Consider a cube of side "H" totally immersed in a fluid, with the top of the cube at depth "h." DERIVE Archimedes' Principle by first calculating the difference in fluid pressure between the bottom and top of the cube. SHOW your steps.
Starting with the fact that water at the top surface will push the cube down (with force Ftop say) and water at the bottom will push the cube up (with Force Fbottom say), then the total upward force which is called the buoyant force is the difference as,
Fbuoyant = Fbottom - Ftop
we can now substitute the values of force by the definition of pressure(F = P*A)
A is the area top and bottom (A = H2)
Fbuoyant = Pbottom*A - PtopA
From the formula of hydrostatic pressure(P = gh)
Fbuoyant = ghbottom*A - ghtopA
Fbuoyant = gA(hbottom - htop)
according to given conditions, htop= h; hbottom= H+h
Fbuoyant = gA*(H+h - h)
Fbuoyant = gAH
where AH is volume of the cube, say V
Fbuoyant = gV
Fbuoyant = gA*(H)
Consider a cube of side "H" totally immersed in a fluid, with the top of the...
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