A cube weight 15N in air and 20N when totally immersed in water. Find the value of the cube of the density.
Please proof read what you wrote. It has got to be backwards.
the density of the cube I suppose :)
displaces water weighing 5 Newtons
5 N = 1000 kg/m^3 * 9.81 * Volume
so
Volume = 5.1* 10^-4 m^3
mass = 20 N in air I think/9.81
= 2.04 kg
so
rho = 2.04 kg/5.81*10^-4 m^3
= 3.51 * 10^3 kg/m^3
or 3.51 times density of water
(rock?)
rho = 2.04 kg/5.1*10^-4 m^3
= 4 * 10^3 kg/m^3
To find the value of the cube of the density, we can use the concept of buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object. This buoyant force depends on the density of the fluid.
Given that the cube weighs 15N in air and 20N when totally immersed in water, we can infer that the buoyant force acting on the cube in the water is equal to the difference in weight between the cube in air and the cube in water.
Buoyant force = Weight in air - Weight in water
Buoyant force = 15N - 20N
Buoyant force = -5N (negative sign indicates that the buoyant force acts in the opposite direction of gravity)
Since the volume of the cube remains the same regardless of whether it is in air or water, the negative buoyant force of 5N corresponds to the weight of the volume of water that the cube displaces.
Now, let's apply Archimedes' principle: the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced.
Density of water = mass / volume
To calculate the volume of water displaced by the cube, we can use the equation:
Volume of water displaced = (Weight of water displaced) / (Density of water)
Since the weight of water displaced is 5N and the density of water is approximately 1000 kg/m³, we get:
Volume of water displaced = 5N / 1000 kg/m³
Volume of water displaced = 0.005 m³
Since the volume of the cube remains the same as the volume of water displaced, we can conclude that the volume of the cube is also 0.005 m³.
Now, to find the density of the cube, we can use the formula:
Density = mass / volume
Since the volume is 0.005 m³, we can rearrange the formula to solve for mass:
Mass = Density × Volume
Now we have all the information we need to find the value of the cube of the density:
Cube density = (density of cube)³ = ((mass of cube / volume of cube) × (volume of cube))³ = (mass of cube)³
But since we don't have the exact mass of the cube, we can't calculate the exact value of the cube of the density with the given information.