Biomedical Engineering Reference
In-Depth Information
Example 7.5
A running child hits his head on a glass door because he did not
notice that the door was closed. At the instant of the collision, the child's velocity
was 3 m/s. The head stops on the glass and its final velocity is zero. Consider that
the mass of the child's head is 3.0 kg and the duration of the collision is 0.01 s. Find
the average decelerating force exerted by the glass door on the child's forehead.
(a) Using (
7.12
), we obtain:
F
¼ð
3
:
0kg
Þð
3m
=
s
Þ=ð
0
:
01 s
Þ;
F
¼
:
900 N
Observe the size of this force, since it is equivalent to laying the child on the
floor and placing on his forehead a mass of 90 kg.
Let us now change the glass door to a cushioned door, which dampens the
collision. In this case, the time interval of the collision changes to 0.10 s. The force
exerted by the cushioned door will be:
F
¼ð
3
:
0kg
Þð
3m
=
s
Þ=ð
0
:
10 s
Þ;
F
¼
90 N
;
one tenth the previous case.
Physical impacts are characterized by a rapid deceleration. The helmets used by
motorcyclists are especially designed to dampen the shock to the head at high
velocity and increase the duration of the impact to decrease the decelerating forces
and to minimize the damage to the head. The role of air-bags is also to increase the
collision time that dampens the crash.
Exercise 7.6
In accidents involving a motorcyclist who rides without a helmet,
death may result if he receives a blow to his head with an impulse of 100 N s. What
should be the maximum velocity of a motorcyclist if he wants to avoid dying?
Consider the mass of the motorcyclist's head to be 5.0 kg.
Example 7.6
A woman of 60 kg mass jumps with stiff legs from a table of 1 m
height onto a hard floor tile. During the collision, a deceleration to a state of rest
occurs in a time interval of 0.005 s. Calculate: (a) the average force exerted on each
foot by the ground; (b) the distance traveled by the body during the collision.
We have to begin by calculating the final velocity of fall when the body reaches
the ground:
p
2
gh
v
¼
;
v
¼
4.47 m/s
¼
16.1 km/h.
