Biomedical Engineering Reference
In-Depth Information
a
required to bring a
body to rest, from a velocity
v,
and the distance
d
to be traveled until it stops is
given by:
Similarly, the relation between the average deceleration
v
2
¼
2
ad
:
(7.9)
As (
7.8
) and (
7.9
) are equivalent, we can set them equal and solving for
a
we find:
g
H
a
¼
d
:
(7.10)
The above equations are valid also for a body under constant acceleration, as in
the case of a car in motion with constant acceleration instead of the fall from a
certain height due to the gravitational acceleration. In this case we can just
substitute the acceleration due to the gravity
g
by
a
¼ Δ
v
/
Δ
t
, i.e., the change in
the velocity in a certain time interval.
The second law of Newton, already presented in Chap.
1
, states that:
m
Δ
v
Δ
F
¼
ma
¼
t
:
(7.11)
After a person jumps from a springboard, for example, during the collision with
the water surface, deceleration occurs until its final velocity becomes equal to zero.
This deceleration is not constant, but its average value can be obtained, by calcu-
lating the difference between the velocity on reaching the water's surface and the
final velocity that is zero, i.e.,
0, divided by time interval. So, during the
collision, the body is subject to a force exerted by the water surface which is also
not constant but its average value can be obtained by:
Δ
v
¼
v
m
Δ
v
F
¼
t
;
(7.12)
Δ
or also through:
mg
H
F
¼
m
a
¼
d
:
(7.13)
The product of the applied force by the time interval during which the force acts
is a physical quantity called the impulse
I
of the force
F
:
¼ F
I
Δ
t
¼
m
a
Δ
t
¼
m
Δ
v
:
(7.14)
0, where
v
is the velocity at the collision and zero, the
final velocity, when the body stops.
Remember that
Δ
v
¼
v
