3:
Data Experiment Collection
Nathan Venger
Date of when experiments were conducted: February 09, 2012
PHY 121IN - Course Number: 23252
Abstract
Two tests were performed regarding the speed of two objects. An additional test was performed
to measure the time it took for an object to fall. The tests were conducted to measure the data
collected. The speeds for the two tests were calculated by dividing the measured distance over
the time it took to complete each designated length. The time in the third test was calculated
through data recording on a stop watch. The tests showed various methods used to record data
and the importance of collecting data without experimental error.
Speed is the measurement of how far an object has travelled over a given time. To
measure speed one needs to know the original and final distances, and the original and final
times that the measured object had travelled. Mathematically speed is expressed as:
Using this understanding of speed the experimenter measured the speed of baseball
pitches. This was conducted to demonstrate how accurately recording data is achievable outside
of a lab.
The fastest recorded baseball pitch was over 100 miles/hour (mph). To reach a speed
of 100 mph, or 44.7 meters/second (m/s), would require talent and skill. The experimenter (and
his two assistants) had neither. Due to this the experimenter estimated his speed, and the speed
of his two assistants would be approximately 32 m/s.
To verify the baseballs pitched velocity the distance the ball was thrown was verified
using a meter tape. The measured distance thrown by the experimenter and his two assistants
was 15 meters. Each individual pitched the baseball three times. The time it took the pitch to be
thrown 15 meters was recorded by a stopwatch. The pitcher notified the time recorder of when
they were to throw the baseball. Upon notification the time began and the time was recorded
until the ball passed a designated line marking 15 meters. After each pitch the time it took pitch
a baseball 15 meters was recorded.
The experimenter was able to pitch a baseball 15 meters in 0.58 seconds, 0.62 seconds,
and 0.6 seconds respectively. This averaged a time of 0.6 seconds. Assistant one had similar
times of 0.54 seconds, 0.59 seconds, and 0.51 seconds, with an average time of 0.55 seconds.
Assistant two recorded times 0.57 seconds, 0.52 seconds, and 0.62 second. Assistant twos
average time was 0.57 seconds. The time it took to pitch the baseball are presented in Table 1
(shown below), as well as the calculated average speed.
Table 1
Collected Data for the time it took to pitch a baseball 15 meters and the speed of the pitch
The average speed was for the experimenter was 25 m/s, for assistant one it was 27 m/s,
and for assistant two it was 26 m/s. This speed was significantly lower than the average speed of
32 m/s original hypothesized for the three participants. The percentage of error between the
hypothesized speed and the actual average speed was calculated. The formula to calculate
percent error is:
Percent Error = (Experimental Error Accepted Value) X 100%
Accepted Value
Based on the formula shown above the percentage of error found between the actual
average speed and the experimental speed (or in this lab the hypothesized speed) for the
experimenter was approximately 22%.
For assistant one the percentage of error was
approximately 16%, for assistant two it was approximately 19%. For all three the average
percentage of error was approximately 19%. The average percentage of error was found by
finding the sum of all percentage errors and dividing the sum by the number of participants in the
experiment (3). Graph 1 (shown on the Graph Section) graphically displays the actual average
speed versus the hypothesized speed.
The second test conducted collected the data (in this test: the time) it took for a ball to
travel six meters horizontally. To conduct the second test a meter tape was used to measure six
meters. The beginning and ending points of the six meters were marked with duct tape. Inside
the marked six meters distance of two and four meters were recorded as well. The object
travelling along the horizontal was a soccer ball with a mass of 0.44 kg. The horizontal floor
was a tile floor. This test was conducted three times. The beginning of it was recorded with the
start of a stopwatch. After the ball had reached the designated distances of two, four, and six
meters the time that it took to reach the distances were recorded. To accurately reflect the time it
took for the ball to reach each designated distance the test was performed three times. Each trial
was performed upon the immediate conclusion of the previous trial. The same time instrument
was used throughout the experiment to ensure greater measurement certainty. The experimenter
rolled the ball during each trial.
The times for each test as well as the average time for each trial are recorded in Table 2
(shown below). Through Table 2 it is possible to see the time it took for the ball to be
Table 2
Collected Data for the time it took to roll a ball six meters, and the time it took the ball to
roll two, four, and six meters
rolled at each designated distance. A graphical representation of Table 2 is found on Graph 2
(shown on the Graph Section). Through proper data collection more information about the ball
is apparent from this collected data. The first crucial information that can be surfaced from Table
2s data is the average speed it took the ball to travel six meters for each trial. Using the formula
for average speed (shown on page 1) the average speed for trial one was approximately 3.07
meters per second (m/s). For trial two the average speed was approximately 2.71 m/s. For trial
three the average speed was approximately 2.68 m/s.
From this information it could be
estimated that the first trial was rolled with the greatest amount of force; yet, is this true? To find
out a comparison of the acceleration during each trial of the ball as it passed each time
designation is needed.
Acceleration for this test was calculated by the rate of final speed minus original speed
divided by final time minus original time. Mathematically it is expressed by the formula:
With all of the inputs calculated it became clear what the acceleration of the ball was at each
designated time. Table 3 (shown below) represents the acceleration of the ball at each designated
time for each trial.
Table 3
The acceleration of the ball during each designated time for each trial
As Table 3 shows for each trial the balls acceleration was greatest during from its starting
distance (0 meters) to two meters. This result is surprising due to the short distance the ball was
rolled. Because the ball was rolled only six meters it was believed (prior to the experiment) that
the balls acceleration would continue to increase as it passed six meters. The results shown on
Table 3, collected from the experimenters original data does not reflect this. What it shows is
that the acceleration decreased between t four and six meters. One possible explanation for this
occurrence is due to the friction caused between the ball and tile floor (known as kinetic
friction). Regardless of what caused the balls acceleration to decrease the information presented
in Table 3 can also provide another interesting result directly related to this second test.
Force is what causes all objects with mass to undergo a change in whatever it was doing.
An example of force can be found in the second experiment demonstrated this lab report. The
ball, prior to being rolled, was static. What caused the ball to change from being static to having
a movement was force. Mathematically force is expressed by the formula:
This formula states that force is equal to the mass of an object multiplied by the objects
acceleration. Using this formula it is then possible to know how much force was initially applied
to the ball. Prior to the experiment the balls mass was measured at 0.44 kilogram (kg). With
this knowledge the force was then calculated using the data from Table 3. The initial force
applied to the ball during the first trial was approximately 1.6 kg[(m)/s(s)] (also known as N).
The initial force applied to the ball for second trial was approximately 1.35 N. The initial force
applied to the ball for the third trial was 1.57 N. The average initial force applied to the ball was
1.51 N.
From the average initial force it is apparent that the ball was rolled with the
approximately the same amount of force for each trial. This is important to note because if
different (and widely varying) amounts of force were applied during each trial it would be
difficult to accurately collect how long it took the ball to travel six meters.
Through the time collected in this second test much can be learned about a ball moving
horizontally on a floor. The first result obtained from this data was the balls speed during each
trial. From speed the balls acceleration was then found. Finally, from acceleration the amount
of force initially applied to the ball was calculated. It is important to remember that these figures
would not have been possible without proper distance and time measuring techniques.
The final performed test concerning data collection involved vertical acceleration due to
gravity. Gravity is the force that causes an object with mass to be attracted to each other.
Gravity is a constant acceleration; on Earth the acceleration of gravity has been consistently
measured at 9.81 m/s2. Although this figure is consistent throughout the planet, it is impossible
to obtain this measurement unless an experiment is conducted in a vacuum. Outside of a vacuum
the measured acceleration of gravity varies. The variance is due to air-resistance. When an
object is in free fall it will accelerate downward (on Earth) at 9.81 m/s 2. Due to air-resistance
this acceleration will decelerate.
The measurement of gravitys acceleration can be found through the distance an object
falls and the time it took for the object cover the given distance in free fall. For this final test the
experimenter dropped an AA size Duracell brand battery two meters from the floor. The time
from the battery being released to the time it hit the ground was recorded a by stopwatch. To
ensure an accurate reflection of the total time it took the battery to hit the floor from two meters
the test was repeated 10 times. The temperature of the room were the experiment was conducted
was 74 degrees Fahrenheit. There was no wind during the time period that the experiment was
conducted. Table 4 (shown in the page below) describes the results of the experiment.
The data collected from Table 4 is important in the consideration of the batterys free fall
acceleration. To determine the batterys acceleration, one must apply the formula for gravity.
Gravity is calculated through a revision of the formula Distance = Gravity(Time 2). By
revising the equation gravity equals: g = 2d/t2
Table 4
The time it takes a battery to fall two meters and the acceleration of its free fall
Table 4 presents the data collected during the final tests 10 trials. It is obvious that some
of the data collected in the 10 trials were collected incorrectly. As previously stated gravity (on
Earth) is a constant acceleration of 9.81 m/s 2. With this known acceleration it is then possible to
disregard trials one, five, eight, and ten because their accelerations are greater than the actual
acceleration of gravity. Due to this it is possible to focus on the more accurately collected data
of trials two, three, four, six, seven, and nine. Table 5 (shown in the page below) describes the
results of the experiment considering only trials two, three, four, six, seven, and nine.
When the trials with an acceleration of less than 9.81 m/s 2 are independently considered
the free falls time it took to drop 2 meters is 0.7 seconds. Applying 0.7 seconds yields an
average acceleration of 8.16 m/s2. It is important to note that the time collected was to the best
of the experimenters ability. Human error due to the reaction time between releasing the battery
and recording the batterys free fall time undoubtedly occurred. At the time of this final test
there were no methods taken into account to accommodate for this aside from performing the test
multiple times. It is also the experimenters belief that human error as described above resulted
in the inaccuracies of the time collected for trials one, five, eight, and ten of this experiment.
Table 5
The amended time it takes a battery to fall 2 meters and its acceleration
To overcome the inaccuracies found in this test produced by experimental error standard
deviation can be applied.
By applying it the variance around a known measure (for this
experiment time) can be to the known average quantity. The formula to calculate standard
deviation is:
For this experiment the results of the formula state that the accepted value is within the + of the
average values. Using the information found from Table 5 the standard deviation for the time it
took for the battery to fall was found. The result found was + 0.053 seconds. This result
signifies that the time it took for the battery to fall two meters based on the experimenters data
collection was within + 0.053 seconds of the (Table 5 calculated) average time of 0.703 seconds.
Adding 0.053 seconds to 0.703 seconds yielded an acceleration of 6.99 m/s 2. Subtracting 0.053
seconds from 0.703 seconds yields an acceleration of 9.46 m/s 2. From this it can be stated that
the time it took for the battery to fall two meters was between 0.65 seconds and 0.756 seconds
with an acceleration between 6.99 m/s2 and 9.46 m/s2.
Prior to the final test being performed the experimenter hypothesized that due to airresistance the acceleration of gravity in their lab would be 7.5 m/s 2. The average acceleration of
gravity found in this experiment using the amended trials was 8.16 m/s 2. The percentage of error
between the hypothesized value and the experimental value was 8%.
The data found in this lab was collected by measuring distance over time. By correctly
measuring the time it took for an object to travel a designated length the experimenter was able
to determine the actual speed a baseball was thrown and compare this their hypothesized speed.
For test two the experimenter rolled a soccer ball on a tile floor and measured the time it took the
ball to travel two, four, and six meters. By collecting the time at each interval the experimenter
was able to find the balls speed and acceleration. From this correctly found data the initial force
applied to the ball was calculated. Without first measuring the time it took the ball to travel with
certainty it would not have been possible to correctly find these rates, and know that the ball was
pushed with a consistent amount of force during each of its trials. Lastly, the time it took for a
battery to fall two meters was measured. This final test was conducted ten times. With multiple
trials the experimenter was able to determine the number of incorrectly measured times versus
experimental times that correctly fit into my acceptable range. By comparing the acceptable
range the experimenter was then able to determine the acceleration (shown by gravity) of the
battery as it fell. This resulted in concluding the difference of acceleration due to air-resistance
versus the acceleration of the battery without air-resistance.
Ensuring that accurate data collection was obtained was essential to the success of this
lap report. Without collecting the appropriate data for this lab report distance and time errors
in results are bound to arise.
With error comes the inability to correctly research ones
hypothesis, repeat the conclusions of the experiment (which therefore would mislead any future
experimenters wishing to repeat the experiment in the given settings), and provide incorrect
results. To properly collect data in ones experiment it is vital that all measuring devices are
calibrated and used repeatedly during the experimentation phase. If new measuring instruments
are introduced it is then incumbent for the experimenter to note the change in instrument. By
ensuring these steps correct data collection is obtainable, and with correct data collected comes
greater experimental and result success for this and any other experiment.
Graphs
Graph 1
Graph 2
Data Collection
Predictions
A. What's the fastest you think you can comfortably pitch in miles per hour?
I believe I could comfortably pitch a baseball 65 miles per hour.
B. What are the reasons for your prediction?
I base this prediction on my age, overall health, and that elite baseball
pitches can pitch a baseball between 90-100 miles per hour.
C. Would you call your prediction a guess, a hypothesis, or something in between?
Explain why.
My prediction is a little bit of both. Based on the evidence of my overall
health, and age I would estimate I pitch a baseball at approximately 65
miles per hour. I dont know if this will be the outcome.
2. Collecting data on pitching speeds
Name
Distance t1(s)
t2 (s) t3(s)
Avg. t (s)
Avg.
Avg. speed
(m)
speed
(miles/h)
(m/s)
Experiment 15 m
0.58 0.62
0.60
0.6 s
25 m/s 56 mi/h
er
Assistant 1
15 m
0.54 0.59
0.51
0.55 s
27 m/s 60 mi/h
Assistant 2
15 m
0.57 0.52
0.62
0.57 s
26 m/s 58 mi/h
Compare your results to your predictions. How well did you predict?
I think my prediction was fairly accurate. I predicted I could pitch a ball at
approximately 65 mi/h. My true average speed was 56 mi/h. This resulted
in a difference of nine mi/h, and a percent error of 16 %.
3. Calculations with computers and spreadsheets
How do the average times and speeds calculated by your spreadsheet program
compare to the manual calculations you made on the same data in Part 2? If they
differ in any way try to explain why.
The velocity found through the experiment was different than the velocity
that I predicted for myself and two other experimenters. The difference
was due to the actual rate the others and I could actually through the ball
versus the hypothesized guess that we could through the ball at.
4. Measuring the motion of a bowling or other large ball
What do you predict will happen to the distance the ball moves as a function of
time? Will the ball move at a steady speed, speed up, or slow down after it
leaves the bowler's hand? Why?
I believe the balls velocity will slow down upon leaving the bowlers hand.
I believe this because I predict that the balls greatest velocity will be its
initial velocity. Once it has left the bowlers hand I predict that due to
friction the ball will slow down and eventually come a rest.
Time:
Time:
Time:
2-m Distance
4-m Distance
6-m Distance
Trial 1
0.74
1.49
1.95
Trial 2
0.88
1.62
2.21
Trial 3
0.75
1.53
2.24
Average time:
0.79
1.55
2.13
Graph your data for the distance your bowling ball traveled as a function of the
rolling-time of the ball. This graphing should be done both by hand and on the
computer. Dont forget to discuss these in your conclusions.
A. Compare the shape of the graphs you produced in Section 4 with the sketches
shown in the lab manual. Would you say that the distance increases with time, t?
Decreases with time? Is it a linear function of t? Is it proportional to t? Explain.
The graph shown above represents the distance in ratio to time for each trial.
By looking at the graph I would argue that it is not a linear function because
there is not a constant ratio between distance and time. Visually the graphs
look almost like parabolas. This would signify that balls velocity is increasing
and the amount of time needed to cover a distance is decreasing. I believe
this occurred because the graph is showing the velocity of the ball for only a
short time period while friction has yet to slow the ball down to a rate leading
to zero.
B. How do the results compare with the prediction you made in Part 4? Were you
surprised?
I was very surprised. I originally predicted that the balls greatest velocity
would have been its original. According to the graph, this was not the
case. According to the graph, the balls velocity is increasing; thus the
initial velocity was not the fastest velocity for the ball.
C. What do you think would happen to the slope, m, of the graph if the ball had been
rolled faster? Would it increase? Decrease? Stay the same?
I believe if there was greater velocity the ball the slope would have been
more curved and representative of a parabola for the time and distance
segment that was represented.