Biomedical Engineering Reference
In-Depth Information
8.8.1 Objectives
• To characterize the association of rubber bands
• To establish the analogy between the association of rubber bands and the
configuration of muscle fibers
8.8.2 Activity 8: Association of Springs
8.8.2.1 Necessary Materials
- Rubber band strip
- Paper clips
- Ruler or tape measure
- Known masses
- Support of masses
8.8.2.2 Association of Springs: In Series and in Parallel
We have already mentioned that in a spring, the change observed in its length
is proportional to the force applied to it (Hooke's law). The constant
k
of
proportionality is called the force constant of the spring. There are two ways to
associate springs: in series and in parallel.
In the association of
N
springs
in series
, one following the other in a linear
sequence, the force on each spring is the same and we observe the following
relation for the resultant elastic force constant
k
S
:
1
k
S
¼
1
k
1
þ
1
k
2
þþ
1
k
N
:
Observe that if the springs are identical, we can write:
k
1
¼
k
2
¼¼
k
N
¼
k
k
N
:
In the association of
N
springs
in parallel
, one beside the other, the change in the
length of each spring is the same and we observe the following relation for the
resultant force constant
k
P
:
and, hence,
k
S
¼
k
P
¼
k
1
þ
k
2
þþ
k
N
:
Observe now that if the springs are identical,
k
P
¼
Nk