FRONTLINE
This experiment encouraged questions from and
stimulated the interest of students in elementary and
junior high schools. Because students can hold the
ring and magnet they can discover that the ring is
made of a non-magnetic metal, thus avoiding any
misunderstanding (for example, that the reason for
the rotation of the ring is based on magnetic adsorption). Furthermore, this experiment helps to explain
the rotation principle of an induction motor and
demonstrates the necessary conditions for its successful operation.
Reference
[1] Sakaki M et al 2004 Computer hard drive
transforms into the most basic of speakers Phys.
Educ. 39 394
Mamoru Sakaki, Faculty of Education, Ibaraki
University, Japan; e-mail: mamo310@mx.
ibaraki.ac.jp and Atsushi Sasaki, Department of
Electrical Engineering, Kushiro National College
of Technology, Japan; e-mail: sasaki@elec.
kushiro-ct.ac.jp.
BOYLE’S LAW
Measuring depth
takes a lot of bottle
On a weekend break in September with my family
in Savudrija – a small village on the northern Adriatic
coast in Croatia – I spent some time on the beach.
There are a number of physical phenomena on the
beach that offer up the opportunity for exciting
physics experiments. This time I was looking for an
experiment in the field of static fluids.
First I started with a simple problem: how do I
measure water depth? The obvious answer is by
using a rope with a stone tied to its end etc. But there
isn’t much physics in this approach, and besides,
this method is useful only for relatively shallow
depths and in very calm seas.
I then remembered the problem about diving with
a rubber balloon. Assuming the water temperature
does not change much at the depths that I can reach,
I can determine water depth from a change in a balloon’s volume using Boyle’s law. However, there
are problems with this approach too. It is very difficult to take measurements of a balloon’s volume
at the bottom of the sea, and by bringing the balloon
up to the surface the information about the change
in volume would be lost. Could I somehow ‘lock’
the volume of the air in the balloon at the seabed
and bring it out to dry land where I could then measure the change? Here is how I did it.
I took an empty 0.5 l drink bottle with a screw
cap. I dived to the desired depth (the bottle may get
flattened a little bit), turned the closed bottle upsidedown (with the cap towards the sea bottom) and I
opened the cap. At this moment some amount of sea
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P H Y S I C S E D U C AT I O N
Figure 1. Tina marks the height of the column of
water in the soda bottle (yes, we have forgotten to
take a ruler to the beach again).
water quickly moved into the bottle, compressing
the air that was trapped in it. I kept the bottle in an
upside-down position so that no air could escape
from it. I carefully closed the bottle, swam up to the
surface and gave the bottle to my 10-year old daughter Tina who measured the height of the water column (figure 1). (It is a good idea to open the upright
bottle before taking measurements, since the pressure inside the bottle is now greater than the atmospheric pressure and so the bottle may get slightly
deformed.) In the meantime I used the ‘rope and
stone’ method to take another measurement of the
same water depth. We repeated the measurements
at five different depths.
Later, using the marked heights on the bottle, we
measured the exact volumes of the water in the bottle with a measuring cylinder. We also determined
the total volume of the bottle (table 1).
January 2005
FRONTLINE
Table 1. Water volume and depth measurements
V (ml)
65
85
127
149
187
V0/V
8.3
6.3
4.2
3.6
2.9
hcalc(m)
1.4
1.9
3.1
3.8
5.3
hrope ±0.05 (m)
1.1
2.0
3.0
3.8
5.3
the volume of the air in the bottle decreases to V0 –V,
where V is the volume of the water in the bottle.
Assuming a constant temperature of the water and
using Boyle’s law,
p0 V0 = p(V0 − V )
one can express the depth h in terms of V in the following way. From
V = volume of water in the bottle; V0 = total volume of
bottle (539 ml); hcalc = depth determined by Boyle’s law;
hrope = depth measured by ‘rope and stone’ method.
The values for depth determined using volume
measurements and Boyle’s law closely match
those found using the ‘rope and stone’ method.
p0 V0 = ( p0 + ρgh)(V0 − V )
one finds
h=
p0
1
.
ρg V0 /V − 1
The change in air volume in the bottle is related
to water depth. The pressure (p) at the distance h
Using this expression I was able to determine hcalc
under the sea surface is the sum of the atmospheric (listed in the third column of the table). Though I
pressure (p0) and the hydrostatic pressure
never doubted that physics works, I admit that I felt
proud when I showed Tina how closely the two sets
p = p0 + ρgh
of depth measurements corresponded.
where ρ is sea water density (1.028 g/ml for north
Adriatic sea) and p0 = 105 N/m2 is atmospheric pressure at sea level. The initial volume of the air in the
bottle measured at p0 is V0. At increased pressure p
Gorazd Planinšič, Faculty for Mathematics and
Physics, University of Ljubljana and The House
of Experiments, Ljubljana, e-mail: gorazd.
[email protected]
RESISTANCE
Flexible graphite pencil forms crucial
component of resistance strain gauge
Resistance strain gauges are sensors that are used
to measure the stress or elongation of solids. These
measurements are based on changes in resistance
of a conductor that is strained together with the solid.
Investigating different machine elements and
materials using resistance strain gauges is of practical importance and has wide applications in technology [1]. Therefore there is a need to familiarize
students with the principle of how resistance strain
gauges work. Flexible pencils, which can be bent
and compressed, can be bought on the Internet or
in novelty shops; these pencils can be used to demonstrate how a resistance strain gauge works.
The pencils are made of an elastic graphite (a composite made from graphite powder and a binding
January 2005
substance) covered by an
elastic plastic casing. The
resistance of the graphite
in a 30 cm long pencil is
about 12 kΩ.
graphite
The ends of the pencil
are prepared by removFigure 1. The graphite ing the sharpened end
in the flexible pencil is
and (if it has one) the
exposed.
metal-mounted eraser.
About 1 cm of the plastic
outer casing is cut off each end so that the upper part
of the graphite is exposed (figure 1). The pencil is
connected with crocodile clips to an ohmmeter and
the resistance of the graphite is measured (figure 2).
shield
P H Y S I C S E D U C AT I O N
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