calc 122 lab report

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



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)



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.



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.

calc 122 lab report

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