Gears Laboratory
Names: __________________________________________________________________
Date: ____________
About this Laboratory
In this laboratory, you will explore how the number of teeth on a gear and its number of rotations
affect the rotation of other interconnected gears. First you are asked to do an initial hands-on
activity in the pre-laboratory to get a feel for what you will see in the applet. Then you will use
technology to assist with further discoveries. Numbers given in the applet are approximations.
All explanations are to be made using sentences.
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I.
Complete the Gears Pre-laboratory sheet
II.
Preliminary Work
•
Recall that there are
our work with gears.
•
Make a factor tree to find the prime factors of 360 and then express 360 in its prime
factored form.
degrees in a circle. We will use this fact as we proceed in
360 =
•
Determine the total number of factors for 360 by making combinations of the prime
factors of 360 and by counting “one” as a factor, although it is not as a prime factor.
WV Robotics Project:
Gears Laboratory Sheet Pyzdrowski,6/25/10 -1
•
The following tables may be used to help you organize all of the factors of 360. Fill in the
missing information. Notice that the second table has the additional factor of 5 for each
cell.
20 = 1
21
22
23
30 = 1
1
2
4
8
31
3
32
•
•
5
20 = 1
21
22
23
30 = 1
5
10
20
40
31
15
2
45
3
9
A gear with 24 teeth has a relationship between the number of teeth and
the angle between two consecutive teeth.
360
=
24
teeth.
degrees, the angle measure between teeth on a gear with 24
360
=
40
gear with 40 teeth.
•
Similarly,
•
Notice that in your tables of factors, both 40 and 24 are listed as factors of
360. Therefore, 360 is divisible by each, yielding a whole number
quotient.
•
Recall that in your pre-lab, one gear had 16 teeth. What is the angle
measure between teeth on that gear?
•
Does16 divide 360 (so that the quotient is a whole number)?
•
Is 16 in either of your tables of factors?
II.
Using the Gears Applet
!
Notice that in the applet the radio button is selected to show 2 Gears.
!
The slider bars under Teeth can be pulled to give the number of teeth on a gear to be
between 8 and 64 inclusive.
degrees, the angle measure between teeth on a
WV Robotics Project:
Gears Laboratory Sheet Pyzdrowski,6/25/10 -2
!
Point to the horizontal slider bars under Teeth and then hold down the left mouse button
to drag to set the number of teeth to 24 (the first gear) and 40(the second gear).
!
Notice the vertical alignment segment associated with each gear.
!
Point to the darkened point on the first gear and then hold down the left mouse button to
drag the wheel counter clockwise. Count the number of revolutions the gear must make
in order to line both gears once again to their respective alignment segments. Record the
number of revolutions that the gear with 24 teeth must make here.
!
Point to the horizontal slider bars under Teeth and then hold down the left mouse button
to drag to set the number of teeth to 40 (the first gear) and 24(the second gear)
respectively and notice the vertical alignment segment associated with each gear.
!
Point to the darkened point on the first gear and then hold down the left mouse button to
drag the wheel counter clockwise. Count the number of revolutions the gear must make
in order to line both gears once again to their respective alignment segments. Record the
number of revolutions that the gear with 40 teeth must make here.
!
In the space provided, make a prime factor tree for each 24 and 40 and then express each
in prime factored form.
24 =
!
40 =
Show work to give the least common multiple of 24 and 40, LCM (24,40). This is the
smallest whole number which both 24 and 40 will divide.
LCM(24,40) =
LCM(24,40)
?
40
!
What is
!
What does this number represent in the gear problem?
WV Robotics Project:
Gears Laboratory Sheet Pyzdrowski,6/25/10 -3
LCM(24,40)
?
24
!
What is
!
What does this number represent in the gear problem?
!
How many degrees must the gear with 40 teeth rotate to line back up the segments?
!
How many degrees must the gear with 24 teeth rotate to line back up the segments?
!
Point to the horizontal slider bars under Teeth and then hold down the left mouse button
to drag to set the number of teeth to 16 (the first gear) and 40(the second gear).
respectively.
!
Show work using the concept of Least Common Multiple to determine how many
revolutions it will take for each, a gear with 16 teeth and a gear with 40 teeth, to line up
to the vertical segment once you start to rotate the first gear counter clockwise.
LCM(16,40) =
Number of revolutions for each gear: 16 teeth
40 teeth
!
How many degrees must the gear with 16 teeth rotate to line back up the segments?
!
How many degrees must the gear with 40 teeth rotate to line back up the segments?
!
Select the radio button in the applet to show 3 Gears.
WV Robotics Project:
Gears Laboratory Sheet Pyzdrowski,6/25/10 -4
!
Point to the horizontal slider bars under Teeth and then hold down the left mouse button
and drag to set the number of teeth to 24 (the first gear) and 40(the third gear). Set the
second gear to a number of your choosing.
!
Point to the darkened point on the first gear and drag the wheel counter clockwise. Count
the number of revolutions the gear must make in order to line both the first and third
gears once again to their respective alignment segments. Record the number of
revolutions that the gear with 24 teeth must make
!
Vary the number of teeth in the second gear and then make a conjecture regarding the
number of revolutions the gear with 24 teeth must make in order to line both the first and
third gears to their respective alignment segments.
!
Select the radio button in the applet to show 4 Gears.
!
Point to the horizontal slider bars under Teeth and drag to set the number of teeth to 24
(the first gear) and 40(the fourth gear). Set the second and third gears to a number of your
choosing.
!
Point to the darkened point on the first gear. Drag the wheel counter clockwise and count
the number of revolutions the gear must make in order to line both the first and fourth
gears once again to their respective alignment segments. Record the number of
revolutions that the gear with 24 teeth must make here.
!
Vary the number of teeth in the second and third gears and then make a conjecture
regarding the number of revolutions the gear with 24 teeth must make in order to line
both the first and fourth gears to their respective alignment segments.
!
Using any four gears that you wish to use, what generalizing statement can you make
about the direction of turn for each of the gears? Does your generalization seem to hold
for three gears? ... two gears?
WV Robotics Project:
Gears Laboratory Sheet Pyzdrowski,6/25/10 -5