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PHL200Y1 Final: January-April Lecture Study Notes for Final Exam

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coralelephant816

21 Apr 2011

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Jennifer Whiting

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Phl200 january-april final exam notes: parmenides: the all is one, plato"s self critic of his theory of forms with parmenides and zeno, plato is subjecting his theory of forms to criticism. 129a eidos (form) of likeness and unlikeness: co-presence of opposites: something can be both like and unlike (eg. tallness and shortness) Tallness itself cannot be both tall and short, therefore, a form cannot have a co-presence of opposites. 2 possibilities for the forms: a) things we can grasp or b) the properties that reside in these things. 2 major ways in which plato and aristotle differ: metaphysics and conception of forms. The forms act as causal accounts for why a person has a certain property (tall, short, beautiful, intelligent, etc. : aristotle"s solution to plato"s theory of forms: the categories. Being in a position: is lying, is sitting. The categories are not just words (linguistic) but also ontological (concerned with existence: example.

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Related Questions

This geometry task may be helpful for devising amathematicalprocedure for the next lab.

A right triangle has legs ofknown lengths 2L and h. Find thelength of the line segment x whichis parallel to side h. Explainyour reasoning. Image in weblinkbelow:

http://paer.rutgers.edu/194/Downloads/194LAB07.pdfRY4bB71082bfFuqzISDrWGDOWfNgGl208qJNQTAhpzWjb_ahDlhGHPLz19S1Eq95&q=cache%3AnpyQu9LlzykJ%3Apaer.rutgers.edu%2F194%2FDownloads%2F194LAB07.pdf%20this%20geometry%20task%20may%20be%20helpful%20for%20devising%20a%20mathematical%20procedure%20for%20the%20next%20lab.%20A%20right%20triangle&docid=5c8a26db354186a31ce6383

POSTSCRIPT: EFFECTS OFASSUMPTIONS

The marbled murrelet is asmall bird that lives in the PacificNorthwest where old-growthforests are close to the sea. It nests inthe forests and feedsoffshore. It is now highly endangeredthroughout its range, whichextends from Northern California toAlaska.

These birds are extremelyvulnerable to loss of their habitat,because they nest exclusivelyin the same old-growth coniferoustrees that are prime targets forlogging. Considerable efforts havebeen made to protect the speciesby restricting timber operations inthe areas in which they areknown to nest. Scientists predicted thatthe population should growback. However until recently naturalistswere puzzledand

dismayed because thepopulation of marbled murrelets did notseem to be recovering oreven stabilizing.

A recent study suggests thereason why this testing experimentin conservation did not confirmthe prediction. The scientistsoverlooked an important assumption:murrelets can also be threatenedby man's activity at sea.Overfishing has severely reduced thepopulation of small,energy-rich fish that murrelets rely upon formost of theircalories.

Climate change of uncertainorigin may have also disrupted thefood chain, and El Nino currentsmay have changed the distributionof the phytoplankton that formsthe base of all marine life.

Further efforts to preservethe marbled murrelet must be basedon accurate assumptions aboutthe origin of their difficulties.

Could naturalists have betterconsidered their originalassumptions years ago? What would yousay?

A mass m rests on a frictionless horizontal table and isconnected to rigid supports via 2 identical springs each of relaxedlength L0 and spring constantk. Each spring is stretched to a length L considerable greater thanL0. Horizontal displacementsof m from its equilibrium position are labeled x and y.

(Diagram insert didn't work, all it really tells you is that xis on the axis of the springs and y is perpendicular to thesprings)

a) Write down the differential equation of motion (i.e.,Newton's Law) governing small oscillations in the xdirection.

b) Same as a but in the y direction (assume that y <<L).

c) In terms of L and L0, calculate the ratio of the periods ofthe oscillations along x and y.

d) If at t=0 the mass m is released from the point x = y = A0with zero velocity, what are its x and y coordinates at any latertime t?

---------------------------

So, I started with just ma = -2kx for a, leading me to thedifferential equation x''(t) + (2k/m) x = 0.

Then I did basically the same thing with y.

However, when I get to c, there's my problem - I don't knowhow I could write any of this in L and L0.

Also, b doesn't really make sense to me because if y is smallwhen compared to L, it seems like there shouldn't be anyoscillation in the y direction.

The answer the back of the book shows for c and d are:

c) Tx/Ty = (1 - L0 / L)1/2

d) x(t) = A0cos( (2k/m)1/2 t)

y(t) = A0cos( (2k(L-L0)/mL)1/2 t)

I have no idea how they got to these answers. Can somebodyhelp me? It has something to do with springs already beingstretched, but it seems they are making an assumption somewherethat I don't understand.

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

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 Â± 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 Â± 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.