While analyzing a sample of one, geologist finds that it weighs 2n in air and 1.3N when immersed in water. Calculate the density of the one

To calculate the density of the object, we can use the formula:

Density = Mass / Volume

Since we are given the weight of the object in air and when immersed in water, we can infer the mass and volume using the concept of buoyancy.

Step 1: Calculate the mass of the object.
The weight of the object in air is given as 2N, which can be considered as the force due to gravity acting on the object.
Using Newton's second law (F = m * a), we know that the force (weight) is equal to the mass times the acceleration due to gravity.
So, the mass of the object is:
mass = weight / acceleration due to gravity = 2N / 9.8 m/s^2 ≈ 0.2041 kg (rounded to four decimal places)

Step 2: Calculate the volume of the object.
The weight of the object when immersed in water is 1.3N, which is equivalent to the buoyant force acting on the object.
According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object.
The weight of the fluid displaced is equal to the weight of the object in air minus the weight of the object in water.
So, the weight of the fluid displaced is 2N - 1.3N = 0.7N.
Using the formula for weight (F = m * g), we can find the mass of the fluid displaced:
mass of fluid displaced = weight of fluid displaced / acceleration due to gravity = 0.7N / 9.8 m/s^2 ≈ 0.0714 kg (rounded to four decimal places)

Now, we know that the volume of the fluid displaced is equal to the volume of the object, as they both occupy the same space.

Step 3: Calculate the density of the object.
density = mass / volume = 0.2041 kg / 0.0714 kg = 2.8571 kg/m^3 (rounded to four decimal places)

Therefore, the density of the object is approximately 2.8571 kg/m³.

To calculate the density of the object, we need to use the principle of buoyancy, 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.

In this case, the weight of the object in air is 2N, and its weight when immersed in water is 1.3N. The difference between these two weights represents the weight of the water displaced by the object.

Therefore, the buoyant force on the object is given by:

Buoyant Force = Weight in air - Weight in water
Buoyant Force = 2N - 1.3N
Buoyant Force = 0.7N

Since the buoyant force is equal to the weight of the water displaced by the object, we can say that the weight of the displaced water is also 0.7N.

Now, the density of an object is defined as its mass divided by its volume. In this case, we can use the weight of the displaced water as a substitute for the mass of the object because the weight of the water is equal to the weight of the object.

Density = Mass / Volume

To find the volume, we need to know the density of water. The density of water is approximately 1000 kg/m³.

Volume = Weight of Displaced Water / Density of Water
Volume = 0.7N / 1000 kg/m³

Now, we need to convert the weight from Newtons (N) to kilograms (kg) to match the units of the density of water.

1 N = 1 kg · m/s²

Volume = (0.7 kg · m/s²) / 1000 kg/m³
Volume = 0.0007 m³

Now that we have the volume, we can calculate the density.

Density = Mass / Volume

We already established that the weight of the object is equal to the weight of the displaced water, so the mass of the object is equal to 0.7 kg.

Density = 0.7 kg / 0.0007 m³
Density = 1000 kg/m³

Therefore, the density of the object is 1000 kg/m³.