A board that is 20 cm wide, 5 cm thick, and 3 m long has a density of 350 kg/m^3. The board is floating partially submerged in water do density 100 kg/m^3. What fraction of the volume of the board is floating above water?;
Density of water = 1000kg/m^3.
V = 3m * 0.20m * 0.05m = 0.03 m^3=Vol.
of board.
1 - (350/1000) = 0.65 = 13/20.
Well, this is a buoyant question! To determine the fraction of the volume of the board that is floating above water, we can use Archimedes' principle. According to this principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
First, let's calculate the volume of the board. Since we know its dimensions, the volume is 20 cm * 5 cm * 300 cm = 30000 cm^3.
Now, let's convert this volume to cubic meters. Since 1 cm^3 is equal to 10^-6 m^3, the volume is (30000 cm^3) * (10^-6 m^3 / 1 cm^3) = 0.03 m^3.
To find the volume of the board that is submerged in water, we need to determine the weight of the water displaced by the board. The volume of the submerged portion is equal to the weight of the board divided by the difference between the densities of the board and water.
The weight of the board can be calculated by multiplying its volume by its density: (0.03 m^3) * (350 kg/m^3) = 10.5 kg.
The volume of the submerged portion is therefore (10.5 kg) / (350 kg/m^3 - 100 kg/m^3) = 0.042 m^3.
Finally, to find the fraction of the volume above water, we subtract the submerged volume from the total volume of the board: (0.03 m^3 - 0.042 m^3) / 0.03 m^3 = -0.04.
Uh-oh, it looks like the board is floating above water more than it's even there! You might want to check your calculations or double-check the provided information. It seems there's a non-physical result here. Let's hope the board doesn't fly off into the sky!
To find the fraction of the volume of the board that is floating above water, we need to compare the density of the board to the density of water.
1. Calculate the volume of the board:
Volume = width * thickness * length
Volume = 20 cm * 5 cm * 3 m
- Convert the width and thickness to meters:
Volume = 0.2 m * 0.05 m * 3 m
Volume = 0.03 m^3
2. Calculate the mass of the board:
Mass = density * volume
Mass = 350 kg/m^3 * 0.03 m^3
Mass = 10.5 kg
3. Determine the buoyant force:
Buoyant Force = density of water * volume of submerged portion
- The submerged portion is equal to the volume of the board times the fraction submerged.
Buoyant Force = 100 kg/m^3 * (0.03 m^3 * fraction submerged)
4. The buoyant force is equal to the weight of the displaced water, which is equal to the weight of the board:
Buoyant Force = weight
weight = mass * gravity
where gravity ≈ 9.8 m/s^2
Buoyant Force = 10.5 kg * 9.8 m/s^2
Buoyant Force = 102.9 N
weight = 102.9 N
5. Set the buoyant force equal to the weight to solve for fraction submerged:
102.9 N = 100 kg/m^3 * (0.03 m^3 * fraction submerged) * 9.8 m/s^2
Simplify the equation:
102.9 N = (0.03 m^3 * 980 N/m^3 * fraction submerged)
Divide both sides by (0.03 m^3 * 980 N/m^3) to solve for fraction submerged:
fraction submerged = 102.9 N / (0.03 m^3 * 980 N/m^3)
fraction submerged ≈ 0.111
6. The fraction of the volume of the board that is floating above water is equal to 1 minus the fraction submerged:
fraction floating above water = 1 - fraction submerged
fraction floating above water = 1 - 0.111
fraction floating above water ≈ 0.889
Therefore, approximately 88.9% of the volume of the board is floating above water.
To figure out what fraction of the volume of the board is floating above water, we need to calculate the volume of the board that is submerged in water and then subtract that from the total volume of the board.
First, let's calculate the volume of the board. The board has a length of 3 m, a width of 20 cm (which is equal to 0.2 m), and a thickness of 5 cm (which is equal to 0.05 m).
The volume of the board is given by the formula: volume = length × width × thickness.
So, the volume of the board is: 3 m × 0.2 m × 0.05 m = 0.3 m^3.
Next, let's calculate the volume of the board that is submerged in water. The density of the board is 350 kg/m^3, and the density of water is 100 kg/m^3.
The fraction of the volume of the board that is submerged can be calculated using the formula: fraction submerged = (density of board) / (density of water).
So, the fraction submerged is: 350 kg/m^3 / 100 kg/m^3 = 3.5.
This means that 3.5 times the volume of the board is submerged in water.
Now, let's calculate the volume of the board that is submerged: volume submerged = fraction submerged × volume of the board.
Therefore, the volume submerged is: 3.5 × 0.3 m^3 = 1.05 m^3.
Finally, to find the fraction of the volume of the board that is floating above water, we subtract the volume submerged from the total volume of the board and then divide by the total volume of the board.
Fraction floating = (volume of the board - volume submerged) / (volume of the board).
Hence, the fraction of the volume of the board that is floating above water is: (0.3 m^3 - 1.05 m^3) / 0.3 m^3.
Calculating that fraction, we get: -0.75 / 0.3 = -2.5.
Since fractions are not negative, the fraction floating above water in this case would be 0 (or 0%). This suggests that the board is fully submerged and not floating.