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Exam_3_S11_Solution

Exam_3_S11_Solution - Name ME 577 Exam 3 1 Suppose someone...

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Unformatted text preview: Name ME 577 - Exam 3 1. Suppose someone is in the weight room exercising. They’ve just finished the aerobic part of their workout and they have started strength training. Now assume that they are starting by doing some leg extensions. Effectively they are in a seated position, pushing up on a foam-covered bar while raising the legs. The knee joint is fixed and the bar always exerts a force normal to the lower leg. For this problem, assume that the tibia makes an angle of 45° with horizontal. (15 points]. First, draw a free body diagram of the lower leg (don't forget the coordinate system). W ' Wing? Describe any lengths or angles you need in variable form. ou hold your leg at 45°, rive an expression for the force developed in the muscles (you may assume smg e—fTe no moment model). You may treat the knee as a fixed point. Q ’ “1E2 Wkl’TUWW ‘ (wuw'c ) l’xr / x p \ ax WT and”; Ag 3“ AC4 .3 Y; 77 \ CV) Elm VT \ \ / M ~ / M9 XIX“; / £9 Z A; w J \. WK a \ Jr 3"“. ffi-Q wéfl v Mi? Slang 9 LVfl a) ~E5/ -— LSFM) r. O / M r (- L .3 L5 \\_fi_~’/ Sly/6 W / LP? ‘3'”9597 r W ‘9 '«X’l ~ muLnl’J ‘WW’O Name Lastly, assume the lower leg is moving and write out the position, velocity, and acceleration of the center of mass of the lower leg in terms of its length and rotation angle. You may assume that the lower leg's mass center is exactly halfway between its ends. How does the muscle force change (anthhe same position of the leg) if the rotation angle is dG/dt = 1.5 rad/s and‘tbfe d29/dt2 = 4 rad/5A2. l :5: zLéér l - Y9; ,2 ca qé : —"£L$9§r‘b Etsefa - T GD zM/L v "/LQ - i L (f / L 4: ': “ab S'fiDrrLP-rfivr 7 ‘vwsiv't‘fl ' 9 w '75 i “Mi: +21, be Name 2. Consider a static analysis of an adult picking up a 30 lbs. child and holding the child at arm’s length (approximately 2.5 ft. from the shoulder). Assuming the shoulder lines up with the vertical axis of the spine, and the distance from the vertebral body to the erector spinae muscle is 2 inches behind the spine, calculate the conlpreflve and shear loads on the spine as well as the nge erector spinae muscle for static conditions. Assume that the head and torso weight 40 lbs. (2 inches in front of the spine) and the two arms weight 10 lbs. (10 points). 1 5Cyl” {Dina/3V4? \ / 3M] ‘ \ 1 WWW 4):? I am 5?me w . . \ SC -_ < aux EWch 5““ l k \ W053 ‘/ ') 6PM l . We u \ W \l \ flitolfl’l i i l “ <1 i was} l SC $5 F a // / l7? E9 A \/ A I N’%' Wcfi 1‘ ( E9 Lawm ‘1 ?,‘5 ~.(:. V/M/ Z soils .w y / f “‘3 “Ac W 4% g‘ 372%? 1: : O , W comma W». - . :\ v S§ a ‘ 3 O E ' "$291. 49¢ —— (NHT-LW" \ wt )1 - ‘2 " - ' M 'v 0 i l / W66 1;, Q d F —— r) ommu‘rcl .— g/wavm We “W” ] EL) E8 I l W J- W 5 > claim {Mu—Ti + J’Mm D C) : {if /‘ €55 ; //—-w Name 3. How many cervical, thoracic, and lumbar vertebrae are there (2 points)? Q r r ‘. Us. WY: We» 5 ovug \ C t :17, \x 9 r W.) Luwvwr 3 g AH” (UQJA gwr L151. 0 L I 4,ch k r f » QM \QDW I 6‘54 KW) ‘ .: y \ ylhlklt ' Y I f ,w 3’ J "I quJerf-UN‘PXQI’M l Jc- 0‘. O gfa‘w\cw’\v a 5 5 - mt ‘ “9L " KOLQLC”) A!“ ‘r . . : SFIV‘DUL: ‘F 2 YR : w . ' \f\\/‘U:\vr:§—. 0 o ' $MN£JWQA~F>€ 0‘ \ {0‘7 " CAL) \J) W w ’ NQO " ' ‘ we . Name 4. Given that the kinetic energy of a particle, T, is émvo v, show that the time derivative of T is 2F 0 v (4 points). \ cy’f 3 ( \ _, m — ( r M U" ”* “ s—» 2 / w M: “q” — w, \rvmv'i .flmaau" w 2 we ”' W k I f b ~~~~~~~~~~~~~ ~ New”; 7 W“ W a9L7MVVQ ‘ d W649; J00“? mu < Name _ __ 5. During the pull stroke demonstrated below, determine whether each of the following joints flex or extend: knee, hips, elbows. Which muscle groups are responsible for each motion? (5 points) Knee {7A LQWQQAA :5"? GDLL axJJri "‘ a §‘ ' l _ . ‘ 4 {gm/0,: m g) Who/h (1 11(4) fiLQ/y c7 fill/oar? g f r e a ( http: / / www.crossfit.com / journal / library/ 50_06_Rowing_Technique.pdf Additional references at: http: / / www.culver.org / students / sports / crew/ rowingstroke.asp ...
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