h=1 cm 1.03 g/cm 1.43 g/cm
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1 ES 43/614: Introduction to Oceanograpy Solution Homeork # 1) Tere i uge lake it contant ater dept 1 cm and an extenion of 5 km. Te ater in te lake i till and unperturbed (noting move). No e drop object, B, C in te lake and ait until everyting become till and quiet again. Uing te buoyancy principle determine o many cm ill te object be ticking out above or te ater level. Ti time oever te denity of te ater i not uniform but it increae it dept (te lake i tratified). Te denity at te urface i 1.3 g/cm 3 and it increae linearly it dept o tat at te bottom it i 1.43 g/cm 3. (ume tat te object ill remain in te ame orientation a tey are o belo en put into te ater. Te denity of ater and of te object are on in Figure 1, togeter it teir eigt.) Figure 1 B =1 cm C =5 cm =1 cm =1.4 g/cm 3 =.95 g/cm 3 =1.6 g/cm 3 urface = 1.3 g/cm 3 WTER bottom = 1.43 g/cm 3 Preure at te bottom of te lake i given by te integral of denity it dept. Denity in ti cae increae linearly it dept = b =
2 g p = g d = g ( ) d = g = g Let u aume tat part of te object ill be above ater WTER Level p = g 1 ub p = g p = p p 1 p = g Lake Bottom We kno tat:
3 p = p p = p 1 g g g = g g g g = = if ub ub = You could ave arrived ub > at ti by applying te buoyancy principle. Ti equation i aying tat te eigt of ater diplaced equal te eigt of te object. Ten part of te object i belo te ater and you need to account for te eigt above te object a ell. need to modify are equation etup. WTER Level p 1 = g p = g p 3 = g p = p p p 1 3 p = g Lake Bottom We kno tat te preure under te block at te bottom mut equal te one everyere ele.
4 p = p p p = p 1 3 g g g = g g = ub if g g = g S = gain you could ave < ub arrived at ti by applying te buoyancy principle. Ti equation i aying tat te eigt of ater diplaced equal te eigt of te object. Ten part of te object i above ater e need to apply te previou equation etup.
5 SOLUTIONS: if you plug in te number.5 cm under ater cm under ater.489 cm above ater For additional credit: at ould appen if object C a a pere it diameter 5 cm intead? Ue ame equation a lat time but kno ue te linear denity equation intead of contant. Te volume of a ubmerged pere i: Vub = ub π r 3 ub No apply te buoyancy prubciple: ub dvub CC = = ub d V d f( ) You ant to olve for ub. Solve ti integral and find te function on te rigt and ide. Ten plot te function f and find te ub for ic f i equal to te left and ide. Tat ill give you te value of o muc te pere i belo te ater. tract tat from te diameter and find tat te pere i above ater of.9 cm.
6 ) Eart Pyiograpy ee map 3) We did not cover in cla te eart geomagnetic field. Hoever baed on te lecture note and reading of te text book aner te folloing: a) Wat i te magnetopere and y i it important? Te magnetopere i a region of pace (above te atmopere) dominated by te Eart magnetic. It i important a it prevent te ig energy carged particle of te olar ind from entering te atmopere. Hoever, ome ig energy carged particle from te olar ind leak into te magnetopere and are te ource of te carged particle trapped in te Van llen belt. b) Wat are te Van llen Belt? fundamental property of magnetic field i tat tey exert force on moving electrical carge. Tu, a magnetic field can trap carged particle uc a electron and proton a tey are forced to execute a piraling motion back and fort along te field line. Te Eart i urrounded by to region of particularly ig concentration of carged particle called te Van llen radiation belt. Te inner and outer Van llen belt are illutrated in te figure (lecture note). Te primary ource of tee carged particle i te tream of particle emanating from te Sun tat e call te olar ind. c) I te frequency of te magnetic reveral a contant? No it i not contant but varie. We do not kno te exact proce tat determine tee reveral. For additional credit: aurora urora are caued by ig energy particle from te olar ind tat are trapped in te Eart magnetic field (in particular in te Van llen Belt). tee particle piral back and fort along te magnetic field line, tey come don into te atmopere near te nort and out magnetic pole ere te magnetic field line diappear into te body of te Eart. Te delicate color are caued by energetic electron colliding it oxygen and nitrogen molecule in te atmopere. Ti excite te molecule, and en tey decay from te excited tate tey emit te ligt tat e ee in te aurora. Te trengt of te aurora i not very trong ence e cannot ee ten during day ligt. urora at Non-Viible Wavelengt Te colliion of trapped carged particle it atmoperic molecule caue pectacular effect in te viible pectrum, but tee excited molecule can alo emit radiation in oter avelengt band.
7 EURSIN PLTE NORTH MERICN PLTE FRICN PLTE CRIBBEN PLTE COCOS PLTE NZC PLTE SOUTH MERICN PLTE
8 continental elve elf break (ignificant increae in lope) fracture one eamount abyal plain mid-oceanic ridge abyal plain ubduction one continental elve deep-ea trenc volcanic arc deep-ea trenc abyal plain ubduction one mid-oceanic ridge tranform fault tranform fault elf break (ignificant increae in lope) primarily granite primarily baalt
9 Ti part of te map i probably produced by ip batymetry, ere a te ret i done by atellite batymetry. It a line and it i mooter. ot pot
10 PCIFIC PLTE PCIFIC PLTE INDO-USTRLIN PLTE NTRTIC PLTE PCIFIC PLTE
11 volcanic arc deep-ea trenc volcanic arc ubduction one ubduction one eamount abyal plain deep-ea trenc tranform fault primarily granite deep-ea trenc abyal plain eamount primarily baalt fracture one tranform fault elf break (ignificant increae in lope) continental elve tranform fault
12 Great barrier reef Mountain rie Plateau Hot pot
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