Question

Archimedes's principle is a useful tool to model the depth to which continents sink into the mantle rock. Consider a continental crust of average density are shown in Figure 1-17. The continental crust sinks a distance d into the mantle rock, with density at its top strata of A. Surrounding the continent are oceans of average density p=1030 kg/m' and depth he. Beneath the ocean is the oceanic crust of thickness hor which has a density sufficiently different from the mantle that it should be considered separately from the mantle. Using the data in the figure, calculate the depth d that the continent sinks into the mantle. Ocean h=6.6km, P =1,030 kg/m Continent Oceanic Crust h -6.0 km, Poc=2,900 kg/m Poc=2.800 kg/m2 Mantle P=3,300 kg/m

Answer 1

The solution of the problem is given below

sobition Dilen continent hoa 6.6km, b= 1030kg/m² loc=2800 kohm hoc bookm, loc= 2900 kolmis breanic wust Mantle Pm23300 kg/m3 king law of floatation Weight of Net upthrust by Continent ocean, - oceanic crust and mantle Let 'A' be the area of cross section of continent & H be the average height. then H- hot hoc t d debth that o the continent sinks into o manite mwing mg = mogt magt mmg mass of mass of masof nass of continent og e displaced - displacea me I mot mot mm be AH = Phot + Po hot - td A a l (hot houtd) = Photlochoet ind d (Pm-fee) = Pecho thao) - Poho-ho, hal ocean displaced Occanić nantes

Page No. Date de lec (hotho) - Poho-lochon - lm -lee - 2800(6.6+6) -1030x6.6 - 2900x6.0 - 3300 - 2800 11082 500 d = 22.2 km