a summation comparable to a direct route from start point to endpoint. Because vector addition utilizing both magnitude and direction will produce a displacement value equal to a direct line between the end and starting points. 3. Variables: Controls: Initial and end points, Lopes Migration Route 3, Elevation Independent: Displacement Dependent: Position 4. Table Design: Control: Lopes Migration Route 3, elevation 1,086’ i r(m) 𝜃 (deg) x:(m) y:(m) 1-6 R 1-6 𝜃 1-6 R 1x-6x R 1y-6y 5. Materials: ● Grand Canyon University Map (Lopes Migration Route 3) ● Compass ● Mobile App based distance tracker (Health app) 6. Procedures: The procedure will vary based on which Lopes Migration Route is taken. For the purposes of this report, route 3 was observed. 1. Ready a compass and method for tracking position and distance such as a mobile app-based service. 2. Proceed to the starting point and angle towards the next point using compass and angle as directed by LMR3. 3. Walk set distance to next point, record position. 4. Repeat steps 2 and 3 for each next point, adjusting angle and distance walked as directed by LMR3 5. Record final position. 6. Calculate displacement between initial point and endpoint via vector addition and compare to direct displacement.

7. Data: i Ri (m) θi (deg) Rx(m) Ry(m) 1 293 334 -128.37 263.20 2 293 29 139.94 252.46 3 257 168 53.19 250.24 4 253 137 172.28 184.75 5 198 101 194.15 37.74 6 137 227 - 99.90 -93.16 Rx: 331.29 Ry:895.23 8. Analysis: After adding all individual vectors, the resultant vector is 954.56 meters. When comparing the calculated resultant vector to the measured resultant vector of 895.23 meters, the percent difference between the two 6.2%.

9. Conclusion: The resultant vector is directly dependent on the length and direction of each of the individual vectors, no matter what order they were added in. If the length or the direction of one of the vectors were to change then both the length and the direction of the resultant vector would change as well. 10. Evaluation: After the completion of this experiment the hypothesis of whether the resultant vector can be obtained through vector addition was supported. Vector addition only relies on knowing both the length and magnitude of each vector to be added, information already given to us at the start of the lab. While vector addition proved to be a simple calculation, walking the distance and rotating to the proper angle was a bit more challenging. This difficulty resulted in a percent difference of 6.2%. This may have resulted from the transition between the pacer’s steps and the actual distance covered or the method used to adjust whenever an obstacle was encountered. Some random errors that may have affected the precision of the lab could have been the obstacles in the way which prevented us from walking at the perfect angle because we couldn’t go through them. To improve the quality of the results a better method of measure both distance and direction would need to be used, instead of relying on the pace of an individual or if they may be obstacles in the way.

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