1. a State Archimedes' principle.
(a) State Archimedes' principle.
(b) Consider a cylinder of cross-sectional area A and height h immersed in a liquid of density ρ. The top of the cylinder is level with the surface of the liquid. The bottom of the cylinder is a distance h below the surface.i Give an expression for the pressure in the liquid just underneath the cylinder at point P.ii Give an expression for the upwards force on the underside of the cylinder due to the pressure in the liquid at a depth, h.iii State an expression for the downwards force on the cylinder due to the atmospheric pressure, Po.iv Derive an expression for the buoyancy force; that is, the net upwards force on the cylinder due to the liquid.v By finding an expression for the weight of the liquid displaced by the cylinder, show Archimedes' principle to be true.vi If the cylinder just floats, what must its density be?
(c) A block of wood of density 1.1×103 kgm−3 has a mass of 100 kg. It is completely immersed in water.i Determine the net force on the block of wood.ii Does the block of wood float or sink?