Four Factor DOE
Lin – Perry – Sikorski
Physics 11A
Lin – Perry – Sikorski
Problem:
To determine if length, mass, surface area or amplitude will have an effect on
the period of a spring bob
Hypothesis:
The length of the spring and mass will have an effect on the period, while the
surface area and amplitude will not have an effect on the period
Materials:
Styrofoam squares (441 cm2, 225 cm2, and 100 cm2)
Metal springs (27 cm, 22.5 cm, and 17 cm)
500 g weight
(2) 200 g weight
Motion Detector 2
LabQuest Pro
Cage
Hook
Ti – Nspire
Folded Paper
Metal Wiring
Procedures:
1.
Randomize data trials using the Ti – Nspire
2.
Set Motion Detector 2 in cart mode
3.
Set Motion Detector 2 directly under the hook
4.
Attach LabQuest Pro to Motion Detector 2 and computer
5.
Place cage over Motion Detector 2
6.
Attach appropriate spring onto the hook
7.
Put on appropriate Styrofoam squares on the metal wiring
8.
Place appropriate weights on the metal wiring
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Lin – Perry – Sikorski
9.
Insert folded paper into the weights so the weights will not come off
10.
Attach assembled components (Spring Bob) onto the spring
11.
Stretch the spring accordingly to the trail
12.
Calculate the period using the LabQuest Pro and record
Diagram:
Figure 1. Diagram of the materials
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Lin – Perry – Sikorski
Conclusion:
The objective of this experiment was to determine which of the four factors
(amplitude, area, length, and mass) will directly affect the period of a spring bob. The
hypothesis was that the factors of length and mass would affect the period of the spring
bob.
Throughout the experiment, the data that was collected was very consistent.
There were no significant outliers in the data in the standard trials. The standard trial
results were 0.85, 0.84 and 0.84, this shows that the data collect was consistent; this
can be seen in the standards graph on the DOE Data and Analysis. Due to the consistent
standard trials, more analysis can be conducted with this data. There were some factors
that might have an effect on the data that was not planned, this includes: the Motion
Detector 2 was not on the right setting and the Data recorded was wrongly interpreted
by a member, thus the analysis was redone. If the experiment was redone, all of the
previous procedures would have done due to the consistent data and the simplicity of
the design of the experiment.
The hypothesis was accepted due to results. From analyzing the data from the
experiment, it can be determined that the length of the spring and the mass did have an
effect on the period of the spring bob. The factor length has an effect of 0.16 seconds on
the period of the spring bob. The mass had an effect of 0.18 seconds on the period of
the spring bob. The other factors of amplitude and area only have an overall effect of
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Lin – Perry – Sikorski
0.01 seconds on the spring bob so it is concluded that only the factors length and mass
had an effect on the period. It can be concluded from the results and from the Dot Plot
from the Data and Analysis, only length and mass has an effect on the period of a spring
bob.
The results from the experiment support the scientific fact that only mass and
length has an effect on the period and this is derived from Newton’s second law. Mass
affects the period because in the equation force = mass X acceleration the force is
constant because the force is determined by the amplitude. If the mass increases in this
case the result is that the acceleration is decreased, if the acceleration is decreased it
takes longer for the spring to complete a cycle thus the period increases. Length affects
the period of the spring bob because in the equation Force = KX = ma the K is increased
if the length is increased the spring constant is decreased. The spring constant decreases
because there are more coils thus it takes less force to displace them. Since the spring
constant decreases the acceleration is also decreased thus it takes more time for the
spring bob to complete a cycle thus it affects the period. Amplitude does not affect the
period because even though the velocity increases, the distance traveled is also
increased thus they are proportional; since they are proportional the period stays the
same. Area does not have a major affect because the Styrofoam does not have a lot of
mass so it does not affect the acceleration; also there is very low air resistance because
the velocity is not great enough for air resistance to affect the velocity. In conclusion,
due to Newton’s second law only mass and length has an effect on period.
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