Practice - The Burns Home Page

ArchimedesArchimedes is said to have discovered his principlein his bath while thinking how he might determinewhether the king’s new crown was pure gold orfake.Gold has a specific gravity of 19.3, somewhathigher than most metals, but a determination ofspecific gravity or density is not easy with airregularly shaped object.ArchimedesA 14.7 kg crown has an apparent weight of 13.4 kg whensubmerged in water. Is it gold?The apparent weight of the submerged crown, w`, equalsits actual weight, w, minus the buoyant force, F B .w'w FobjectBVg watergVw'w Fw w' FWe can find the specific gravity :B objectwaterBgVobjectVg w w Vg F w w'water water BArchimedes realised that if the crown is weighed inair and weighed in water, the density can dedetermined.objectwater N 14.7kg9.8kgw 11.3w w' N N 14.7kg9.8 13.4kg9.8kg kg This corresponds to adensity of 11,300 kg/m 3(that of lead)Alternate solutionLet’s find thevolume of thedisplaced water(this is also thevolume of thecrown)We can nowdetermine thedensity of the crownw w' F14.7kg 13.4kg g gVcrownmVcrowncrown14.7kg1.310mkg113073mB waterwatergVwaterwater3 kg 1.3kg 1.000 x 103 V m 1.3kgVwater 3 kg 1.000 x 103 m 3 31.310m3 3waterPractice• A lead weight is fastened to a largestyrofoam block and the combinationfloats on water with the water levelwith the top of the Styrofoam blockas shown.• If you turn the Styrofoam + Pbupside down, what happens?A) It sinks B)styrofoam C)PbstyrofoamPbPbstyrofoamD)styrofoamPbPage 9