Q.a cube of wood 20cm on each side,floats in water so that 30% is above the surface of the water,and 70% is below.what is the density of the wood(justify the answer)
i.what mass of lead mass has to be placed on the top of the block of wood,so that it wi;; just be totally submerged.
ii.what volume of lead mass has to be placed on the top of wood.so that it will just be totally submerged.
iii.instead of placing weights on the top of the wood,how much force would have to be exerted on the wood to submerge it.
densities in gm/cm3: water-1.0,Iron-7.8,lead-11.3
Correction: Dc = 0.7g/cm^3.
To find the density of the wood, we can use the fact that the cube floats in water with 30% above the surface and 70% below. This suggests that the density of the wood is equal to the density of water, as it is able to displace an equal volume of water and thus experiences an equal buoyant force.
Now, let's proceed to answer the other questions:
i. To determine the mass of lead required to fully submerge the cube, we need to calculate the buoyant force acting on the lead. The buoyant force has to equal the weight of the lead for it to be fully submerged.
The weight of the cube fully submerged in water is equal to the weight of the displaced water, which can be calculated by finding the volume of the cube below the water surface and multiplying it by the density of water. Since 70% of the cube is below the water, the submerged volume can be found as (70/100) * (20 cm)^3.
The weight of the cube submerged in water is equal to the weight of the displaced water, which is (submerged volume) * (density of water).
Now, to find the mass of the lead needed, we equate the weight of the lead to the weight of the cube:
(mass of lead) * (acceleration due to gravity) = (submerged volume) * (density of water) * (acceleration due to gravity)
Plugging in the values, we have:
(mass of lead) * (9.8 m/s^2) = ((70/100) * (20 cm)^3) * (1.0 g/cm^3) * (9.8 m/s^2)
Solving for the mass of lead, we get:
mass of lead = ((70/100) * (20 cm)^3) * (1.0 g/cm^3)
ii. To find the volume of the lead mass required to fully submerge the cube, we divide the mass of lead obtained above by the density of lead:
volume of lead = (mass of lead) / (density of lead)
iii. To determine the force required to submerge the cube, we need to calculate the net force on the cube. This net force will be equal to the weight of the cube minus the buoyant force acting on it.
The weight of the cube can be calculated by finding the mass of the cube and multiplying it by the acceleration due to gravity.
The buoyant force acting on the cube is equal to the weight of the displaced water, which is (volume of the cube) * (density of water) * (acceleration due to gravity).
Hence, to calculate the force required to submerge the cube, we subtract the buoyant force from the weight of the cube:
force = (weight of the cube) - (buoyant force) = (mass of the cube) * (acceleration due to gravity) - ((30/100) * (20 cm)^3) * (1.0 g/cm^3) * (9.8 m/s^2)
Note: Remember to convert all units to a consistent system, such as meters or centimeters, before performing any calculations.
Vb = 0.7 * 20^3 = 5600 cm^3. = Vol. below surface.
Vb = (Dc/Dw) * Vc. = 5600
(Dc/1) * 20^3 = 5600
Dc = 5600/20^3 = g/0.7 cm^3 = Density of
the cube of wood.
1. Mass of cube = 20^3cm^3 * 0.7g/cm^3=
5600 Grams. = 5.6 kg.
To totally submerge the block, its' density must be increased to 1:
(5600+g)/20^3 = 1.0
5600 + g = 20^3
g = 20^3-5600 = 2400 Grams added.
2. V = 2400g * 1cm^3/11.34g = 212 cm^3.
3. The force = The wt. of the water
displaced:
8000cm^3 * 1g/cm^3 = 8000g = 8 kg of water displaced.
F = m*g = 8kg * 9.8N/kg = 78.4 N.