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During an independent lab project you conduct an experiment to determine the acceleration due to gravity. You conduct one trial by following your procedure and obtain a result of 9.8 +/- 0.5 m/s2. With the reference value of g = 9.801 +/- 0.001 m/s2. Is your result accurate? Is it precise compared to the reference value? What steps could you take to improve your experiment.

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Casey Durgan
Casey DurganLv2
10 Nov 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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.

Theory: Topics that you should be familiar with are: significantfigures, least count and estimated fraction, systematic and randomerrors, accuracy versus precision, percent difference and percenterror. These topics should have been covered in class already (orperhaps in an introduction to the lab manual or in a handout). Itis assumed that the instructor has discussed how to use the massbalance, etc.
Introduction: The goal of section I of this experiment is tomeasure (to the correct least count and estimated fraction) andcalculate (to the correct number of significant figures) thedensity of a metal ball and compare it to a table of accepteddensities (?=7.8x103 kg/m3).
To accomplish this goal keep in mind that: ? = m/V and Vsphere =(4/3) p r3
In the space below create a data table, show your calculations indetail, and compare your measured answer to accepted values givenabove. (Would you calculate a percent error or a percentdifference?)
1
II. Is g (the acceleration due to gravity) a constant? If so, whatis it?
1) SetuptheFree-FallApparatusasdemonstratedbytheinstructor.
2)MeasurethetimeittakesforthemetalballtofallthroughthesuggesteddisplacementsshowninDataTable 1. Be sure to do 4 trials for each fall and take the averageof your time and displacement. For each trial measure thedisplacement and record your results as precisely as possible. Becareful how you measure the displacement!
Data Table 1
Displacement (meters) Time
Trial 1
___.40___ m .281 s
______.40_ m .284 s
___.40____ m .283 s
____.40___ m .285 s
Average Displacement =.40 m Average time .0285 s
Trial 2
____.60___ m .357 s
____.60___ m .358 s
_____.60__ m .347 s
____.60___ m .347 s
Time (seconds)
Average Displacement = .60 Average Time = .352
Trial3
_.80____ m .402 s
_.80____ m .401 s
_.80______ m .402 S
_.80___ m .401 s
Average Displacement = .80 m Average Time =.401 s

Trial4
__ 1.00____ m .454 s
___1.00____ m .453 s
___1.00____ m .463 s
___1.00____ m .453 s
Average Displacement = 1.00 m Average Time =.455 s
3)PlotDisplacement(usetheaveragedisplacement)asafunctionofTime(usetheaveragetime)usingacomputer software that you know the best. (Does Displacement orTime go on the “vertical” (or y) axis? Make sure that you label theaxes of your graph properly and give the graph a descriptivetitle.), Please include (0,0) point.
4)UsetheCurveFitFunctiontotrytofindthecurvethatistheclosestfitforthegraph.Whichofthefollowing curve types gives the best fit? Try each to findout.
a) linear fit? b) quadratic (power 2)? c) exponential? d) Power?
The curve with the correlation coefficient (R) closest to 1 has theclosest fit. (e.g. 0.997 is better than 0.956)
5)Printthecurvewiththeclosestfit(oneforeachmemberofthelabgroup).Besureyourgraphincludesthe equation for your fit.
6)Canyoudeterminetheexperimentalaccelerationofgravityfromthisgraph?Explainhowandshowyourwork.
7)Ifalinearfunctionisnotthebestfitofyourplotfromstep3),howwouldyouplotdisplacementandtimeso that the resulting plot is linear? Explain. (Ask your instructorfor a hint if you are not sure of what to do, but be sure to thinkabout it for a while before you ask.)
3
8)Printacopyofthegraphforeachlabpartnershowingalinearfittoyourdataandproperlylabeledaxes.
9)Canyoudeterminetheexperimentalaccelerationduetogravityfromthisgraph?Explainandshowyourwork.
10) How do your experimental values of “g” compare with theaccepted value (g = 9.80 m/s2) for the acceleration of gravity?Give a mathematical comparison using what you learned aboutmeasurements previously. (Show work)
4
Question and further procedures
1. What is the greatest source of error in performing theexperiment? Is this error random or systematic? Explain.
2. At this point you should have calculated g in two different ways(A quadratic graph, and a linear graph). Which technique do youthink is best? Do all two techniques give the same answer? If not,which technique do you think has the most error?
3. How might you modify your procedures to determine whether or notg depends on the mass of the falling object? Do the experiment andcalculate g using your favorite technique.

You are a student in a science class that is using the following apparatus to determine the value of g. Two photogates are used. (Note: You may be familiar with photogates in everyday living. You see them in the doorways of some stores. They are designed to ring a bell when someone interrupts the beam while walking through the door.) One photogate is located at the edge of a table that is 1.00 m above the floor, and the second photogate is located directly below the first, at a height 0.500 m above the floor. You are told to drop a marble through these gates, releasing it from rest a negligible distance above the upper gate. The upper gate starts a timer as the ball passes through its beam. The second photogate stops the timer when the ball passes through its beam. (a) Prove that the experimental magnitude of free-fall acceleration is given by gexp = (2?y)/(?t)2, where ?y is the vertical distance between the photogates and ?t is the fall time. (b) For your setup, what value of ?t would you expect to measure, assuming gexp is the standard value (9.81 m/s2)? (c) During the experiment, a slight error is made. Instead of locating the first photogate even with the top of the table, your not-so-careful lab partner locates it 0.50 cm lower than the top of the table. However, she does manage to properly locate the second photogate at a height of 0.50 m above the floor. However, she releases the marble from the same height that it was released from when the photogate was 1.00 m above the floor. What value of gexp will you and your partner determine? What percentage difference does this represent from the standard value of g?

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