calc 122 lab report
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7/18/2019 Calc 122 Lab Report
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Pranav Reddy
Rebecca Gelfer
Preston Eni
Sept 3, 2015
Physics 150
Data Analysis and Measurement Uncertainty
Part One—Reaction Times
Measurement of Your Reaction Times
1.
2. Rebecca’s mean was the lowest, however we cannot be sure that her reaction time was
the fastest because her reaction time has a range from 0.34 to 0.36 seconds while
Preston’s range is from 0.34 to 0.38 seconds, meaning it is possible for Preston to be
faster than Rebecca given our data set.
Formulate and Test a Prediction About Your Lab Section’s Reaction Times
1. The groups we compared were women and men; the average reaction time for women
was 0.42 seconds with an uncertainty of 0.04 seconds while the average reaction time for
men was 0.345 seconds with an uncertainty of 0.007 seconds.
2. We propagated the error using the means and uncertainties calculated from individual
data points; the uncertainty would have been the same if we had recalculated it using the
raw data.
Trial 1 (s) Trial 2 (s) Trial 3 (s) Trial 4 (s) Trial 5 (s) Mean (s)Pranav 0.38 0.37 0.36 0.36 0.38 0.37±0.01
Rebecca 0.31 0.32 0.35 0.37 0.36 0.35±0.01
Preston 0.33 0.32 0.32 0.43 0.39 0.36±0.02
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3. We can determine with certainty that the reaction time for men is faster than the reaction
time for women. Evolution may have selected for men with faster reactions as hunting, a
primarily male activity in prehistoric times, advantaged those members. In contrast, the
same selection may not have occurred for women as their daily activities likely did not
require faster reaction times.
Part Two – Water Draining
Measure the Time it Takes For Water to Drain Out of a Container
1. The quadratic best fits our data set. The equation is h(t)= 0.0001125t^2+ (-0.01913)t+
0.8129 where h is height in meters and t is time in seconds. The h(t) function estimates
the height at time 0 to be 0.556 m; a meter stick was not available for use, but the number
seems to make sense given an estimation of the height of the pipe that we did.
2.
Height of Water (m) vs Time(s)
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3. The water pressure at the top of the pipe is greater so the water goes down faster and the
slope is thus steeper. As the water level decreases, the water pressure decreases and thus
the water goes down slower and the slope is less steep, hence the shape of the graph.
Further analysis
1. We split up the graph into 15 second intervals beginning at 20 seconds. The segment that
was best modeled was the second segment, from 35 to 50 seconds. It had RMSE value of
0.137 (as compared to 0.247, 0.150, 0.205 for first, third, and fourth segment
respectively). The fluid was draining over that time interval and it was approximately in
the center of our data collection range.
2. Coefficient improved during the middle of the data collection; this might be because
Bernoulli’s equation doesn’t explain edge cases very well, like the times at the beginning
and the end of the data collection, while it does model the average case of draining fairly
well.
Conclusion
In the first part of the experiment, we measured the reaction times of individuals and
attempted to determine if there was a statistically significant difference between men and
women. We found there was a significant difference, including our uncertainty values, that men
reacted more quickly than women. Possible errors that may have influenced our data include
differences based on gender to the mechanism of measuring reaction times (i.e. male eyes
finding green light easier to detect than those of women) and variation in computers and
processing abilities.
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In the second part of the experiment, we attempted to determine the height of a cylinder
of water using the weight and rate of draining of the cylinder. We modeled the draining of the
water to a quadratic equation and found a fairly good fit (RMSE = 0.0024). Possible sources of
error include oscillations in the YZ plane caused by collisions with the work surface upon which
the sensor was positioned. The exit hole may also not have been perfectly circular which could
have caused irregularities in the water flow out.
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