Biomedical Engineering Reference
In-Depth Information
∫
Ftdt
()
=Δ
m V
(5.8)
where
dt
is the duration of the force(s) and
Δ
V
is the change in linear velocity. If
F
(
t
)
is idealized as a step function of duration
Δ
t
, then
()
Ft t
Δ= Δ
m V
Using Newton's second law,
Δ
Δ=
v
impulse
t
=
(5.9)
a
f rce
The impulse-momentum relationship is an important means of determining
what motion results from an applied force. Impulse-momentum is also important
in absorbing the generated forces. For example, when an athlete reaches out with
the glove to catch a ball and as the ball contacts the glove, the arms flex inward to
increase the time of force application. Unskilled players often keep the glove in the
same place at impact and all the forces are applied over one instant, which could
lead to loss of control of the ball or pain. This concept is discussed in Section 5.5.1.
EXAMPLE 5.3
A 59.5-kg volleyball player with one prosthetic leg is trying to block a ball for which he has
to jump. During the jump, his feet are in contact with the ground for 500 ms. If his ground
vertical reaction force during the jump is 1,000N and his total body velocity at touchdown
is
−
0.50 m/s, determine his total body vertical velocity at jump takeoff. Assume that the
applied force is constant during the duration.
Solution: From the impulse-momentum relation,
t
(
)
∫
(
)
(
)
Ftdt
()
mV
V
F
F t
mV
V
=
−
→−
=
−
21
g
w
21
0
(
)
(
)
(
)
[]
[]
[]
[]
(
)
[
]
2
1,000 N
−
59.5 kg * 9.81 m s
⎡
⎤
0.5 s
=
59.5 kg
V
− −
0.5
m s
⎣
⎦
2
V
3m s
=
2
5.2.5 Gait Analysis (Motion Analysis)
While a person walks, each foot repeats the same pattern of movement: (1) the
foot comes on the ground, (2) the foot rests on the ground, (3) the foot lifts off the
ground, and (4) the foot swings through the air. This is called a gait cycle. During
this cycle, legs experience varying forces. These forces are necessary to support the
entire body, to perform the desired motion, and to sustain the impact from the foot-
floor contact. Gait analysis is a systematic study of the motion of an individual.
