Geomorphic History of the Allen Creek Drainage Basin, Jefferson ...

Description

• fiche de synthèse - matière potentielle : local bedrock formations
• cours - matière potentielle : road

Geomorphic History of the Allen Creek Drainage Basin, Jefferson County, Wisconsin Brad Blumer August 4, 2006 University of Wisconsin – Whitewater Internship with The Friends of the Allen Creek Watershed Under the direction of Dr. Peter Jacobs

• galena dolostone
• glacial sediments
• wisconsin glaciation
• laurentide ice sheet
• creek drainage basin
• larger areas of permafrost collapse than the active glacier
• stratigraphic section
• study area
• bedrock

Sujets

• Formation
• Jacobs
• Jefferson County
• Wisconsin Department of Natural Resources
• Waukesha County, Wisconsin
• Abstract
• Université du Wisconsin
• Míchigan
• Wisconsin

Informations

• Publié par: choun
• Nombre de lectures: 22
• Langue: English

Extrait

Physics 161:Black Holes:Lecture 5:12 Jan 2011

Professor: KimGriest

5 MoreSpecial Relativity; Gravitational Time dilation 5.1 Timedilation and length contraction by spacetime diagram Last time we saw how to calibrate spacetime diagrames.We can use that result to derive the famous time dilation:moving clocks run slow to stationary observers. Numerically we can calculate for time dilation for event B, considering starting a clock at the origin 20202 220 0 (event A). Δs=−Δt+ Δx=−Δt+ Δxa clock tick at event B, Δ. Fort=t, Δx=x, Δt=t. In 0 theOEvent B occurs, lab frame:x= Δx=vΔt, and time occurs att= Δt. InO, the moving frame, 0 00 Δx=x= 0 since events B and A occur at the some place (OSois not moving in its own frame). √ 02 22 22 20 2 0 −Δt+ 0 =−Δt+ Δt v=−(1−v)Δt, or Δt= Δt /1−v=γΔtis the time dilation you. This learned before in special relativity. One can similarly find out the length contraction you learned about in SR. If you remember the derivation, you will remember that it is more tricky than the time dilation calculation.The reason for the trickiness is easy to see in the spacetime diagram.Consider the origin as point A and a ruler of length 0 aIt lies along thelaid out on a spacecraft with its far end at point B. How does that look?xaxis, which 0 we have just seen how to find (the set of points which all havetNow draw the sideway hyberbola= 0. of all proper distancesa. Ifwe just project the point B onto thexaxis we find the wrong answer, that the ruler lookslongerBy length of ruler in the lab framein the lab frame.What have we done wrong? we mean the distance between the two ends measured at the same lab frame timetthe distance. Thus between points A and B is not the distance we are after.We need to follow point A up in time until it 00 reaches the same timetWe know theas point B has.taxis has the same angle from the 45line as the 0 A-B segment, so we can just go along thetaxis until we get as high as point B. Now the length of the ruler as measured in the lab frame is the difference inxWeof the two ends measured at the same time. see the ruler is shorter as measured in the lab frame as expected.

5.2 Otherspecial relativity you need to know This class has special relativity as a prerequisite, so I’m not going to cover much more.However, you should look over the book to refamiliarize yourself with several topics.For example, you should 2 22 22 understandE=mc. Infact, your need to know that the real equation isE= (mc) +(pc) , where 2 22 pWithis the momentum.c= 1 this is more suggestively written:m=E−p, and we see that the rest mass is an invariant in much the same way that the intervaldsalso should be familiar withis. You 2 relativistic energy and momentum:E=mγc, andp=mvγTaylor expanding the relativistic. Try

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