Physics 121 11/19/10 Prof. E. F. Redish 1 11/19/10 1 Physics 121 11/19/10 2 Physics 121 11/19/10 3 Physics 121 Ei= Ef12mvi2+12Ii2+ mghi=12mvf2+12If2+ mghfmgh =12mvf2+12If2= v / Rmgh =12mvf2+12IvfR 2=12mvf2+12IR2 vf2=12m 1+ImR2vf2vf2=2gh1+ImR2Physics 121 11/19/10 Prof. E. F. Redish 2 11/19/10 4 Physics 121 11/19/10 5 Physics 121 V (m3) m (kg) VmVm==11/19/10 6 Physics 121Physics 121 11/19/10 Prof. E. F. Redish 3 11/19/10 8 Physics 121 2211AWAW=11/19/10 9 Physics 121 11/19/10 10 Physics 121 F A The force takes its direction from A. FpFpAA==Pressure has no direction! It acts in all directions at once!Physics 121 11/19/10 Prof. E. F. Redish 4 11/19/10 11 Physics 121 T T T T 11/19/10 12 Physics 121 11/19/10 14 Physics 121 F = p0 A (could be outside air pressure or due to external weights) A fluid of uniform density p0A pA W = mgPhysics 121 11/19/10 Prof. E. F. Redish 5 11/19/10 15 Physics 121 gdpppAApAdgpAApVgpAApmgFFupdown+==+=+=+=0000A d * We assumed uniform density. Is this OK? For water ( ~ 1000 kg/m3) yes. For air ( ~ 1 kg/m3) OK for meters — not km. 11/19/10 16 Physics 121 d1 d2 p1 p2 11/19/10 17 Physics 121 d1 d2 p1 p2 mgVgAddgFAgdpgdpFAppFgdppgdppApApFnetnetnetnet===+==+=+==)()()(1210201220210112The buoyant (upward) force = the weight of the fluid
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