Biomedical Engineering Reference
In-Depth Information
Examples 1.8 and 1.9 and Exercise 1.11 have shown clearly that the pressure
exerted by the weight of a person will become larger as the contact area of this
person with the ground becomes smaller. In this way, if the seat of a couch supports
the pressure of the body when the person is seated, the couch cannot necessarily
support the weight if this person stands on it, mainly on one foot. The effect of the
area on the pressure is easily verified in the sand of a beach, by changing from a
tennis shoe to a high-heeled shoe.
The concept of pressure will be reviewed and discussed in terms of compression
on intervertebral discs in Chap.
7
.
1.9 Answers to Exercises
K
q
1
q
2
r
2
Exercise 1.1
Electric and gravitational forces are, respectively, equal to
F
E
¼
G
m
1
m
2
and
F
G
¼
r
2
. In the case of electric forces, they can be positive (repulsive) or
negative (attractive), depending on the sign of the charges
q
1
and
q
2
with both positive
or both negative and one of them positive and the other negative, respectively. It is
known that charges of opposite signs attract and same signs repel. In the case of
gravitational force, there is only the force of attraction, since there is no negative mass.
The intensity of these forces in the first case depends on the values of the charges and
in the second case on the masses of the bodies. The constants of proportionality
K
10
11
Nm
2
/kg
2
are universal constants.
Note that, as
G
is very small, the gravitational attraction between any two bodies is
very difficult to observe. Both forces decrease with the square of the distance.
10
9
Nm
2
/C
2
and
G
¼
9
¼
6.67
Exercise 1.2
(a) Will be larger; (b)
R
87 N. Note that, since the weight,
F
1
,
is maintained, the resultant of the applied force can be changed by modifying the
angle between the forces, which can be done by changing the position of the leg
horizontally.
¼
Exercise 1.3 R
¼
15 N upward, pulling the head.
Exercise 1.4 F
¼
24 N.
Exercise 1.5
Force of reaction
10
3
N. It is a contact force.
¼
3,000 N
¼
3
Exercise 1.6
The gravitational force of 5 N and the normal force of 5 N are applied
on block A. The gravitational force of 10 N, normal force of 5 N exerted by block A,
and the normal force of 15 N are applied on block B. The total force on the table
due to the weights of the two blocks is 15 N. Observe that the value of the last force
does not depend on the order of the blocks placed above it.
Exercise 1.7
The forces on blocks A and B are the same as in Example 1.3, without
the normal due to the table. The weight of 3 N acts on block C, the normal force
of 15 N exerted by block A and the normal force of 18 N. The total force on the
