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A right angle pipe OAB is shown in Figure 1. Replace the 750-N tensile force, which the cable exerts on point B by a force-couple system at point O. Figure 1 STEPS: 1) Calculate the unit vector nBC and the resulting tension vector TBC. 2) Calculate the unit vector nAC and the magnitude of the TBC along line OC. LEARNING OUTCOMES: 1) Calculate a unit vector, given two (x,y,z) coordinates (3-D). 2) Calculate a force vector in the direction of a specific unit vector (3-D). 3) Calculate the magnitude of a force vector along a given direction (3-D). COMMENTS: 1) Difficulty Level: 9/10. Part 1 Enter the coordinates of points A, B, and C and the tension magnitude in Figure 2. (X,Y,Z) (m) O (0, 0, 0) j B (1.6, -0.4, 0.7) C (0, 0.7, 1.2) i k ROC nOC O TBC = 750 N nB C Figure 2 Note to programmers: Points O and C are exact. Point B must be to one decimal point. Part 2 The displacement vector in the direction of the tension TBC (RBC) is: R BC -1.6 i + 1.1 j + 0.5 k (m) Note to programmers: Numerical entries must be to one decimal point.. Part 3 The magnitude of the RCB is: R BC 4 =2(m) Note to programmers: Numerical entries must be integers. Part 4 So the unit vector in the direction of the tension T is: 1 n AB 1.6 i - 1.1 j - 0.5 k (m) 2 Note to programmers: Numerical entry must be an integer. Part 5 Therefore, the tension vector TBC is: 1 TBC 750 -1.6 i + 1.1 j + 0.5 k (N m) 2 Note to programmers: Numerical entry must be exact. Part 6 So, the tension vector TBC is: TBC -600.0 i + 412.5 j 187.5 k (N) Note to programmers: Numerical entries must to 1 decimal place. Part 7 In order to calculate the couple at point O, we must define a vector from point O to a point on the force (any displacement vector from O to the force will work). The most convenient point is point C, because the mathematics is relatively simple. With this in mind, the displacement vector from point O to C (ROC) is: R OC 0 i + 0.7 j + 1.2 k (m) Note to programmers: Numerical entries must be exact. Part 8 In order to shift the tension TCB to point O, we must include a couple. The couple (or, in general, the moment) at point O (MO) is the ROC X TCB, which is: M O = R OC X TCB 0 i + 0.7 j + 1.2 k X -600.0 i + 412.5 j 187.5 k (Nm) Tutorial: How to perform a 3-D Cross-Product (http://www.randjanimations.com/Wiley_Flash_Development/meriam_voiceovers/statics/T 16_3d_cross_product/T16_3d_cross_product.html) Note to programmers: Numerical entries must be to 1 decimal point Part 9 By performing the calculations of the cross-product, MO becomes: MO = ROC X TCB -626.3 i + -720.0 j + 420.0 k (Nm) Note to programmers: Numerical entries must be to 1 decimal point Part 10 So the magnitude of MO is MO = (-626.3)2 + -720.0 + 420.0 = 1042.0 (Nm) 2 2 Note to programmers: Numerical entries must be to 1 decimal point Part 11 And finally, the statically equivalent force-couple system is: TO = 750 N j MO = 1042.0 Nm i k O Figure 3 Note to programmers: Variable TO is an integer and MO must be accurate to 1 decimal point. Notes to programmers Font Coding: 1) Blue underline indicates an INPUT box. 2) Red indicates notes. 3) Black indicates static text.

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posted: | 12/19/2011 |

language: | English |

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