Biomedical Engineering Reference
In-Depth Information
forces increase to
W
sin 40
¼
0.64
W
, which can be the cause of back pain. It is
known that a disc is much less resistant to shear stress than to compressive stress.
Hence, among the exercises to alleviate low back pain should be one to decrease the
lumbosacral angle.
7.9 Bone Fractures in Collisions
When somebody falls from a springboard into the water, or when he or she collides
with a glass door or into something accidentally, what are the types of force subject
on them? To respond to this question, let us begin by analyzing the equations that
govern the movement of accelerated or decelerated bodies. We will verify that the
crucial quantity for this question is the duration of the collision.
An object falling freely, that is, simply dropped from rest at a certain height, falls
under the action of gravitational acceleration. The distance
H
traveled by a body in
free fall during an interval of time
t
can be written as:
1
2
gt
2
H
¼
:
(7.6)
As already used
,g
is the acceleration due to gravity. We say that this body
undergoes a uniform accelerated motion
3
and the distance traveled increases with
the square of the time interval because its velocity increases with time. As the object
was released from rest, its initial velocity was equal to zero and the final velocity
can be calculated from:
v
¼
gt
;
(7.7)
meaning that the velocity increases proportionally with time. Substituting
t
of (
7.6
)
into (
7.7
), the final velocity is obtained:
p
2
gH
v
2
¼
2
gH
;
v
¼
:
(7.8)
Note that the final velocity does not depend on the mass of the object, i.e., it will
be the same for a piece of paper or a heavy lead ball, if the force of the air resistance
during its fall is neglected.
3
This is valid if the altitude is not very high, which will be the case here considered. Otherwise, the
resistance to the motion by the air increases with the velocity, so that for any falling body there is a
limiting velocity for which there is no longer any net acceleration and the velocity ceases to
increase, becoming constant.
