Experimental Activities - Biomechanics of the Human Body - page 144

8.8 Chapter 6 : Muscle Force

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