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Physics 125
Discussion #20 Solution
1
Problem 1: Stress on the Shin Bone
Compressive strength of our bones is important in everyday life. Young’s modulus for
bone is about 1.4×10
10
N/m
2
. Bone can take only about a 1.0% change in its length before
fracturing. What is the maximum force that can be applied to a bone whose minimum
crosssection area is 3.0 cm
2
? (This is approximately the crosssection area of a tibia, or
shin bone, at its narrowest point.)
N
10
2
.
4
)
01
.
0
)(
m
10
)(3.0
N/m
10
4
.
1
(
4
2
4

2
10
max
0
max
×
=
×
×
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ Δ
=
L
L
YA
F
Problem 2: Hooke’s Law and Young’s Modulus
Hooke’s law for a tensile stress can be written as
F
x
=kx
, where
x
is the object’s change in
length, and
k
is the force constant.
1.
Write the force constant,
k
, in terms of the rod’s original length,
L
0
, crosssection
area,
A
, and the Young’s modulus, Y.
0
0
0
L
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