Biomedical Engineering Reference
In-Depth Information
v
is said to have a kinetic energy equal to one-half
m
×
v
×
v
(written as
m
∙
v
2
/2). Energy content reflects the ability to do work, defined as move-
ment of mass through distance. The total energy of a group of objects
is conserved if no external forces act on the objects; however, the total
kinetic energy is only conserved if
e
= 1 for all impacts. Impacts for
which
e
= 1 are called elastic and do not produce any lasting change of
shape in the objects involved. When
e
< 1, the impact is called inelastic;
some kinetic energy is converted to other forms (heat, sound, etc.) or
stored within the objects as a result of each impact, and these calcu-
lations become more difficult. As opposed to kinetic energy, which is
possessed by a body in motion, potential energy is possessed by a body
due to its position or state. For example, gravitational potential energy
is energy due to its elevation relative to a lower elevation. This can be
calculated by
m
×
g
×
h
(written as
m
∙
g
∙
h
), where
g
is acceleration due
to gravity and
h
is the height/position of the object. Potential energy can
be converted into kinetic energy, but unlike kinetic energy, it cannot be
transferred directly from one object to another.
Therefore, we may understand the ability of materials to bear and dis-
tribute forces by considering them in a static way, introducing additional
forces that arise from changes in velocity or position.
additional problems
PROBLEM 1.6
In Figure 1.11a, suppose t
ha
t forces
A
,
C
, and
J
act at a p
oi
nt
P
. Find the
resultant of these forces
(
R
and the vertical component
R
v
.
ANSWER:
G
raphic.
See Figure 1.11b. The line of action of
R
is shown,
R
= 210 N.
R
is also shown;
R
v
= 110 N.
Numeric.
The simplest way is to resolve the three forces into verti-
cal and horizontal components, since
R
v
will then equal the sum of the
vertical components.
(a)
(b)
J
A
R
R
v
J
C
γ
A
β
1 cm = 50 N
C
α
FIGUre 1.11
resultant force (Problem 1.6).
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