MAE 241 Hands on Project #2 (01)

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West Virginia University *

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Aerospace Engineering

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Oct 30, 2023

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Original by Eric Davishahl WVU MAE 241 Statics Hands-on Project #2 Due by 11:59 pm on Monday, September 18, 2023 Statics Modeling Kit Worksheet 2.1 3D Concurrent Force System Acknowledgement This material is based upon work supported by the National Science Foundation under grant numbers DUE #1834425 and DUE #1834417. Any opinions, findings, and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the views of the NSF. This project has been modified from the original NSF work. Purpose The purpose of this activity is to practice using position vectors and 3D unit vectors for equilibrium analysis of a 3D concurrent force system. You will also practice using your calculator, or other programs, to solve the resulting linear system of equations. Learning Goals  Draw neat free-body diagrams for particle equilibrium problems.  Determine the direction and sense of tension forces in ropes and cables from given geometry information on a problem figure.  Apply the equations of equilibrium to solve particle equilibrium problems in 2D and 3D.  Solve linear systems of three equations that arise from 3D particle equilibrium problems.  Design cable support systems to hold an object in a specified position and/or orientation. Supplies 3D coordinate system model 3D printed box of statics knowledge Cord (3 lengths) Masking tape for 1 inch unit vector and a marker to draw and direction arrow Cord locks Metal ring Ruler Problem Statement The box of statics knowledge block is suspended by three cables that connect points A , B, and C to the ring at point D as shown. Points B and C lie in the xy plane. Point A is on the yz plane. In this activity we will explore how the tensions in the three cables relate to the geometry of the system.

Original by Eric Davishahl Instructions Use your modeling kit to complete the tasks below. Terms in bold represent important vocabulary that you should work to understand during this activity. It is expected that you will have to do analytical work on paper to support your provided answers. You may use this assignment to record and calculate the required information or you may use a separate sheet of paper. For your group submission, an Excel spreadsheet is used to report your solution. Please transfer the data collected and analyzed to this Excel document. Only one member of the team is to submit the Excel file. A survey is to be completed individually by each group member. Submission details are provided below. Tasks Part 1: Group Information 1. Enter your team ID and exchange your names and any contact information . Identify the team leader who will upload the final documents. Team ID: Names: Part 2: System Layout 2. Review the layout of your system . Collect data needed to analyze the system. Provide the fixture ID of the system and the block weight: Fixture ID: Block Weight: Using the supplied ruler, measure the location of each attachment point of the cables to the block and to the walls. Note that the origin needs to be defined. It is suggested to use the point where the three plans intersect. Keep as many significant digits in your calculation as possible but report your answer to four significant digits. Enter the point coordinates of your system using the inch scale in the table below: x A = ¿ y A = ¿ z A = ¿ x B = ¿ y B = ¿ z B = ¿ x C = ¿ y C = ¿ z C = ¿ x D = ¿ y D = ¿ z D = ¿ Part 3: Equilibrium Analysis

Original by Eric Davishahl The goal of this analysis is to determine the tension forces in all three cables. 3. Place a unit vector using masking tape (cut to 1 inch) on the three cords to indicate the direction in which the tension force in each cord acts on the ring. Write the unit vector name on the tape. 4. Next complete the free-body diagram of the ring and box assembly. Be sure to label all forces and include a coordinate system. We could determine the coordinate direction angles of each force vector and add these to the FBD analogous to how we add angles in 2-D, but we won’t. It is easier to work with unit vectors to represent the force directions in 3D equilibrium analysis. 5. Compute the unit vectors ^ u DA , ^ u DB and ^ u DC . Keep as many significant digits in your calculation as possible but report your answer to four significant digits for each unit vector component. Be sure the sense of each (indicated here by the subscript order) represents the sense of the force acting on D and matches the unit vector on the model. ^ u DA = ¿ ^ u DB = ¿ ^ u DC = ¿ 6. The vector form of the equilibrium equation for the FBD you drew above is:

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