A paperweight weighs 6.9N in air. When it is completely submerged in water it appears to weigh 4.3N. A) What is the volume of the paperweight? B) What is the density paperweight? The density of water is 1000kg/m3.
To find the answers to the given questions, we need to use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's break down the steps to solve this problem:
Step 1: Find the buoyant force in water
The apparent weight of the paperweight in water is the actual weight of the paperweight minus the buoyant force. From the given information, we can calculate the buoyant force as follows:
Buoyant force in water = Actual weight of paperweight - Apparent weight of paperweight in water
= 6.9 N - 4.3 N
= 2.6 N
Step 2: Find the volume of the paperweight
The buoyant force experienced by the paperweight in water is equal to the weight of the water displaced by the paperweight. Since the buoyant force is given by the formula: Buoyant force = density of water x volume of displaced water x gravitational acceleration (g), we can rearrange the formula to find the volume:
Volume of displaced water = Buoyant force in water / (density of water x gravitational acceleration)
Plugging in the values:
Volume of displaced water = 2.6 N / (1000 kg/m^3 x 9.8 m/s^2)
≈ 0.000265 m^3
Since the volume of displaced water is equal to the volume of the paperweight, the answer to part A is approximately 0.000265 m^3.
Step 3: Find the density of the paperweight
Density is equal to mass divided by volume. Since density of water is given as 1000 kg/m^3 and volume of the paperweight has been calculated, we can rearrange the formula to find mass:
Mass = Density x Volume
Mass = 1000 kg/m^3 x 0.000265 m^3
≈ 0.265 kg
Now, we can calculate the density of the paperweight:
Density of the paperweight = Mass of the paperweight / Volume of the paperweight
= 0.265 kg / 0.000265 m^3
≈ 1000 kg/m^3
Therefore, the density of the paperweight is approximately 1000 kg/m^3.