Introduction
of the category “Work”
It takes time for the
students of 7th grade to distinguish the everyday meaning and the
scientific meaning of the term “Work”.
We introduce a short
conspectus of the lesson visualising of the main idea.
The purpose of this lesson
is construction of understanding of the
category "work of a force".
To achieve this goal the
sequence of problems is offering to the students.
In what situation a person get more tired:
- ether he will lift the weight of 10 Í by the height of 1 ì, or if he
will lift the weight of 20 Í by the height 1 ì?
- ether he will lift the weight of 10 Í by the height of 1 ì, or if he
will lift the weight of 10 Í by the height 2 ì?
- ether he will lift the weight of 20 Í by the height of 1 ì, or if he
will lift the weight of 10 Í by the height 2 ì?
The students, proceeding from the life experience, intuitively give the
correct answer on the problem. Then the new situation is offering.
The tractor pulls the trailer. Between the tractor and the trailer is the
spring scale fixed. In what case the gas spending will be more:
- either the spring scale shows 100 kN and the tractor pass 5 km or if
the spring scale shows 100 kN and the tractor pass 10 km?
- either the spring scale shows 100 kN and the tractor pass 5 km or if
the spring scale shows 200 kN and the tractor pass 5 km?
- either the spring scale shows 100 kN and the tractor pass 10 km or if
the spring scale shows 200 kN and the tractor pass 5 km?
During the answers on this problem the students formulate the idea, that
when the force decreases 2 times and the path is increased 2 times, the
spending of a fuel are the same.
Now we can go to the next
stage of the lesson, i.e. designing of new physical quantity. In both of cases
two physical quantities are considered: a force and path. We need to find out
how from these two physical quantities is possible to construct a third one,
which would allow to compare the spending made and quantitatively would be the
same for the third situations of the problem?
In Physics “to construct” mean to connect algebraically. In the simplest
situation we have four possible algebraic connections between two variables,
those are addition, subtraction, multiplication and division. Because we do not
know in advance what kind of algebraic operation would be correct, we have to
check all of them. To make the checking more visual we construct two tables and
use for the analysis dates from the third questions of the given problems.
F
|
S |
F+S |
F-S |
F*S |
F/S |
|
20 |
1 |
|
|
|
|
|
10 |
2 |
|
|
|
|
F
|
S |
F+S |
F-S |
F*S |
F/S |
|
100 |
10 |
|
|
|
|
|
200 |
5 |
|
|
|
|
Performing simple calculations we obtain the following
dates.
|
F |
S
|
F+S |
F-S |
F*S |
F/S |
|
20 |
1 |
21 |
19 |
20 |
20 |
|
10 |
2 |
12 |
8 |
20 |
5 |
|
F |
S |
F+S |
F-S |
F*S |
F/S |
|
100 |
10 |
110 |
90 |
1000 |
10 |
|
200 |
5 |
205 |
195 |
1000 |
40 |
The purpose of
the analysis of the tables is to detect a repeatability. The sense of the
repeatability is to be following; for the situations, when we intuitively know
that the spending of energy (tiredness) or fuel which should be equal, also the
numerical values of certain combinations of quantities mast be equal. We can
see that this “rule” is valid for the product of force and distance. Hence, we
can assign to this product a new letter, a new word and to obtain after that a
new physical quantity.
Doing that we
have obtained the physical quantity “Work”, which is by the our definition W =
F*S.
Now we can start
studying the properties of the new quantity by solving more problems.
Please, keep in
mind, that we cannot eliminate form our table analysis such possibilities as
addition and subtraction, because for the 7th grade students a
dimensional analysis is not introduced yet.