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PHY 1321 Lecture 5: Measuring techniques

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School
University of Ottawa
Department
Physics
Course
PHY 1321
Professor
Andrzej Czajkowski

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PHY 1321 Full Course Notes
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Document Summary

Every experiment in the elementary laboratory involves measurement. The kind of measurement will depend on the particular experiment, but there are certain basic measurements which are common to many different experiments. The following notes are intended to be a guide to the correct use of some common laboratory instruments and to suggest good measuring techniques. We use electronic balances which are accurate to on their last digit ( g). Make sure to level and zero the balance before using it. Time measurements can be made using an electronic timer, which is accurate to 0. 01s. When measuring a time interval it is necessary to add an uncertainty of 0. 2s to 0. 5s. due to the human reaction time. Hence to achieve higher accuracy for a period of oscillation, measurements should be made over many periods (e. g. , over 100 periods). Example: period of oscillation of a mass-spring system.

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Related Questions

Could you please proofread and correct scientifically andgrammatically my work, thanks ^_^

Here itis:
The percentage error was found to be 0.186% and 6.66%respectively.

This implies that the predicted value of the freefall accelerationis fairly accurate while the predicated value of deceleration isnot as much. The encountered errors were due to severalexperimental and human limitation was that the experiment involved.The experimental limitation was due to the uncertainty of theclinometer which was ± 0.5o.

I.e. In our calculation, a difference of 0.5o can lead to adifference of 40 - 80 cm in height as shown below:

The human limitations was due to the human eye being unable todetect the exact point on the track at which the gondoladecelerates. This is because the braking happened very quickly.This adds an uncertainty to the location of deceleration when theangels are being measured.

In addition, the human ability cannot decide on the exact period oftime at which the gondola freefalls or decelerates. This is due tothe human reaction speed being unable to exactly determine thestart time of the momentary freefall and deceleration. The timetaken for humans to react cannot be measured thus it cannot besubtracted from the findings to get an accurate timing.

All of these limitations that have affected the accuracy of theresults could be avoided to some extent by marking the exact zonesrequired on the track of the giant drop as well as using anelectronic angle measurer to measure the angles . Additionally, theusage of an electronic timer to measure periods of the freefall anddeceleration is also suggested.

During the analysis, finding an average to the deceleration in theaccelerometer reading (using Logger Pro) was only estimated usingthe human naked eye. This is because an average could not be takenelectronically. Thus, there is also some uncertainty involved inthe theoretical value.

NOTE:

The value for freefall acceleration obtained from thevideo-analysis technique was 9.754 ± 0.3237 m/s2. 9.754 m/s2 has apercentage error of :
0.469%

This value indicates it is fairly accurate and can be used as aconforming result to the theoretical value. The error involved isdue to the fact that the video was shaking, thus plotting thevelocity/ time graph of the gondola at different times wasnegatively affected; although the axes was roughly re-set at everyframe.

3. 3 Stratosphere-troposphere exchange

The rate of exchange of air between the troposphere and thestratosphere is critical for determining the potential of variouspollutants emitted from the surface to reach the stratosphere andaffect the stratospheric ozone layer. One of the first estimates ofthis rate was made in the 1960s using measurements of strontium-90(90Sr) in the stratosphere. Strontium-90 is a radioactive isotope(half-life 28 years) produced in nuclear explosions. It has nonatural sources. Large amounts of 90Sr were injected into thestratosphere in the 1950s by above-ground nuclear tests. Thesetests were banned by international treaty in 1962. Following thetest ban the stratospheric concentrations of 90Sr began to decreaseas 90Sr was transferred to the troposphere. In the troposphere,90Sr is removed by wet deposition with a lifetime of 10 days (bycontrast there is no rain, and hence no wet deposition, in thestratosphere). An intensive stratospheric measurement network wasoperated in the 1960s to monitor the decay of 90Sr in thestratosphere. We interpret these observations here using a 2-boxmodel for stratosphere-troposphere exchange with transfer rateconstants kTS and kST (yr-1) between the tropospheric andstratospheric reservoirs. The reservoirs are assumed to beindividually well-mixed.



Let mS and mT represent the masses of 90Sr in the stratosphere andin the troposphere respectively. Observations of the decrease inthe stratospheric inventory for the period 1963-1967 can be fittedto an exponential mS(t) = mS(0)exp(-kt) where k = 0.77 yr-1.

1. Write mass balance equations for mS and mT in the 1963-1967period.

2. Assuming that transfer of 90Sr from the troposphere to thestratosphere is negligible (we will verify this assumption later),show that the residence time of air in the stratosphere is tS =1/kST = 1.3 years.

3. Let m'T and m'S represent the total masses of air in thetroposphere and the stratosphere, respectively. Show that theresidence time of air in the troposphere is tT = tS (m'T/m'S) = 7.4years. Conclude as to the validity of your assumption in question2.

4. Hydrochlorofluorocarbons (HCFCs) have been adopted asreplacement products for the chlorofluorocarbons (CFCs), which werebanned by the Montreal protocol because of their harmful effect onthe ozone layer. In contrast to the CFCs, the HCFCs can be oxidizedin the troposphere, and the oxidation products washed out byprecipitation, so that most of the HCFCs do not penetrate into thestratosphere to destroy ozone. Two common HCFCs have trade namesHCFC-123 and HCFC-124; their lifetimes against oxidation in thetroposphere are 1.4 years and 5.9 years, respectively. There are noother sinks for these species in the troposphere. Using our 2-boxmodel, determine what fractions of the emitted HCFC-123 andHCFC-124 penetrate the stratosphere.