Biomedical Engineering Reference
In-Depth Information
where
F
is the magnitude of the force (in newtons) exerted by the spring,
x
is
the observed variation in the spring length (in meters), and
k
is the elastic constant
of the spring, measured in N/m.
In the case of a rubber band, used here, the change in the length,
Δ
x,
of the elastic
cannot be directly proportional to the magnitude of the applied force,
F
, because the
profile of the elastic, that is, its cross-sectional area changes significantly with
the increase of the force. Therefore, the recommended procedure is to construct a
calibration curve that relates
F
to
Δ
x
. Whenever a rubber band is used as a spring
scale, one has to measure initially the increase in the length of the elastic for a
known force and from the graph of
F
versus
Δ
Δ
x
determine the corresponding
magnitude of the applied force.
8.3.2.1 Procedure
Construction of a spring scale (dynamometer)
1. Cut a rubber band to obtain a strip.
2. Redo two paper clips, as shown in Fig.
8.3
, to transform them into hooks.
3. Tie one clip at each extremity of the rubber band and the spring scale is ready.
Calibration of the Spring Scale
4. Measure the length,
x
o
, of the outstretched elastic of the rubber band spring
scale, from end to end, in meters.
5. Make a small hole near the mouth of a plastic bottle, as shown in Fig.
8.4
,to
hook one of the clips of the spring scale.
6. Pour one unit of mass into the bottle and measure the length of the stretched
rubber band strip,
x
1
, in meters.
7. Determine the increase in the length of the rubber band strip, by calculating the
difference
x
1
-
x
o
.
8. Fill out Table
8.1
with the value of the force,
F
, exerted on the rubber band
(in newton, N, or in an arbitrary unit of force, a.u.f.) and the corresponding
Δ
x
(in meter, m) obtained through calculation.
Consider: 1 N as the weight force that acts on a mass of 100 g,
or: 1 a.u.f. is the weight force that acts on 1 a.u.m.
9. Repeat procedures 6, 7, and 8 submitting, successively, the spring scale to two,
three, four and five units of mass.
10. Construct the calibration curve of the spring scale, that is, the graph of the
magnitude of the applied force,
F
, as a function of the corresponding observed
change in the length,
x
, of the rubber band.
11. Determine the weight and the mass of an object by hanging it in place of the pet
bottle and measuring
Δ
x
. Then, use the spring scale calibration curve.
Δ
12.
W
__________ (kg or a.u.m.).
13. Construct and calibrate another spring scale made with a rubber band strip.
¼
__________(N or a.u.f.)
m
¼
