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PHL100Y1 Lecture : Hume 1.02.2011.docx

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byzantiummuskrat913

29 Feb 2012

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If you assume things will be like there were like in the past you can claim, but why would you make an assumption. There is no reason to think that what has passed is relevant at all. What you experience according isn t causal but constant conjunction. We have causal beliefs for which we are better off for having. He is worried why it is that we make the assumption that the future is like the past. Here is a case of conjunction you have experienced. When you try to cross the street you wait till the opposite light turns red, but you have to wait a sec in case some jerk crosses. Reason why drivers stop is because they are caused to by a presence of a red light. If you throw an egg against a wall it will break. When an a is followed by a b eventually when you see an impression of an.

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Related Questions

The given explanation for solving the problem did not go into agreat deal of detail on deriving the 2nd equation: v^2=2ukgX. I'massuming that this equation is generated from an equation forconstant acceleration V^2= Vo^2 + 2a(X-Xo) and understanding thatthe sum of the horizontal (or vertical forces) is SumF=ma and theonly force acting on the mass is friction force, therefore,uk(m1+m2)g=(m1+m2)a and ukg=a.

My questions is this:
In the explanation, there seems to be an assumption that Vo is 0.Why can this assumption be made?

I'm probing because I've been following the explanation to answerthe question, and I continue to get it wrong.

Thank you,
SJ

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.