Exam 1-solution_Feb2018.pdf

Exam 1-solution_Feb2018.pdf - Exam I Name Master Solution...

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Unformatted text preview: Exam I Name: Master Solution 1282308 Introduction to Biomechanics Spring 2018 #1a A person is resting on a board which is supported by a scale (5) and a fulcrum (F). The person is 5.5 feet tall (W2150lb) and the board is 6 feet long (B =10lb). The combined weight of the patient and board is supported by a scale (which reads S=30|b), and a force at the fulcrum. The distances from the fulcrum to the scale S is 10" xs=40”and to the board's center of , gravity is xb=10”. i———77 40" 1 Answer the following: - Sketch the free body diagram of the patient and board. - Derive an expression for xc, the distance of the person's center of gravity from the fulcrum, in terms of B, S, W, xb, and xs. 0 Compute xc, the distance from the fulcrum to the person's center of gravity 15 points S=30|b. F=??Ib. Z? :20 "37 :: (30nd 2: 1V} :0 (”B-M0) +(bJextz) —~ ($140) :0 2 -Q1“3 4 g 2: € .- 0 'l’ 0 A xx: '2 ./__,_%O'"’ (-0 ii :— ”w 1-7553 1 {S‘b Exam l Name: 1282308 introduction to Biomechanics Spring 2018 #1b The femoral neck is modeled as a combination of cylinder and hemisphere as shown below. Given that the volume for a semi—sphere = 21Tr3f3 and centroid Z with respect to base of hemisphere is 3rl’8 If h = 6 cm and r = 3 cm, calculate the following c Total votume, V of the femoral neck . Total first moment Q. . The centroid w.r.t. cylinder base. Show all calculations and include appropriate units. 15points ,omL le‘ufité «.— 31;: #F max, (ogfi>(9l) A C5>97 1(6) (3 2 an,“ a fitzfl+€la)e72“ ‘ 7") 8),: 5% (r (9m. (1" 7% U ' 2h A. V‘: C C h. ""9010 41/12 (5 *3» g ~rC 31" ref / jig—3K a y 3 "r 4 2r 4&3“:ng ’: 7"“ CK) ( “é” +6) Cl- J‘l Pr go'fl j : ' r: 4021' fin.g f— 4(3Q’fl” Coordinate Transformations 0 Rotation of base vectors (general) x ... 0036 --sin6 x’ y n sing c059 y' x 8036 sine).- . “sing cost? ? [If] w[cos(x',x) cos(x'fiy) _ x M cos(y’,X) 008(k)») - y 00505:, x) cos(x', y) cos(x':, z) x WSW: x) 0030”, y) 0050’: Z) I y 005(2'} x) 005(2', y) 003(2’, 2:) 2 H Where cos(a, b) is the cos of the angle between the 'a‘ and 't)‘: axes. Exam | Name: Master Solution 1281308 Introduction to Biomechanics Spring 2018 #2 Gait data is captured in camera system as shown. The knee joint is shown-as (0, 0) in local axis (x‘. y') along the longitudinal axis of the tibia. ... x’ The position of end of the foot (the star) is given by Them: 3mg (-60, -215) in the local frame (x’, y’) coordinate system. We would like to get this data in term of inertial coordinate (x, y) system which is located at (-720, -150) as shown in the diagram. («no-150) \ (ed-215) / X Find the location of the foot in (x, y) system. 20 points Pm, = PX. — (0x — 0x‘) = —60 — (— 720 — 0) = —60 + 720 = 660 PM... = P,. —(0y—0y')= —215—(—150~0)= 4154.150 = "65 Px _ cost? —sin6 Pm,“ _ cos(x,x') cos(x,y') Pm,” _ (30330 005120 660 _ 0.867 —0.5 660 _ 604 P. ' Sim? (3036 PM, _ cos(y,x') cos(y,y') PM, ' 00560 00530 —65 “ 0.5 0.867 —65 _ 273 Exam i Name: Master Solution 128308 introduction to Biomechanics Spring 2018 #3 The goal is to quantify the muscle and joint efforts in weight lifting as shown below. it is assumed that torso is resting on the table and the table is providing support against the weight that is lifted. Here are details on anatomy: a) Arm is '40 cm at 30 degrees to X—axis, forearm is 30 cm at 120 degrees to X—axis, b) The pectoraiis major muscle attaches 5 cm from the glenohumeral joint and it is 30 degrees to arm (or parallel to X—axis) c) Triceps' Is attached 1. 5 cm along the ulnar bone from the humeraulnar joint and it is attached on the upper arm at 1. 5 cm from the glenohumeral joint d) ignore the weight of the upper arm and forearm. The person is lifting a total of 600 N weight as shown below. 1. Assume that the pectoralis major muscle is the only muscle supporting the upper arm. Draw a FBD of the upper and lower arm together to determine the magnitude of the pectoralis major muscle force and the joint reactions at the shouider. 2. Draw a FBD of the forearm only including all musCle forces and joint reactions; do not -‘ calculate 30 points fly so Cosfil % | 4D C0580} Exam I 128308 Introduction to Biomechanics Name: Master Solution Spring 2018 Exam i Name: 128:308 Introduction to Biomechanics 4. Circle the correct answer. 1. 2. The stress is measured as 100 Nlmmz. This is same as a. 1 GPA b. 100 KPa c. 100 MPa d. 100 N In coordinate transfer, you do this first a. Translate first b. Rotate first c. Both translate & rotate together d. None of the above The first area moment (in = lsz; the unit of (boy is mm mm2 mm3 mm“ anew In elbow joint, biceps are a. Flexor, has long head and short head b. crosses shouider and eibow joint c. both (a) and (b) d. None of the above Two dimensional Forearm free body diagram includes joint reactions and bicep muscle force. Given the external loads, 3. Muscle force can be oalcuiated b. Joint reactions can be calculated c. Both (a) and (b) d. Neither (a) nor (b) Master Solution Spring 2018 (20 Points) 6. in gait analysis, we like to capture fiexion—extension of hip, knee and ankle joints. Therefore, motion in following plane must be recorded. Coronal of frontal plane Sagittal plane Transverse ”of horizontal plane Cardinal plane Fit-9.5”?“ With respect to arm, hand is a. Medial to arm 13. Anterior to arm c. Posterior to arm d. None of the above Diarthrosis or freely movable joint, bones are a. Coated with articular cartilage, b. Enclosed in capsular ligament c. Lined by a synovial membrane d. All of the above 9 None of the above 9. Flexion of shoulder is provided by a. Peotoralis major b. Biceps brachia c. Anterior fiber of deltoid d. Posterior fibers of deltoid e. All of the above f. Not an accurate list 10. The elbow joint actually is a. Humeroulnarjoint b. Humeroradial joint 0. Proximal radioulnar joint (1. All of the above ...
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