PHL100Y1 Lecture : humes 2.docx

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rubyclam306

9 Apr 2012

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No such thing as chance, ignorance if the real cause of any event has the same influence on the understanding and begets a like species of belief or opinion. Moral ideas are obscure and confusing chief obstacle to our improvement in the moral or metaphysical sciences is the obscurity of the ideas and ambiguity of terms. Difficulty of math is length of interferences. No ideas in metaphysics that are more obscure or uncertain than power, force, energy, necessary connexion. All ideas are nothing but copies of our impressions or that it is impossible for us to think of any thing which we have not felt with our senses. When we look at external objects and consider the operation of causes we are not able to discover any power which binds the effect to the cause. We find that one does follow the other.

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?

Learning Goal: To understand length contraction and timedilation.

An inertial frame of reference is one in which Newton's laws hold.Any frame of reference that moves at a constant speed relative toan inertial frame of reference is also an inertial frame. Theproper length l_0 of an object is defined to be the length of theobject as measured in the object's rest frame. If the length of theobject is measured in any other inertial frame, moving with speed urelative to the object's rest frame (in a direction parallel tol_0), the resulting length l is given by the length contractionequation

l = l_0\sqrt{1-\frac{u^2}{c^2}} ,

where c is the speed of light. Similarly, if two events occur atthe same spatial point in a particular reference frame, and anobserver at rest in this frame measures the time interval betweenthese two events, the time interval so measured is defined to bethe proper time Delta t_0. When the time interval is measured inany other inertial frame, again moving with speed u relative to thefirst frame, the resulting time interval Delta t is given by thetime dilation equation

\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{u^2}{c^2}}} .

a. Suppose that you measure the length of a spaceship, at restrelative to you, to be 400 \rm m. How long will you measure it tobe if it flies past you at a speed of u = 0.75c?
Express the length l in meters to three significant figures.

b. The spaceship from Part A has a large clock attached to itsside. This clock ran at the same rate as your watch when you werein the same reference frame. How much time Delta t will pass onyour watch as 80 \rm s passes on the clock attached to theship?
Express your answer in seconds to three significant figures.

c. Two spaceships, named A and B, are flying toward each other withrelative speed 0.800c. If the captain of ship A fires a missile,counts 10.0 \rm s on his watch, and then fires a second missile,how much time Delta t will the captain of ship B measure to havepassed between the firing of the two missiles?
Express your answer in seconds to three significant figures.

d. The captain of ship B knows that ship A uses 2-m-long missiles.She measures the length of the first missile, once it has finishedaccelerating, and finds it to be only 0.872 \rm m long. What is thespeed u of the missile, relative to ship B?
Express your answer in meters per second to three significantfigures. Use c = 3 \times 10^8 \; \rm m/s.

Please answer fully... thank you

MAC, Inc. (the company you work for) has decided to move forwardwith a feasibility
study for a product it wishes to manufacture and sell. This productis a particle launcher that should have the capability, for everyactivation, of launching two particles into the air at twodifferent times and at two different angles of elevation, in anautomated fashion so that they both land at the same distance fromthe launch point at the same time. For example, let P1 and P2 betwo particles, let T1 and T2 be two times, and let theta1 andtheta2 be two angles of elevation. Once activated, the launchershould be able to operate so that particle P1 is launched at timeT1 with an angle of elevation theta 1, and particle P2 islaunched
at time T2 with an angle of elevation theta2.
The launcher must be configured by a technician, prior to eachactivation, so that the
initial speed is set for the launcher, and the distance from thelauncher to where both
particles will land is set. For each activation of the launcher,the initial speed will be the
same for both particles. Once the technician has set the initialspeed and desired distance,
the launcher must calculate the angles of elevation to use and howmuch time to wait in
between particle launches. Then, when the technician activates thelauncher, both
particles will be launched at the appropriate angles of elevationand at the appropriate
times so that they both land at the configured distance from thelauncher at the same time.
The launcher, based on its calculations, will change the angle ofelevation to be ready for
the second particle launch. The launcher, however, must flash awarning for the
technician if the information the technician used to configure thelauncher does not result
in a two-particle launching solution.
Certain assumptions must be made. It is assumed that that launchercan always change
the angle of elevation to get ready for the second particle launchfaster than the time
delay calculated for the second particle launch. It is assumed thatthe units for speed are
meters per second, that the units for distance are meters, and thatgravity is 9.8 meters per
second squared. It is assumed that gravity is the only force actingon the motion of the
particles after launch, and that there is no wind to be considered,so that the particles land
at a point exactly in line with the direction the launcher ispointed.
The questions that must be answered and written up in anengineering report are as
follows:
1. Given the initial speed and desired landing distance for theparticles, find the
mathematical expressions that must be used to find 1, 2, and thetime delay
between particle launches.
2. Determine under which conditions the launcher will not be ableto perform the
operation requested, and will consequently flash a warning to thetechnician.
3. Each particle launched will follow a path of motion that isparabolic. Show that
the vertex of the parabola for each particleâs path occurs at thesame distance from
the launcher.
4. Along the path of each launched particle, there will be amaximum curvature.
Find that maximum curvature for each launched particle.

PHL100Y1 Lecture : humes 2.docx

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