4 cos. Intermediate exam: Mechanics for MWT: 8TB00. February 25, 2014, 13:45-14:30. Code 8TB00, MWT bachelor. Biomedical Engineering

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1 Intermediate exam: Mechanics for MWT: 8TB00 February 5, 04, 3:45-4:30 Code 8TB00, MWT bachelor Biomedical Engineering Eindhoven University of Technology This is a closed book exam. The use of a laptop and/or electronic calculator is not allowed. This exam consist of 7 questions. The total score that can be obtained is 00 points, and the number of points per question is indicated. Each question has only one correct answer. Please encircle the correct answer on the answer sheet in a clear way. Question (0 points): The basis {e x,e y,e z} is right handed and orthonormal. Consider the vectors a 3e x 4e and y b 3e 4e. Which of the following statements is correct? y a) ab 5 z b) ab 6e e 9e x y z c) for the smallest angle between both vectors it holds that d) ab 9e e 6e e x y y z 4 cos 5 Question (0 points): The vectors a and b have a non-zero length and their directions do not coincide. A new basis is defined using vectors { abc,,}. Which of the following operations would produce a vector c that is usable for this new basis? a) ab b) a b c) a b d) ab

2 Question 3 (0 points) The basis {e x,e y,e z} is right handed and orthonormal. Relative to this basis, two matrices and a column are defined: cos sin 0 cos sin 0 A sin cos 0 ; B sin cos 0 ; c Which of the following statements is correct? a) B A b) B A T c) d) cos sin T c A sin cos cos sin Ac sin cos

3 Question 4 (0 points) A speed skater is holding his right leg in the position as shown in the picture. To investigate the forces and moments working on and in the right leg in this position, a simplified model is made. In this model the force acting on the ankle is indicated by F A, the weight of the lower leg by F L and the weight of the upper leg by F U. It can be assumed that these forces act halfway the length of the upper and lower leg and that no moments act at the ankle. Forces due to movement and inertia can be ignored. Using the model, the moment working in the knee M K and the moment working in the hip M H is calculated. Which of the following statements is correct? a) M K MH lf U b) M K c) M H d) M H lf U lf 0 U lf H lf L

4 Question 5 (0 points) A man is preventing an oil drum with weight F G and diameter D from running down a slope (angle ) by pulling a rope that is rolled around the drum. The man is pulling with a force of magnitude F T. It can be assumed thatt there is no slip between the drum and the slope and that the rope runs parallel to the slope. A free body diagram of the drum is shown next to the figure below. In this diagram the x- direction is chosen parallel to the slope and the y-direction normal to the slope. Which of the following is correct? a) FT c) FT DFG d) FT F G b) FT F sin G sin F tan G

5 Question 6 (0 points) A bar with length l is loaded by a force F B at B and by a force F C halfway its length at C (seee figure a). The direction of the forces is indicated in the figure. It is known that F B =0 [N] and F C =30 [N]. To determine the forces and moments within the bar, a virtual cut is made and internal forces and moments are introduces as indicated in figure b). The internal normal force N as a function of the distance from A is described by: a) b) x x c) 40 0 x d) 0 0 x

6 Question 7 (0 points) The movement of body segment with mass m length l and moment of inertia I is tracked by a camera system to measure its angular acceleration and its center of rotation. During an exercise, the center of rotation was found to be at point C at /3 off its length while the angular acceleration was. Based on this information the moment M needed for this angular acceleration was calculated. A C B Which of the following calculations is correct? a) 4 M ml I b) M I c) M 4 ml d) 36 M ml I

7 Formuleblad behorende bij het vak mechanica voor MWT 8TB00 Vector rekenen Inproduct (inner product): ab. a b cos Uitproduct (vector product): c ab ; c a b sin Tripelproduct (triple product): a b c a b c Dyadisch product (dyadic product): ab p a b p Bewerkingen waarbij een vectorbasis wordt gebruikt: vector notatie Inproduct (inner product): ab a b a b a b x x y y z z Uitproduct (vector product) ab ab ab e ab ab e ab ab e y z z y x z x x z y x y y x z Dyadisch product (dyadic product): ab axbxexe x+axbyexey axbzexez abee y x y x abee y y y y+abee y z y z abee abee abee z x z x z y z y z z z z Bewerkingen waarbij een vectorbasis wordt gebruikt: kolom notatie Inproduct (inner product): T abab x x ab y y ab z z Uitproduct (vector product) ab y z ab z y ab azbx axbz ab x y ab y x Dyadisch product (dyadic product): ab x x ab x y ab x z T ab ab y x ab y y ab y z ab z x ab z y ab z z

8 Matrix operaties Ab c AB C Ia a en: IA AI A A A I Krachten en momenten De component F t van een kracht F in de richting van een eenheidsvector e wordt gegeven door: F Fe e t Moment bepalen t.o.v. punt P, terwijl kracht F aangrijpt in Q: M x x F Q P Evenwicht (equilibrium) F 0 M 0 Beweging en massatraagheid (movement and inertia) Kracht voor het versnellen van een massa: F ma Moment voor een hoekversnelling (angular acceleration) van een puntmassa op afstand R: M mr Moment voor een hoekversnelling (angular acceleration) van een object rond zijn as: M I

9 Antwoordblad tussentoets Mechanica voor MWT: 8TB00 5 februari 04 3:45-4:30 Achternaam en voorletters: Identiteit nummer: Opleiding: Omcirkel op dit blad de juiste antwoorden. Er is maar één juist antwoord per vraag. Als je een correctie wilt maken, schrijf dan naast de vraag het juiste antwoord ) a b c d ) a b c d 3) a b c d 4) a b c d 5) a b c d 6) a b c d 7) a b c d

10 Answers: ) b ) b 3) a 4) c 5) b 6) d 7) d