A solid weighs 6.4 kg in air and 5.6 in water. Find the density of the solid
To find the density of the solid, we can make use of Archimedes' principle, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Given that the solid weighs 6.4 kg in air, we can say that its weight is 6.4 kg times the acceleration due to gravity (g ≈ 9.8 m/s²), which gives us a weight of W_air = 6.4 kg × 9.8 m/s² = 62.72 N.
Now, in water, the solid weighs 5.6 kg. Using the same calculation, we find that its weight is W_water = 5.6 kg × 9.8 m/s² = 54.88 N.
Since the weight difference between the two measurements represents the buoyant force acting on the solid when submerged in water, we can calculate this difference:
Buoyant force = W_air - W_water = 62.72 N - 54.88 N = 7.84 N
The buoyant force is equal to the weight of the water displaced by the solid. We can use this information to calculate the volume of water displaced by the solid using the density of water.
The density of water is typically 1000 kg/m³.
Density = mass/volume
We can rearrange this formula to solve for volume:
Volume = mass/density
Volume of water displaced = (buoyant force due to water) / (density of water) = 7.84 N / (1000 kg/m³) = 0.00784 m³
Now, since the solid weighs 6.4 kg, we can calculate its volume using the same formula:
Volume of solid = mass / density of the solid = 6.4 kg / density of the solid
So, the volume of the solid is 6.4 kg / density of the solid.
Finally, we can calculate the density of the solid by equating the volume of the solid to the volume of water displaced:
6.4 kg / density of the solid = 0.00784 m³
Now we can solve for density of the solid:
density of the solid = 6.4 kg / 0.00784 m³ ≈ 816.33 kg/m³
Therefore, the density of the solid is approximately 816.33 kg/m³.
Archimedes said Force up = weight of fluid displaced.
It displaced 6.4-5.6 = 0.8 kg of water
so its volume is
V = .8 kg (m^3/1000kg) = 8*10^-4 m^3
so its density is (6.4 /8)10^4 kg/m^3
=8000 kg/m^3
might be iron