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Issue:
applying mathematics to exercises with
real - life context
„What do you know about the greenhouse effect?”
INTRODUCTION
Do you know?
- The greenhouse effect has a great impact especially on glaciers
-Climate change, its getting warmer causes continuing melting process
of glaciers
-In constant climate conditions glaciers’ balance would not be disturbed
- Rainfalls result in the growth of a glacier. When it reaches extreme size,
the pressure causes its melting
- The factors that increase the process of melting are: friction between
the glacier and the ground as well as geothermal energy of the Earth
- Temperature rise causes melting and withdrawal of glaciers
- Glaciers’ melting is a long-lasting
process due to their great mass.
It was thought that glaciers might
disappear completely after many
years
- An alarming phenomenon was
noticed: climate getting
results in huge changes
warmer
-There is a great difference between the same places now, and decades ago.
A glacier of a dozen metres has become replaced with lakes and bare rocks
Notice Pedersen Glacier’s change of the landscape;
There is a meadow instead of a glacier.
Źródło: globalwarmingart
Glaciers are also disappearing in Europe
This graph shows how little is going to remain of the
Alpine glaciers providing they are under the influence of
rising temperature.
On Kilimanjaro, the highest African mountain,
the glacier has already lost 80% of its mass
Preserving the current speed of melting, the glacier on Kilimanjaro is
expected to disappear by 2020-2030 .
Source: NASA
The speed of melting and growth of glaciers does not only depend on
temperature.
Another important factor is the amount of rainfall.
Disappearing of glaciers started more than 100 years ago
together with temperature rise connected with the growth of
the Sun radiation, which has been continuing since the end
of the 50’s in the 20th century.
The current temperature rise caused mainly by the enlarged amount of greenhouse
gases in the atmosphere causes further faster melting of glaciers.
Exercises
Task 1
There are three ice cubes in the shape of a cube with the
edge of 1 inch each.
Assuming that the melting will be taking place in the same
conditions and time, determine in which case the ice
cubes will melt faster:
- Case 1
- Case 2
a) What kind of phenomenon can we observe in both
cases?
b) Justify your answer using the formula that describes this
phenomenon: (Q:t)=k·S(ΔT:ΔL)
c) Describe the meaning of every variable in the given
formula.
d) Calculate using the units of inch, centimetre and
millimetre. Present the result with the accuracy of 0.01.
Task 2
From an ice cube with the edge of 1 inch, a part was
taken from its quoin. This part is a cuboid with the
following dimensions: 0,25 inch, 0,5 inch, 0,25 inch.
Will this “cut” cube melt faster than a normal one?
Justify your answer using suitable calculations and the
picture of the cubes.
1 in.
Solution:
The variables used in the given formula (Q/t)=k·S(ΔT/ΔL) denote:
Q -…………………………………………….
t -………………………………………………
(Q/t) -………………………………………….
ΔL -…………………………………………….
S - ……………………………………………..
ΔT -…………………………………………….
Solution
Task 1 :
For three disjoint cubes there is
S=……………………..inches2=………………..cm2=………………..=mm2
For one triple cube there is
S=……………………..inches²
=………………..cm²
=………………..=mm²
Solution
Task 2 :
For the whole cube
S=……………………..inches²
=………………..cm²
=………………..=mm²
The “Cut” cube has
S=……………………..inches²
=………………..cm²
=………………..=mm²
Prepared by :
Małgorzata Fornal
Monika Wrona
Translated by :
Justyna Niezgoda