BiomExtraExcer

BiomExtraExcer - Biomechanics Concepts and Computation...

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Unformatted text preview: Biomechanics Concepts and Computation Extra exercises and Answers Version 1.4 Cees Oomens September 2010 Eindhoven University of Technology Department of Biomedical Engineering Tissue Biomechanics & Engineering Contents 1 Extra exercises of chapter 1 page 1 2 Extra exercises of chapter 2 3 3 Extra exercises of chapter 3 4 4 Extra exercises of chapter 4 8 5 Extra exercises of chapter 5 9 6 Extra exercises of chapter 6 22 7 Extra exercises of chapter 7 25 8 Extra exercises of chapter 8 32 9 Extra exercises of chapter 9 39 10 Extra exercises of chapter 10 45 11 Extra exercises of chapter 11 54 12 Extra exercises of chapter 12 57 13 Extra exercises of chapter 13 61 14 Extra exercises of chapter 14 63 15 Extra exercises of chapter 15 66 16 Extra exercises of chapter 16 69 17 Extra exercises of chapter 17 74 18 Extra exercises of chapter 18 77 ii 1 Extra exercises of chapter 1 1.1 Exercises 1 .1 Consider a Cartesian xyz-coordinate system, specified with the or- thonormal basis vectors { vectore x ,vectore y ,vectore z } . (a) Within this system a plane is spanned by the vectors vectora and vector b , spec- ified by: vectora = 16 vectore y − 15 vectore x vector b = 20 vectore z − 15 vectore x Determine the unit normal to this plane (vector with length 1 per- pendicular to the plane). Why is the solution not unique? (b) In addition the following vectors vector b , vector c en vector d are defined: vector b = 3 vectore x + 2 vectore y vector c = 5 vectore x − vectore z vector d = vectore x + vectore z Express ( vector bvector c ) · vector d in the basis vectors { vectore x ,vectore y ,vectore z } , where ( vector bvector c ) is the dyadic product of the vectors vector b and vector c . 1 2 Extra exercises of chapter 1 1.2 Answers 1 .1(a) vectorn = ± (0 . 64 vectore x + 0 . 6 vectore y + 0 . 48 vectore z ) The solution is not unique; the normal can be oriented in two op- posite directions. (b) ( vector bvector c ) · vector d = 12 vectore x + 8 vectore y 2 Extra exercises of chapter 2 3 3 Extra exercises of chapter 3 3.1 Exercises 3 .1 A board with length 6 a is fixed to the wall in point A with a hinge. The board is able to rotate freely around the joint. In a point B at a distance 3 a of A, the board is kept in horizontal position by means of a cable, tied to the board in B and fixed to the rigid wall in point C. The mass of the board is M P (see figure). Cable and board can be assumed to be rigid (undeformable) structures. A box, with length 2 a and mass M K is placed on the board. The front of the box is exactly placed at the front edge of the board. The gravitation acceleration is g . 3a 2a 4a A B C a Fig. 3.1. (a) Draw a free body diagram of the construction to enable the calcu- lation of the reaction forces in points A and C....
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BiomExtraExcer - Biomechanics Concepts and Computation...

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