Question

A sample of an unknown material appears to weigh 300N in air and 200N when immersed in alcohol of density 700kg/m^3 . What is the volume and density of the material

Answer 1

To solve this physics problem, the buoyant force is calculated as 100N, and then the volume of the material is determined to be 0.01454 m³. Using these values, the density of the material is found to be approximately 2121 kg/m³.

Step-by-step explanation:

The solution to this problem requires an application of Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

First, we calculate the buoyant force when the material is submerged in alcohol:
Buoyant Force = Weight in air - Weight in alcohol

300N - 200N = 100N

The volumes of fluid displaced by the material in alcohol can be found through the relationship:
Buoyant Force = Volume of Displaced Fluid x Density of Alcohol x g (acceleration due to gravity)

We rearrange for volume:

Volume = Buoyant Force / (Density of Alcohol x g)

Volume = 100N / (700kg/m³ x 9.81m/s²)

Note that 1N = 1kg·m/s², which simplifies the units:

Volume ≈ 0.01454 m³

Finally, we find the density of the material using the formula:
Density = Mass / Volume

Here, mass of the material is equal to the weight in air divided by g, assuming earth-like conditions.

Density = 300N / (9.81m/s² x 0.01454 m³)

Density ≈ 2121 kg/m³

Answer 2

the volume of the material is 0.0145 m^3 and its density is 20690.3 kg/m^3.

Step-by-step explanation:

To solve the problem, 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.

Let's first find the weight of the unknown material in air:

W_air = 300 N

Next, let's find the weight of the unknown material in alcohol:

W_alcohol = 200 N

We can find the buoyant force acting on the material by subtracting the weight in alcohol from the weight in air:

F_buoyant = W_air - W_alcohol = 300 N - 200 N = 100 N

According to Archimedes' principle, this buoyant force is equal to the weight of the alcohol displaced by the material:

F_buoyant = ρ_alcohol * V * g

where ρ_alcohol is the density of the alcohol, V is the volume of the material, and g is the acceleration due to gravity.

Substituting the values we know:

100 N = 700 kg/m^3 * V * 9.81 m/s^2

Solving for V:

V = 0.0145 m^3

Finally, we can find the density of the material by dividing its weight in air by its volume:

ρ_material = W_air / V = 300 N / 0.0145 m^3 = 20690.3 kg/m^3

Therefore, the volume of the material is 0.0145 m^3 and its density is 20690.3 kg/m^3.