© The Norwood Science Center 2006
The Norwood Science Center
Forces
Grade 4
BACKGROUND INFORMATION:
Simple machines are tools or devices that have no or few
moving parts. These machines allow us to accomplish a task with the
application of less force. The tradeoff with simple machines is the
less energy must be used for a longer time or applied over a longer
distance.
Let us take a door for example. A door is a simple machine; it
is a lever. The fulcrum (the hinge edge) is at one end; the load (the
door) in the middle and the force applied is at the opposite end
compared to the fulcrum. Therefore, the door is a second class lever.
Imagine a door that has one of those automatic closers. This
makes the door harder to opens since one must push the door and
the closer open at the same time. The easiest way to push open the
door is to apply pressure, or force, as far away from the hinges as
possible. That is why the doorknob is on the edge of the door on the
opposite side of the door from the hinges.
If the doorknob was in the middle of the door, you would be
able to open the door by exerting the force over a smaller distance,
but you would have to use a greater force. If the doorknob was in the
middle of the door, the situation would represent a different class of
lever, but that is to be discussed at a later time.
GearsGears are wheels with teeth. In our classroom discussion we
will examine gears that are directly connected; the teeth on one gear
are touching (meshing) and moving the teeth on a second gear.
Students will be using Gear kits from Delta Science; all the
photographs are of those materials.
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
When two gears are connected, we can move one gear by the
application of energy, the second gear moves as the energy is
transferred from the teeth of the first gear to the teeth of the second
gear. In our lesson, the gear that receives the energy from a person
will have a handle. This gear with the handle will be called the drive
gear.
The second gear, which is moved by the master (drive) gear,
will be called the following gear. If there are several gears connected
in a row, the master gear operates the first following gear, which
operates the second following gear in what can be called a gear train.
In a standard gear train, where the gears are lined up in one
plane, the drive gear will make the following gear rotate in the
opposite direction compared to the drive gear. Each gear is
succession will show a reversal in direction. This is a very simple,
easily identifiable pattern that is a critical aspect of gear operations.
Two of the functions of gears in this unit are:
• To reverse the direction of rotation of a gear.
• To increase or decrease the speed of rotation of a gear.
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
BLACKBOARD INSTRUCTION:
Ratio -> two values related by division. This is more commonly
known as a fraction.
If value A is related to value B this relationship can be expressed as
the following:
A, A/B, A:B or A is to B.
B
When the phrase gear ratio is used, the ratio being studied is the
physical size relationship of the drive gear (the input gear or the effort
gear) to the driven (the output or the load) gear. There are three
common ways to relate gears, the circumference, the diameter or the
radius. These are all equivalent measures since they are related by
constants, including pi.
The most reliable measure of a gear is the number of teeth on the
gear. This is actually a measure of gear circumference. In this
lesson the gear ratios will be based upon the number of teeth on
respective gears.
In the first part of this lesson students are to place a 30-tooth drive
gear onto the base. The 30-tooth drive gear turns a 10-tooth driven
gear. The calculation of the gear ratio for this setup is as below.
You might want to tell the students two ratios related by equality is a
proportion.
Drive gear = 30 teeth
Driven gear
10 teeth
=
30
10
=
3
1
The units cancel each other out and the ratio can be simplified.
However, it is common practice to leave the value as fraction even if
it is an improper fraction. In this case, the gear ratio for the 30-tooth
gear to the 10-tooth gear is 3 to 1.
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
The size relationship between gears is important. However, a more
practical concern is the relationship between the number of turns
each gear makes. Quite often we know how fast a drive gear turns
and we need to calculate the size of the driven gear to produce a rate
of turns (rotation) that solves a given problem.
Looking at the gear pair in the previous example, we need to
determine the rotation ratio for the two gears. For that we need to
know how many times the driven (load) gear turns with one rotation of
the drive (effort) gear.
The methods by which students identify these values are outlined in
the lesson plan. The calculation is as follows:
# turns drive gear = 1
# turns driven gear
3
It can be concluded that the 10-tooth gear will rotate 3 times for every
single rotation of a 30-tooth gear. There is an interesting relationship
between gear ratios and rotation ratios. See if the students can figure
it out by using a few different gear pairings.
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
TITLE:
GEAR RATIOS
PURPOSE:
What size gear spins faster?
MATERIALS:
(per pair of students)
Gear Bag A
PROCEDURE:
01.
Pair students; distribute one Gear Bag A per pair.
02.
Students are to remove the blue base from Bag A. See Figure
1 below.
Figure 1
03.
Students are to remove the largest of the three gears from Bag
A. Students are to count the number of teeth that go around
the edge of the gear. (The teeth of the gears are split to allow
the gears to act as pulleys. The students should ignore this
groove when counting gear teeth.)
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
04.
From that point in the lesson the largest gear will be referred to
as the 30-tooth gear.
05.
Students are to place the 30-tooth gear in any of the holes on
the base.
06.
Students remove the handle from Bag A and insert it into the
center of the 30-tooth gear. The appropriate way to turn the
gear is by use of this handle.
07.
Students remove the smallest gear from Bag A. They are to
count the teeth. From this point on the smallest gear is referred
to as the 10-tooth gear.
08.
Students are to place the 10-tooth gear into the base so the
gear teeth of the two gears mesh together. An example of
meshing teeth is shown below.
09.
Students take out the pointer and place in the center of the 10tooth gear. This will assist the students when they count gear
rotations.
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
10.
At this point the teacher should review clockwise and
counterclockwise. The most important aspect of this early
portion of the lesson is adjacent gears turn in opposite
directions.
11.
Students are to identify the gear ratio for the two gears.
12.
Students are to identify which of the two gears is larger. They
are to rotate this gear one complete turn. As they do this they
are count the number of times the smaller gear rotates for each
single time the larger gear rotates.
13.
Students calculate the rotation ratio of the two gears.
CONCLUSION:
1.
Students should see that as one gear moves, the adjacent gear
moves (rotates) in the opposite direction.
2.
Smaller gears rotate faster compared to larger gears. Another
way of expressing this is that smaller gears rotate more times
compared to the rotation of larger gears
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
TITLE:
GEAR RATIOS (with idler gears)
PURPOSE:
Build a working gear train
Identify properties of gear trains
MATERIALS:
(per pair of students)
Gear Bag (A)
PROCEDURE:
01.
Pair students; distribute one Gear Bag A per pair.
02.
Allow students to review the work they did in the Gear Ratio
lesson.
03.
Students are to place a 30-tooth drive (effort) gear and a 30tooth driven (load) gear on the base. The teeth should be
meshed, handle and pointer in the appropriate gears. See
figure below.
04.
Students calculate the gear ratio and rotation ratio for the two
gears.
05.
Students are informed they will add a 10-tooth idler gear
between the 30-tooth driven (effort) gear and the 30-tooth
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
driven (load) gear. When the drive (effort) gear handle is
turned, the drive gear should turn the idler gear that turns the
driven (load) gear. See Figure below.
06.
Before the students are allowed to construct the gear train,
they must calculate the gear ratios and rotation ratios for the
three gear train. The students must predict any changes that
are to be seen in the action of the final gear due to the inclusion
of an idler gear of different size.
07.
After students record predictions regarding changes in the drive
(load) gear they can assemble the gear train. They can see if
the predicted correctly, and if they missed any changes.
Gear Ratios Gr. 4
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© The Norwood Science Center 2006
SOLUTION:
The gear ratio between the drive (effort) gear and the idler gear
is 3 to 1. This was calculated in the previous lesson. That means
there is a rotation ratio of 1 to 3. For every rotation of the drive
(effort) gear there will be three rotations of the idler gear.
Looking at the next pair of gears (idler and driven) the gear ratio
is 1 to 3, which gives a rotation ratio of 3 to 1.
Looking at the gear train, one rotation of the drive (effort) gear
produces three rotations in the idler gear. These three rotations
produce one rotation in the driven (load) gear.
Therefore, the idler gear does not change the rotation ratio
between the drive (effort) and driven (load) gear.
The only change seen as a result of the inclusion of an idler
gear is the driven (load) gear now rotates in the same direction as the
drive (effort) gear.
In summary, idler gears do not change the rates of rotation of
driven gears, but they can be used to change the direction of the
rotation of the driven gears.
Gear Ratios Gr. 4
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