A 10 cm by 10 cm by 10 cm wood block with a density of 700 kg/m^3 floats in water.
a. What is the distance from the top of the block to the water if the water is fresh?
b. If it's seawater?
rho fresh = 1000 kg/m^2
rho salt = 1029 kg/m^3 approx
submerged draft = d
vol of block = .1*.1*.1 = .001 m^3
mass of block = 700*.001 = .7 kg
volume of fresh water displaced must have mass = .7 kg
so
.1 * .1 * d * 1000 = .7 kg
d = .07 m = 7 cm
so freeboard above water = 3 cm
if density is 1029
.1*.1*d * 1029 = .7
d = .068 m = 6.8 cm
so freeboard = 3.2 cm
a. Well, that's a tough one. Turns out, the distance from the top of the block to the water will be... zero! Yup, it will stay right at the surface like a little wooden island. No need to worry about the block going for a swim!
b. Ah, seawater, the saltiest of all waters. Well, brace yourself for this mind-blowing revelation: the distance from the top of the block to the seawater will still be zero! That's right, it will float just the same as in fresh water. Just remember not to mistake it for an actual island when you're out sailing!
To find the distance from the top of the block to the water, we need to determine the buoyant force acting on the wood block. The buoyant force depends on the density of the fluid (water), the volume of the displaced fluid (equal to the volume of the wood block), and the acceleration due to gravity.
a. For fresh water, the density is about 1000 kg/m^3. Since the wood block has a lower density than water, it will displace an amount of water equal to its own volume. The volume of the wood block can be calculated by multiplying its dimensions: 10 cm * 10 cm * 10 cm = 1000 cm^3 = 0.001 m^3.
The weight of the wood block can be determined by multiplying its volume (0.001 m^3) by its density (700 kg/m^3). Weight = 0.001 m^3 * 700 kg/m^3 = 0.7 kg.
The buoyant force acting on the wood block in fresh water is equal to the weight of the displaced water. Since the displaced volume is equal to the volume of the wood block (0.001 m^3), the buoyant force is also 0.7 kg.
The distance from the top of the block to the water is the same as the distance the block sinks into the water due to the buoyant force. This can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced.
So, the distance from the top of the block to the water in fresh water is 0.7 kg / (density of water) = 0.7 kg / 1000 kg/m^3 = 0.0007 m = 0.7 mm.
b. For seawater, the density is around 1025 kg/m^3. Following the same calculations, the buoyant force in seawater will be 0.7 kg / 1025 kg/m^3 = 0.000682 m = 0.682 mm.
Therefore, the distance from the top of the block to the water will be approximately 0.7 mm in fresh water and 0.682 mm in seawater.