Ebony is one of the densest of all woods. Suppose a block of ebony with a volume of 2.5 × 10−3 m 3 is submerged in fresh water. If the apparent weight of the block is 7.4 N, what is the density of ebony? Assume the water has a density of 1.0 × 103 kg/m3 .
1301.73
To find the density of ebony, we can use the formula:
Density = Mass / Volume
We are given the volume of the ebony block as 2.5 × 10^(-3) m^3.
To find the mass of the ebony block, we can use the apparent weight of the block in water. The apparent weight is the difference between the weight of the block in air and the buoyant force acting on it in water.
Apparent Weight = Weight in Air - Buoyant Force
The weight of the ebony block in air is equal to its mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s^2.
Weight in Air = Mass * Gravity
Since we are given the apparent weight of the block as 7.4 N, we can find the weight in air using the formula:
Weight in Air = Apparent Weight + Buoyant Force
To calculate the buoyant force, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Buoyant Force = Weight of Displaced Fluid
The weight of the displaced fluid can be calculated using the density of water (given as 1.0 × 10^3 kg/m^3) and the volume of the ebony block.
Weight of Displaced Fluid = Density of Water * Volume
Now we have all the necessary information to calculate the density of ebony:
Density = Weight in Air / Volume
Let's plug in the values and calculate the density:
To find the density of ebony, we need to use the concept of apparent weight and buoyancy.
Apparent weight is the weight of an object measured when it is submerged in a fluid. In this case, the apparent weight is given as 7.4 N.
Buoyancy is the upward force exerted by a fluid on an object submerged in it. It depends on the density of the fluid and the volume of the object submerged.
Given information:
Volume of ebony (V) = 2.5 × 10^(-3) m^3
Apparent weight (F_apparent) = 7.4 N
Density of water (ρ_water) = 1.0 × 10^3 kg/m^3
We can calculate the buoyant force using the formula:
Buoyant force (F_buoyant) = ρ_water * g * V
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the values into the formula:
F_buoyant = (1.0 × 10^3 kg/m^3) * (9.8 m/s^2) * (2.5 × 10^(-3) m^3)
Now, to determine the density of ebony (ρ_ebony), we can use the following equation:
ρ_ebony = (F_apparent + F_buoyant) / V
Substituting the given values:
ρ_ebony = (7.4 N + (1.0 × 10^3 kg/m^3) * (9.8 m/s^2) * (2.5 × 10^(-3) m^3)) / (2.5 × 10^(-3) m^3)
Calculating the density of ebony gives the solution to the problem.