Elementary Principles 20 - 3.9 (cont'd) WB WA h b2 hs 2 h2...

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3- 4 3.9 (cont’d) W h s B h b h ρ 2 After object is jettisoned W A 2 2 Let V A = volume of jettisoned object = W g A A (5) Volume displaced by boat : VA h h db p b 22 2 =− di (6) Archimedes = E Wd B VgW 2 Subst. for V d 2 , solve for hh pb W pgA B wb −= ( 7 ) Volume of pond water : hVV h W pg W wp pd A p B w A A 56 7 2 bg bg bg ,& 2 solve for 2 p w BA p h pw pA p V WW h Ap g g A ⇒= + + (8) + + for in 7 solve for subst. 8 b w p B A B h V A W W W 2 , (9) ( a) Change in pond level ()() ( ) 83 21 11 0 WA AW A A pp W A W p Wp p W Ag p p p p gA ρρ < ⎡⎤ →< ⎢⎥ ⎣⎦ the pond level falls (b) Change in boat level W Ag pA V A p p A A A p A pW b A p A W p b 94 5 0 0 111 0 + L N M M O Q P P = F H G I K J +− F H G I K J F H G I K J L N M M M M O Q P P P P > > > bgbg ±²³ ± ² ´´ ³ ´´ the boat rises 3.10 (a) bulk 33 3 2.93 kg CaCO 0.70 L CaCO L CaCO L total kg / L == 205 . (b) WV g bag bulk
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