GGRB02H3 Lecture : Scale

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blueserval947

2 Feb 2012

School

UTSC

Department

Geography

Course

GGRB02H3

Professor

Rajyashree Narayanareddy

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Document Summary

No such thing as scales pre-existing, how are they made. Useful to spatially order of our world. Used by both human and physical geographers who assumed that the world is inherently hierarchically compartmentalized into global, national. Space through the idea of scale; hierarchy of the world. Kant in contrast argued that neither time nor space were objective, real things. Rather they are subjective constructs through which humans make sense of the world. For kant, order is the result not of categorization imposed on it by our brains (so no material basis) Disagree with predetermined natural order (geographical units) Time and space are not real/have no materialistic basis to kant. Building upon kant geographers put forth idealist notion of scale: mental images useful to thinking about no material basis to scale articulated a kantian view of scales: they are subjective artistic. Peter haggett measured scales through orders of magnitude : distances to demarcate difference scales pioneered spatial science tradition within geography.

Related Questions

Prob. 2. Two converging lenses, A witha focallength of +2.0cm and B

with a focal length of +5.0cm, areplaced 14cmapart. An object is

place 3.0cm to the left of lensA.

A) Use graphical methods, to scale, toconstruct theray diagram

with a measurement of the final imageposition andheight; and

B) Use the lens equation determinethecharacteristics of the

image.

Prob. 3. A prism with angles 45Â°,45Â°, and 90Â° is tobe used to turn a

beam of light through a 90Â° angle.What is theminimum index of

refraction for the material of theprism that willgive the total

internal reflectionneeded?

Prob. 4. A tarantula is sitting 4.5min front of aconcave spherical mirror

with radius of R =1.4m.

A) Construct a ray diagram to scaleshowing theobject, image and

the mirror. Determine graphicallythecharacteristics of the image.

B) If the image is 5.0cm tall, howhigh is thetarantula?

Prob. 5. A Youngâs double slitapparatus has theslit separation of

0.12mm and the distance between theslits and theviewing

screen is 55 cm.

A) If monochromatic light ofwavelength Î» = 550x10-9mpasses

through the slits, calculate thedistance betweenthe central

(bright) fringe and the adjacentbright fringe.

B) Now imagine that you are usingX-rays, Î»=1x10â9minstead of

visible light in this experiment. Whatwould theslit separation

need to be in order to have thedistance betweenthese first two

bright fringes be1cm?

Prob. 6. Acombination of blue light (n=1.60) andred light (n=1.50)is

incident on the surface of a flatglass plate.Because of dispersion

there are two refracted rays. Draw adiagram showingthe incident

and both refracted rays, indicatingthe red and theblue rays.

Calculate the angle between therefracted blue andred rays.

Extra Credit

An important question to consider when thinking about globalwarming is, "If the ice sheets near the poles melt, how much willthe sea level rise?" This seems like a difficult question, giventhe odd shapes of both the ice sheets and the oceans. But there aresome accurate approximations that allow the answer to be estimatedfairly accurately with reasonably simple calculations.

The critical idea is that both the thickness of the ice sheets andthe amounts of the sea-level rise are extremely small compared tothe radius of the earth. The radius of the earth is about 2/p x 107m -- more than 6000 kilometers. The ice sheet thicknesses we willbe concerned with are single digit miles and the sea level riseswill be in dozens of feet. As a result, in thinking about them, wecan essentially ignore the curvature of the earth. We can imaginepeeling the map of the earth off a globe and flattening it out (bymaking cuts, not by stretching it, so that we preserve the area).Then, both the ice and the sea level rise can be treated as right(not tilted) cylinders (though with funny shaped bases and tops).Since we know that the volume of a right cylinder is the area ofthe base times the height, we can easily estimate all the volumeswe need. A schematic picture of this approximation (with the heightof the ice mass greatly exaggerated -- you couldn't see it if Ididn't) is shown below. The error in these approximations is on theorder of the height of the cylinder considered divided by theradius of the earth; a very small number.
a. Assume that (after flattening the surface of the earth in ourimaginations) the ice sheet to be considered covers an area, A, andhas a thickness, d. The oceans currently cover about 75% of theearth's surface, and note that the surface area of a sphere is 4pr2where r is the radius of the sphere.

Generate an equation that will allow you to calculate h, the heightthe ocean levels will rise due to the melting of a an ice sheet interms of A, d, and r

b. As shown in the combined satellite photo on the right (fromGoogle Earth), Greenland is covered by a sheet of ice. This ice hasbeen measured to have a mean thickness of about 2 km. Recentobservations indicate that this ice sheet is beginning to retreat-- that it is melting at an accelerating rate.

Using the depth of the ice sheet and the scale given on thepicture, estimate how much sea level rise would be produced by themelting of the entire ice sheet lying on Greenland. (Note: You caneasily look this information up on the web. But the goal of thisproblem is in part to develop your estimation skills for thepurpose of building your ability to decide for yourself whether anygiven piece of information you find on the web is reasonable orbogus.)

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.

GGRB02H3 Lecture : Scale

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