A student found that a brass cylinder weighs 74.04g in air and 66.11g in water (density 0.998g/cm3). What is the density of brass?
To find the density of brass, we can use Archimedes' principle, which states that the weight of an object in water is equal to the weight of the displaced water.
Step 1: Find the weight of the water displaced by the brass cylinder.
The weight of the water displaced can be found by subtracting the weight of the brass cylinder in water from its weight in air.
Weight of displaced water = weight of brass cylinder in air - weight of brass cylinder in water
Weight of displaced water = 74.04g - 66.11g
Weight of displaced water = 7.93g
Step 2: Use the density of water to find the volume of the displaced water.
Density of water = 0.998g/cm^3
Volume of displaced water = weight of displaced water / density of water
Volume of displaced water = 7.93g / 0.998g/cm^3
Volume of displaced water = 7.94 cm^3
Step 3: Use the volume of the displaced water to find the volume of the brass cylinder.
Since the volume of the water displaced will be equal to the volume of the brass cylinder, we can conclude that the brass cylinder has a volume of 7.94 cm^3.
Step 4: Use the weight of the brass cylinder in air and its volume to calculate the density of brass.
Density of brass = weight of brass cylinder in air / volume of brass cylinder
Density of brass = 74.04g / 7.94 cm^3
Density of brass = 9.32 g/cm^3
Therefore, the density of brass is 9.32 g/cm^3.
To find the density of brass, we need to use Archimedes' principle, which states that the weight of an object submerged in a fluid is equal to the weight of the fluid displaced by that object.
First, let's calculate the weight of the brass cylinder in air and in water.
Weight in air = 74.04 g
Weight in water = 66.11 g
Next, we need to determine the weight of the water displaced by the brass cylinder. We can do this by subtracting the weight of the brass cylinder in water from the weight of the brass cylinder in air.
Weight of the water displaced = Weight in air - Weight in water
Weight of the water displaced = 74.04 g - 66.11 g
Weight of the water displaced = 7.93 g
Now, since density is defined as mass per unit volume, we need to find the volume of the water displaced by the brass cylinder.
Density of water = 0.998 g/cm3
Mass of the water displaced = 7.93 g
Volume of the water displaced = Mass of the water displaced / Density of water
Volume of the water displaced = 7.93 g / 0.998 g/cm3
Volume of the water displaced = 7.94 cm3
Finally, to find the density of brass, we divide the mass of the brass cylinder by the volume of the water displaced.
Density of brass = Mass of the brass cylinder / Volume of the water displaced
Density of brass = 74.04 g / 7.94 cm3
Density of brass ≈ 9.32 g/cm3
Therefore, the density of brass is approximately 9.32 g/cm3.
the cylinder displaces (74.04 g - 66.11 g) of water
divide the mass of the displaced water by the given density
... this gives the volume of the cylinder
divide the weight of the cylinder by the volume ... this is the density