Note to Instructor: This activity
is used as an early exercise to prepare the students for understanding
the general expansion of objects. This idea is important for understanding
how satellites can measure the slight expansion of the ocean water as it
warms up. Students will observe the slight expansion of a sponge
as it is moistened, and quantify this expansion using a ruler. The
ocean waters expand in a similar way, and the height increase is measured
with satellites.
As an introduction to measuring the expansion of
objects, we will study the expansion of a sponge as it soaks up water.
You will be using a pencil and a ruler as a way to directly measure
the changing height of a sponge as it expands.
Measuring an expanding sponge
Before placing the sponge on the table, use the ruler to measure how thick
it is, and record here: ____________
Place the dry sponge flat on a table, and rest a pencil on top of it as
shown.
Place a ruler in a vertical position as shown, with zero resting on the
table, so the pencil's point is resting near the ruler markings.
Record the pencil tip's position on the ruler: ______________________
Is the pencil tip position the same as the sponge thickness? ________
Explain why or why not: _______________
Students may not realize the thickness of the pencil
will affect the measurement.
Purpose of this question: Not all measurements, even
simple ones like this, are "direct." The sponge thickness is an "indirect"
measurement; students need to subtract their two measured values to find
it.
Use the spoon to add water to the sponge, being careful not to disturb
the pencil.
Measure the new location of the pencil's tip: _______________________________
Calculate the difference in thickness: ____________________
Calculate the percent change in the pencil's position: __________________
Calculate the percentage change in the sponge's thickness: _________________
The idea of percent change in thickness is necessary
for understanding "coefficient of thermal expansion" of ocean water, later.
Pick up the sponge, and use the ruler to directly measure the new thickness,
and change in thickness.
Do you get the same change in thickness as before?
Explain why or why not. ________________________
Measuring the sponge
a second way
Imagine that you cannot measure the height of the pencil tip from the base
of the sponge (the floor), but you must now measure down, from an
overhead reference point (such as the underneath of the table).
The purpose of this second part of the activity relates
to issues of accuracy and precision. Here, a much longer "baseline"
is used, and it is much more difficult to measure the sponge's thickness
change to the same accuracy.
Satellite measurements of the ocean surface use this
much more difficult way of measuring distances. The satellite's orbit
corresponds to the tabletop. The satellite measurement must be done
to a very high accuracy.
Measure the thickness of your second, dry sponge, and record here: ____________________
Place this second, dry sponge on the floor, and position it so that it
is underneath a classroom table.
Place the pencil on the dry sponge, as before.
Measure the distance from the table to the pencil tip: _______________
Make a note of where on the table you are measuring from, because
you will be repeating this measurement!
Carefully add water to this second sponge, and watch it swell up.
Re-measure the distance down from the table to the pencil tip, and record:
______________________
Calculate the percentage change in this distance: ____________________
How does this percentage compare with the percentage change measured before?
_____________
Calculate the difference in the pencil's position, which is the change
in the sponge's thickness: ___________
Pick up the wet sponge and measure its new thickness directly: ___________
Calculate how much its thickness changed, based on these direct measurements:
_____________
Describe the differences in these two measurements.
If you could choose one of these two methods to measure the sponge's thickness
change, which would you use? __________________________________________________
Describe why you would use this method, and not the other: ________________________
Be prepared to defend your answer in class discussion!
Students should describe how the percentage change
in the second activity is much smaller than in the first, even while the
actual quantity that is changing (the change in thickness of the sponge)
is the same.
Satellite Measurements
Instead of measuring down from the eight of a tabletop (less than one meter),
consider how this measurement is done from an orbiting satellite.
The TOPEX satellite is approximately 1,300 km up in space (1,300,000 meters).
Calculate the percentage change in the measurement from this satellite
if the height changes by 1 cm (0.01 m).
Discuss any problems that you think might arise when the satellite tries
to make this measurement.
Measuring the sponge
a second way