A wood cube 0.20m on each side has a density of 730kg/m3 and floats levelly in water.
Part A
What is the distance from the top of the wood to the water surface?
Part B
What mass has to be placed on top of the wood so that its top is just at the water level?
A. Hb=(Do/Dw)*Ho=(730/1000)*0.2=0.146 m
Below the the water.
Ha = 0.2 - 0.146 = 0.054 m Above water.
B.Mc=V*D = 0.2^3m^3 * 730kg/m^3=5.84 kg.
= Mass of cube.
(Mc+Mo)/Vc = Dw(Density of water).
(5.84+Mo)/0.008 = 1000kg/m^3
5.84 + Mo = 8
Mo = 2.16 kg = Mass of object to be added.
To answer Part A, we need to determine the fraction of the wood cube's volume submerged in water. Let's use the formula:
Fraction submerged = density of object / density of fluid
Given that the density of the wood cube is 730 kg/m^3 and it floats levelly in water, which has a density of 1000 kg/m^3, we can substitute the values into the formula:
Fraction submerged = 730 kg/m^3 / 1000 kg/m^3
Fraction submerged = 0.73
Since the wood cube is floating levelly in water, the fraction submerged is equal to the fraction of the wood cube's height submerged. Since the cube has sides of 0.20 m, the height submerged can be calculated as follows:
Height submerged = fraction submerged * side length
Height submerged = 0.73 * 0.20 m
Height submerged = 0.146 m
Therefore, the distance from the top of the wood to the water surface is 0.146 m (or 14.6 cm).
Now, to answer Part B, we need to determine the mass that needs to be placed on top of the wood cube in order for its top to be just at the water level.
Let's assume the mass that needs to be added to the wood cube is m kg. We know that the volume of the submerged part of the wood cube is equal to the volume of water displaced by it.
Volume submerged = m / density of fluid
Since the density of water is 1000 kg/m^3 and the volume submerged is given by the height submerged multiplied by the base area of the wood cube:
Height submerged * base area = m / density of fluid
Substituting the known values:
0.146 m * (0.20 m)^2 = m / 1000 kg/m^3
Simplifying the equation gives us:
0.00584 m^3 = m / 1000 kg/m^3
Multiplying both sides by 1000 kg/m^3:
5.84 kg = m
Therefore, the mass that needs to be placed on top of the wood cube in order for its top to be just at the water level is 5.84 kg.
Part A:
To find the distance from the top of the wood cube to the water surface, we need to determine how much of the wood cube is submerged in the water.
First, let's find the volume of the wood cube. The volume of a cube is calculated by multiplying the length of one side cubed, so in this case, the volume of the cube is (0.20m)^3 = 0.008m^3.
Next, we'll find the weight of the wood cube in air. Weight is calculated by multiplying mass by the acceleration due to gravity, which is 9.8 m/s^2. Using the formula weight = density x volume x gravity, we have weight = 730 kg/m^3 x 0.008 m^3 x 9.8 m/s^2 = 56.896 N.
Since the wood cube is floating levelly in water, its weight is balanced by the buoyant force acting on it. Thus, the buoyant force is equal to the weight of the wood cube, which is 56.896 N.
We can determine the volume of water displaced by the wood cube using Archimedes' principle. According to Archimedes' principle, the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object. Therefore, the volume of water displaced by the wood cube is equal to the volume of the wood cube itself.
The volume of water displaced is given by the formula volume = mass / density, where density is the density of water. The density of water is generally equal to 1000 kg/m^3. Thus, the volume of water displaced is equal to 0.008m^3.
Since the wood cube is fully submerged, the distance from the top of the wood cube to the water surface is equal to the height of the wood cube, which is 0.20m.
Part B:
To find the mass that needs to be placed on top of the wood cube so that its top is just at the water level, we need to determine the additional weight required to balance the buoyant force acting on the wood cube.
Since the wood cube is floating levelly in water, the buoyant force is equal to the weight of the wood cube. Therefore, to balance the buoyant force, the additional weight placed on top of the wood cube should be equal to its weight, which is 56.896N.
Using the formula weight = mass x gravity, we have 56.896N = mass x 9.8 m/s^2.
Solving for mass, we find mass = 56.896N / 9.8 m/s^2 ≈ 5.8 kg.
Therefore, approximately 5.8 kg of additional mass needs to be placed on top of the wood cube so that its top is just at the water level.