IB Physics SL
Play-doh Deformation Investigation
Research Question: How does the height from which a play-doh sphere is dropped affect the amount of
flattening of its deformation in the impact?
Hypothesis: The diameter of the flattened surface of the play-doh sphere will increase as the height
from which it is released increases. As the height increases, the play-doh sphere will have more
potential energy (𝑃𝐸 = 𝑚𝑔ℎ). When it is released, the energy will be transformed into kinetic energy
1
(𝑃𝐸 = 𝐾𝐸 = 2 𝑚𝑣 2 ). The greater the height, the greater the speed of the play-doh sphere will be upon
impact with the floor. It will take more time to stop the play-doh sphere if its velocity is greater as seen
by the impulse formula (𝑚∆𝑣 = 𝐹𝑡), meaning a greater deformation.
Manipulated Variable: Height of release
The height of release will be measured with a tape measure from the bottom of the play-doh
sphere at eye level in order to minimize systematic and random errors.
Responding Variable: Diameter of flattened surface of play-doh sphere
The play-doh sphere will be dropped unto the poster board and the flattened surface will be
traced unto the poster board before removing the sphere. The diameter will then be measured with a
ruler. Deformation may not always be a perfect circle; therefore, four different diameters will be
measured so as to get a good average of the diameter of the deformation.
Controlled Variables: Size of play-doh sphere; Initial velocity; Environmental Conditions
The size of the play-doh sphere will be controlled by using a mold to make the play-doh spheres
as uniform as possible. The play-doh sphere will be released so that the initial force is minimized and
constant for each trial so that the initial velocity is the same. The experiment will be done indoors on the
same floor type so that there is no wind affecting the sphere’s path and the texture of the floor is
controlled.
Materials:







8 play-doh 141 g cartons
Two semi-circle bowls
Tape measure
Ruler
Spherical weight
Poster board
Stairs or ladder
IB Physics SL
Diagram:
Procedure:
1. Use the bowls to mold the play-doh sphere. Make sure to add a spherical weight to the center
of the sphere to add mass to the play-doh sphere in order to prevent the play-doh from
rebounding once it hits the floor.
2. Place the poster board on the floor underneath where the play-doh sphere will be released.
IB Physics SL
3. Using stairs or a ladder when needed to reach the height, hold the play-doh ball with one hand
on each side and measure the height of the play-doh sphere, coming to eye level with the
bottom of the play-doh sphere, with the tape measure.
4. Release the play-doh sphere, being careful not to add any force to the play-doh sphere.
5. Watch the play-doh sphere drop to make sure that it does not rebound at all when it hits the
floor.
6. Trace the bottom of the play-doh sphere where it touches the poster board with a pencil before
picking it up.
7. Pick up the play-doh sphere and set it aside.
8. Remove any excess play-doh that stuck to the poster board by scraping it off with a ruler and
stick it back on the play-doh sphere.
9. Estimate and mark the center of the circle that was drawn from the deformation.
10. Draw four different diameters as evenly spaced as possible through that center using a ruler as
shown above in the diagram.
11. Measure the diameters to the millimeter and record each of the four diameters.
12. Repeat steps 1-11 five times for each of the five different heights of 140 cm, 210 cm, 280 cm,
350 cm, and 420 cm.
Raw Data:
The following table shows the data recorded for each of the five trials of the five different heights as
well as the four diameters measured.
1
The uncertainties were calculated to be 2 of the smallest increment of the measuring device. Therefore,
since the diameters were measured to the nearest millimeter, the uncertainty was determined to be
±0.05 cm. Although the smallest increment of the tape measure used to measure the height was
millimeters, the height was measured to the nearest centimeter, making the uncertainty ±0.5 cm.
Table #1: Raw Data
Height (cm)
±0.5 cm
Trial 1
140
7.4
7.3
7.6
7.7
210
7.3
7.8
8.0
7.5
280
8.6
8.4
8.7
8.0
350
9.0
8.6
Trial 2
7.5
8.0
7.5
7.4
8.6
8.1
8.2
8.4
8.9
8.5
8.6
8.8
8.8
9.6
Diameters (cm) ±0.05 cm
Trial 3
Trial 4
7.0
7.9
7.1
7.8
7.5
6.6
7.4
7.7
8.4
7.9
8.5
8.4
7.9
8.3
8.0
7.6
9.1
8.4
9.2
8.6
8.0
8.3
9.2
8.7
9.1
9.6
8.8
9.1
Trial 5
7.4
7.0
6.9
7.5
8.2
8.1
7.4
7.9
8.5
7.8
8.6
8.1
8.5
8.6
IB Physics SL
420
8.7
8.3
9.2
9.6
9.9
9.8
9.2
9.3
9.2
9.1
9.0
10.0
9.7
9.2
9.6
9.9
9.9
9.5
9.2
9.1
9.8
9.8
9.4
9.2
9.2
8.8
9.4
10.0
10.1
9.8
Four diameters were measured as shown in the diagram because the deformation of the play-doh was
not a perfect circle. The following table shows the average diameter for each trial which was calculated
through
𝑠𝑢𝑚 𝑜𝑓 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑠
.
4
Table #2: Average Data
Height (cm)
±0.5 cm
Trial 1
140
7.5
210
7.65
280
8.425
350
8.65
420
9.625
The average of the trials were then calculated through
Trial 2
7.6
8.325
8.7
9.225
9.325
Diameter (cm) ±0.05 cm
Trial 3
Trial 4
7.25
7.5
8.2
8.05
8.875
8.5
9.2
9.25
9.725
9.55
𝑠𝑢𝑚 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
.
5
Trial 5
7.2
7.9
8.25
8.775
9.825
Average
7.41
8.025
8.55
9.02
9.61
Processed Data:
To find the representative value for each height along with its error, the difference between the average
diameter and the diameter for each trial was found. The uncertainty is the maximum difference rounded
to one significant figure at the decimal place of the smallest increment of measurement used. The
average was also then rounded to the same decimal place. The percentage uncertainty was calculated
by first finding the relative uncertainty, or error, through
𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦
and
𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
100%, rounding to the nearest percent.
The following process is shown below for the height of 140 cm.
Table #3: Average diameter for height of 140 cm
Trial Diameter (cm)
∆𝑑 = |𝑑𝑎𝑣𝑔 − 𝑑𝑖 |
𝑖
𝑑
𝑑𝑎𝑣𝑔 = 7.41 𝑐𝑚
1
7.5
0.09
2
7.6
0.19
3
7.25
0.16
4
7.5
0.09
5
7.2
0.21
then multiplying by
IB Physics SL
Since the greatest absolute value of the change in diameter is 0.21, the uncertainty is rounded to 0.2 so
that the uncertainty only has one significant figure. Therefore, the representative value of the diameter
of the deformation of the play-doh after it was dropped from a height of 140 cm is (7.4±0.2) cm.
0.2
The percentage uncertainty for this result is 7.4 × 100% = 3%, after rounding to the nearest percent.
The table below presents all the representative values of diameters after the uncertainty has been
calculated with the average.
Table #4: Processed Data
Height (cm)
𝑑𝑎𝑣𝑔 (cm)
±0.5 cm
140
7.41
210
8.025
280
8.55
350
9.02
420
9.61
∆𝑚𝑎𝑥
𝑑 = (𝑑𝑎𝑣𝑔 ± ∆max ) 𝑐𝑚
0.21
0.375
0.325
0.37
0.285
7.4±0.2
8.0±0.4
8.6±0.3
9.0±0.4
9.6±0.3
Percentage
Uncertainty
3%
5%
3%
4%
3%
Graph:
Diameter of deformation
12
y = 0.0077x + 6.36
Diameter (cm)
10
8
6
4
2
0
0
50
100
150
200
250
300
350
400
450
Height of Drop (cm)
The best-fit line for the data is linear with a slope of 0.0077. The graph passes through all the error bars;
therefore, there are no outliers and all the data points support the best-fit line. The error bars for the xaxis are not visible behind the blue diamonds, which denote the data points, since the scale of the x-axis
is much larger in comparison to the size of the error bars. However, since the line goes through all the
blue diamonds, it also goes through the x-axis error bars.
IB Physics SL
The following graph shows the maximum and minimum slope in order to evaluate the extreme values
possible and the deviation present in the data.
Diameter of deformation
12
y = 0.0077x + 6.36
10
Diameter (cm)
y = 0.006x + 6.756
8
y = 0.0097x + 5.8403
6
4
2
0
0
50
100
150
200
250
300
350
400
450
Height of Drop (cm)
Conclusion:
The best-fit line for the data points is linear, which supports the initial hypothesis stating that the
diameter of the deformation of the play-doh sphere is linearly dependent on the height from which it is
released. The slope of the line is 0.0077, which indicates that as the height of the drop increases, the
diameter of the deformation also increases, but not considerably. There must be a significant change in
height to notice an increase in the deformation.
Evaluation:
In order to better determine the accuracy of the experiment, the graph needs to be extrapolated until
the y-axis. Although trials were not done for heights shorter than 140 cm, the graph can still be
extrapolated by using the slope and y-intercept of the equation governing the line of best fit.
IB Physics SL
Diameter of deformation
12
y = 0.0077x + 6.36
Diameter (cm)
10
8
6
4
2
0
0
50
100
150
200
250
300
350
400
450
Height of Drop (cm)
Although the graph does go through all the error bars, the line does not go through the origin. Instead,
the y-intercept is 6.36 cm. It is important to consider that even if the play-doh sphere is not dropped
and only gently placed on a flat surface, the area of the play-doh sphere in contact with the surface will
never have a diameter of 0 cm. Therefore, the graph will not pass through the origin. The y-intercept
suggests that the diameter of the deformation of the play-doh sphere if it is just set down on a surface
will be 6.36 cm.
Experimenting with five different heights of even intervals consisting each of five trials was sufficient to
provide the data needed to support the hypothesis. Also, because the deformation of the play-doh was
not a perfect circle, measuring the diameter in four different points around the deformation, as shown
in the diagram, gave a good estimate of the average diameter. Outlining the play-doh sphere’s
deformation on the cardboard after it was dropped facilitated in measuring the diameters. Furthermore,
the errors obtained in the experiment are not large. All of the percentage uncertainties are 5% or less,
indicating a decent error relative to the measurement. However, the graph had to be extrapolated
significantly to find the y-intercept.
Although the uncertainties for the height were calculated to be ±0.5 cm, the actual uncertainty was
probably much greater. The bottom of the play-doh sphere was lined up with the height at eye-level to
the nearest centimeter as best as possible; however, accuracy was difficult to ensure. A realistic
uncertainty would be much greater, approximately ±2 cm, but this uncertainty is still small compared to
the measurements. The initial velocity of the play-doh sphere may have also varied slightly due to the
method used to drop the play-doh sphere. Depending on whether both hands released the play-doh
sphere at exactly the same time or not, the play-doh sphere would sometimes spin a little while falling.
Although this did not considerably influence the results, the consistency of dropping the play-doh
sphere would need to be better controlled. Additionally, a tape measure was used to measure the
IB Physics SL
height because it was the only measuring device available that was long enough to measure up to 420
cm. However, the tape measure is flimsy and may not have been held perfectly straight for each trial,
slightly influencing the results.
While investigating before conducting the experiment, it was found that play-doh would rebound off the
floor if it was dropped. It was important that the play-doh did not rebound because of the method being
used to measure the diameter of the deformation. In order to make the experiment possible, a weight
was added inside the play-doh sphere when molding it. However, the weight used was nuts and bolts
taped together to form a sphere so it was not perfectly spherical. Also, when placing the weight in the
play-doh sphere, it was difficult to ensure that the weight was being placed in the center of the play-doh
sphere. Depending on how off-center the weight was, this may have contributed more to the spinning of
the play-doh sphere as it fell because the heavier side would rotate until it faced downwards.
Throughout the experiment, the same amount of play-doh was used to mold the sphere each time. The
play-doh that got stuck to the cardboard after being dropped was scraped off each time. However, some
play-doh may still be left behind. Therefore, the play-doh sphere for first trials was probably slightly
more massive than the play-doh sphere for the last trials. Yet, this method was chosen because
weighing the play-doh sphere on an appropriate scale to ensure that the sphere always had the same
amount of play-doh presented two other problems: the play-doh might stick to the surface of the
balance and the play-doh would already deform when set down on the balance. All the trials for the
experiment were done at one time in order to prevent the play-doh from drying. However, the play-doh
by the end of the experiment was probably a little dried out compared to the initial play-doh. The
changing dryness of the play-doh would influence how much the play-doh deforms.
Improvements:
The method for measuring height needs to be improved in order to provide more accurate results. This
could be done by using a stiff measuring device and a straight edge to better align the bottom of the
play-doh sphere with the height measurement. Also, a spherical weight would provide better
consistency and would help in minimizing how much the play-doh sphere spins while falling. More
heights should also be tested so that the graph does not need to be extrapolated as much, minimizing
the possibilities of error. A measurement should be taken for the deformation if the play-doh sphere is
just placed on the surface to support the value found for the y-intercept.