Question

3. Archimedes' Principle states that the buoyant force on an object partially or fully submerged in a fluid is equal to the weight of the fluid that the object displaces. For an object of density po floating partly submerged in a fluid of density pf, the buoyant force is given by F P19 SA(y)dy, where g is the acceleration due to gravity and A(y) is the area of a typical cross-section of the object. The weight of the object is given by W = Pog S-n" A(y)dy. y=L-h y=0 h - y=-h (a) Show that the percentage of the volume of the object above above the surface of the liquid is 100% f - Po PF (b) The density of ice is 917 kg/m3 and the density of seawater is 1030 kg/m3. What percentage of the vlue of an iceberg is abo ve water? (c) An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts?

Answer 1

a) using Archimedes principle, webave w a ļ Algs dj . > ܘܒܕܢ A cy) dy L-h = Po S. A cy) dy se s A cy dy ch ņ -h is equal to total volume of RH s of this ean the object . s A cy) dy = 6 total -h whilst Lits is , L-h L-h If Į A cys dy I s A cysdy - If Į Algody ch CS Scanned with CamScanner

Qah L-h But Vabove water I Algdy L-h 4 total A cy) dy total - Pf Vabove eater 0 => so v total Il of 3 total (Se - Po) - > Cf Yaraveneiter ? Vabove water px - So >> = total .. Percentage volume above waith Vabove wath Vtotal 7100 = ( Pf ç -Po o) x100 (Ans) b) = 917 kg / m3 f 10 30 kg/m3 CS Scanned with CamScanner

percentage volume above water f-Po X100 an (1030-917) X100 1030 = 10.97% ñ 11% Cans) e it No. When the ice floats on water, displaces its own weight weight of water Let y be the volume of water displaced. Ons melting the ice will exactly this volume v of water and just fill up the space e which the form ex ice displace. CS Scanned with CamScanner