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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
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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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- Fall '17
- Biceps brachii muscle, Glenohumeral joint, pectoralis major muscle, femoral neck, Master Solution