Biomedical Engineering Reference
In-Depth Information
0, the potential energy decreases to zero. However, the ground
reference datum should be carefully chosen to fit the problem in question.
Normally, it is considered to be the lowest point that the body takes during
the given movement. For a diver, it could be the water level; for a person
walking, it would be the lowest point in the pathway.
2. Kinetic Energy . There are two forms of kinetic energy (KE), that due
to translational velocity and that due to rotational velocity,
With h =
1 / 2 mv 2
translational KE
=
J
(6.15)
where v
=
velocity of center of mass, m/s
1 / 2 2
rotational KE
=
J
(6.16)
where I = rotational moment of inertia, kg · m 2
ω = rotational velocity of segment, rad/s
Note that these two energies increase as the velocity squared. The polarity
of direction of the velocity is unimportant because velocity squared is always
positive. The lowest level of kinetic energy is therefore zero when a body is
at rest.
3. Total Energy and Exchange within a Segment . As mentioned previously,
the energy of a body exists in three forms so that the total energy of a
body is
E s =
+
+
PE
translational KE
rotational KE
(6.17)
1
1
2 mv 2
2 I ω 2
= mgh +
+
J
It is possible for a body to exchange energy within itself and still maintain
a constant total energy.
Example 6.3. Suppose that the baseball in Example 6.1 is thrown vertically.
Calculate the potential and kinetic energies at the time of release, at maximum
height, and when its reaches the ground. Assume that it is released at a height
of 2 m above the ground and that the vertical accelerating force of 100 N is
in excess of gravitational force. At release,
100 m/s 2
a
=
( as calculated previously )
t 1
v
=
adt
=
at 1 =
100 t 1
0
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