Buoyancy of block?

Question

i knwo this is a simple question but for some reason i cant get my head around it..grrr

a ten kilogram block of metal measuring 12 cm x 10cm x10cm is suspened from a scale and immersed in water. the 12 cm dimension is vertical and the top of the block is 5 cm bekiw the surface of the water.
a)what are the forces acting on the top and bottom of the block? (use po of 1.0130x10^5N/m^2

b)what is the reading of the spring scale?

c)show that the buoyant force equals the difference between the forces at the top and the bottom of hte block.

thanx for ur help

Answer 1

Part of this problem has to do with hydrostatic pressure - the pressure in fluids that aren't moving.

For our purposes, the important equation is:

P = D g H + Pa

http://en.wikipedia.org/wiki/Hydrostatic_pressure#Hydrostatic_pressure
http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html

P is the pressure (in Pascals or N/m^2) at a depth of H (meters) below the surface of a fluid with density D (in kg/m^3) in a gravitational field of strength g (about 9.8 m/s^s on the surface of the Earth). Pa is the atmospheric pressure above the fluid.

In our case, the area of the top and the bottom are the same, at 10x10 cm^2 = 0.01m^2

We know the depth, the density, the air pressure (assume one atmosphere :-), and g so we can compute the pressures at the top and bottom of the block.

Force = pressure x area so we can compute the two forces.

The two forces differ. The bottom force is pushes up and is higher than the top force pushing down. The block experience a net push from the water equal to the difference.

The pressure at the top and the pressure at the bottom differ by:

delta pressure = (D g Hb + Pa) - (D g Ht + Pa)
= D g (Hb - Ht)

where Hb and Ht are the depths of the bottom and top of the block, respectively.

So the two forces differ by: D g (Hb-Ht) A.

but (Hb-Ht) is just the height of the block and height times area is just the volume.

So the two forces differ by D g V.

But D V is just the mass of water in volume V, the volume displaced by the block. So D g V is the weight of that water.

The weight of the displaced water is thus equal to the buoyant force, the net force of the water on the block, which addresses part c.

http://en.wikipedia.org/wiki/Buoyancy

The net weight of the submerged block, as registered on the scale, is the weight of the block in air minus the buoyant force.

Answer 2

C maintains to be the comparable (as quickly as the block is totally underwater) because of the fact the quantity of the block that's decrease than water will advance the buoyancy will advance. I.e. buoyancy rigidity = the burden of water displaced by the article. as quickly as the block is a hundred% underwater then the buoyancy will stay consistent (assuming your no longer talking approximately loopy deep ocean stages the place water may be compressed at extensive depths).