A geologist finds that a Moon rock whose mass is 9.97 kg has an apparent mass of 6.40 kg when submerged in water. What is the density of the rock?
thank you very much
Oh, a Moon rock playing hide-and-seek with its density! Let's solve this mystery together. To find the density of the rock, we need to use the formula: Density = Mass / Volume.
Since the rock's mass is given as 9.97 kg, we now need to determine the volume of the rock. The apparent mass of the rock when submerged in water is 6.40 kg. This decrease in apparent mass is due to the buoyant force acting on the rock when it is submerged.
To find the volume, we can use Archimedes' principle. The buoyant force is equal to the weight of water displaced by the rock. In this case, the apparent loss in mass (3.57 kg) represents the weight of the water displaced.
Now, assuming a density of water of 1000 kg/m³, we can calculate the volume of the rock:
Volume = Mass of water displaced / Density of water
Volume = 3.57 kg / 1000 kg/m³ = 0.00357 m³
Now that we have the volume, we can calculate the rock's density:
Density = Mass / Volume = 9.97 kg / 0.00357 m³ ≈ 2,786.43 kg/m³
So, the density of the rock is approximately 2,786.43 kg/m³. Keep an eye out for more rock-shenanigans in the future!
To find the density of the Moon rock, we can use the formula:
Density = Mass / Volume
To determine the volume, we need to find the difference between the mass of the rock in air and the apparent mass of the rock when submerged in water.
Given:
Mass of rock in air (m1) = 9.97 kg
Apparent mass of rock in water (m2) = 6.40 kg
Step 1: Calculate the volume of the rock.
Volume = m1 - m2
Volume = 9.97 kg - 6.40 kg
Volume = 3.57 kg
Step 2: Calculate the density.
Density = Mass / Volume
Density = 9.97 kg / 3.57 kg
Density = 2.79 kg/m^3
Therefore, the density of the Moon rock is approximately 2.79 kg/m^3.
To find the density of the rock, we can use the formula:
Density = Mass / Volume
First, let's find the volume of the rock. We know that the apparent mass of the rock when submerged in water is 6.40 kg. This apparent mass is actually the difference between the mass of the rock in air and its net buoyant force in water.
The net buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the water displaced by the object.
The weight of the water displaced is given by the formula:
Weight of water displaced = Density of water * Volume of water displaced * Gravitational acceleration
Since the rock is fully submerged in water, the volume of water displaced is equal to the volume of the rock.
Now, let's calculate the volume of water displaced:
Volume of water displaced = Apparent mass of the rock / (Density of water * Gravitational acceleration)
The density of water is approximately 1000 kg/m³, and the gravitational acceleration is approximately 9.8 m/s².
Volume of water displaced = 6.40 kg / (1000 kg/m³ * 9.8 m/s²)
With this, we can now calculate the volume of the rock, which is equal to the volume of water displaced.
Now, substitute the volume of the rock and its mass into the density formula:
Density = Mass of the rock / Volume of the rock
Density = 9.97 kg / Volume of the rock
By plugging in the values, you can calculate the density of the rock.
The mass of an equivalent volume of water would be 9.97-6.40 = 3.57 kg
Divide 9.97 by 3.57 for the specific gravity: 2.793
The density is 2.793 x (density of water) = 2.793 g/cm^3 = 2793 kg/m^3