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14:125:308:
Introduction to Biomechanics
Spring 2007
Homework Assignment #2
Due 2/06/07
Problem 1: (Center of Gravity and Coordinate Transform)
NOTE:This is an old exam question
You are preparing to run some tests on cadaveric femur bones with a stainless steel bone plate
attached, and you need to find the center of mass of the bone plate/bone composite in the xy
plane.
If you assume that the bone can be approximated as a small, hollow ellipse
(representing the medullary canal) and a bigger ellipse (representing cortical bone), and that the
bone and plate are uniform and identical in thickness into the page, and you are given the
information below, find
:
A) the center of mass of bone plate/bone composite
in the original (unprimed)
coordinate frame
AND
B) the location of the center of mass in the translated, rotated, primed frame, where
the origin is (7,2.5) relative to original frame and rotated as indicated.
.
Some useful information
Bone density: 1.3 g/cm
3
Marrow density: 0 g/cm
3
(the marrow is removed prior to testing)
Stainless steel density: 7.5 g/cm3
Area of outer ellipse: 8.0 cm2
Area of inner ellipse: 1.6 cm2
Area of bone plate:
0.9 cm2
Center of outer ellipse (cm) (x,y):
(0,0)
Center of inner ellipse (cm) (x,y):
(0.2, 0.4)
Center of bone plate (cm) (x,y):
(1.6, 0)
Note: Schematic not to scale
x
y
x'
y'
40
°
(7cm,2.5cm)
x
y
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View Full Document 14:125:308:
Introduction to Biomechanics
Spring 2007
Homework Assignment #2
Due 2/06/07
A) In order to find the center of mass of the bone plate/bone system we need to find the center of mass of
the bone (The center of mass of the plate is given).
We first have to Mass of the bone
( ) ( )
kg
t
t
cm
cm
t
cm
g
A
A
t
M
e
innerelips
e
outerelips
bone
bone
32
.
8
4
.
6
3
.
1
6
.
1
0
.
8
/
3
.
1
2
2
3
=
⋅
⋅
=
−
⋅
⋅
=
−
⋅
⋅
=
ρ
Now the COM of the bone is
( )
( )
()
cm
COM
cm
t
t
M
A
Y
A
Y
t
Y
cm
t
t
M
A
X
A
X
t
X
bone
bone
relipse
Centerinne
relipse
Centerinne
relipse
Centeroute
relipse
Centeroute
bone
COMbone
bone
relipse
Centerinne
relipse
Centerinne
relipse
Centeroute
relipse
Centeroute
bone
COMbone
)
10
.
0
,
05
.
0
(
10
.
0
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This note was uploaded on 01/31/2012 for the course BIOMEDICAL 208 taught by Professor Zhann during the Spring '11 term at Rutgers.
 Spring '11
 Zhann

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