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27 Nov 2019

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 âverticalâ (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 âgâ 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.

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 âverticalâ (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 âgâ 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.