Question

A solid object weighs 12.42 N in air. When it is suspended from a scale and submerged in water, the scale reads 5.10 N. Find the density of the object. (Use 1000.0 kg/m³ for the density of water.)

Answer 1

To calculate the density of the object, subtract the submerged weight from the weight in the air to find the buoyant force, then calculate the object's volume and divide its mass by this volume. Thus the object's density is 1,697 kg/m³.

Step-by-step explanation:

To find the density of the object, we use the weight of the object in air and the weight when submerged in water. The difference in the two weights gives us the buoyant force, which is equal to the weight of the water displaced by the object. By using the density of water, we can calculate the volume of water displaced, which is also the volume of the object. The object's density is then found by dividing its weight in air by its volume.

Firstly, calculate the buoyant force:

• Buoyant force = Weight in air - Weight in water
• Buoyant force = 12.42 N - 5.10 N = 7.32 N

Then, find the volume of the object using the density of water (1,000.0 kg/m³) and the formula for buoyant force (which is the weight of the fluid displaced):

• Volume = Buoyant force / (density of water * gravity)
• Volume = 7.32 N / (1,000.0 kg/m³ * 9.81 m/s²)
• Volume = 7.32 N / 9,810 N/m³ = 0.000746 m³

Lastly, calculate the density of the object:

• Density = Weight in air / Volume
• Density = 12.42 N / 0.000746 m³
• Since weight (N) = mass (kg) * gravity (m/s²), and gravity is 9.81 m/s²:
• Mass = Weight in air / gravity = 12.42 N / 9.81 m/s² = 1.266 kg
• Density = 1.266 kg / 0.000746 m³ = 1,697 kg/m³

The object's density is 1,697 kg/m³.

Answer 2

The density of the object is calculated using Archimedes' principle. By finding the weight of water it displaces when submerged, we determine the object's volume. The object's density is then found to be 1698.2 kg/m³.

Step-by-step explanation:

To calculate the density of the object, we'll use Archimedes' principle which states that the buoyant force on a submerged object is equal to the weight of the fluid it displaces.

The apparent weight loss of the object when submerged is the weight of the water displaced.

Firstly, we find the weight of the water displaced by the object: 12.42 N - 5.10 N = 7.32 N.

Since weight is the product of mass and gravity (W = m*g), we can find the mass of water displaced by dividing the weight of the water displaced by the acceleration due to gravity (9.81 m/s²): mass of water displaced = 7.32 N / 9.81 m/s² = 0.746 kg.

Using the density of water (1000.0 kg/m³), we find the volume of water displaced, which is also the volume of the object: volume of the object = mass of water displaced / density of water = 0.746 kg / 1000.0 kg/m³ = 0.000746 m³.

To get the density of the object, we divide its weight in air by the volume we just calculated: density of the object = weight in air / (volume of the object * g) = 12.42 N / (0.000746 m³ * 9.81 m/s²) = 1698.2 kg/m³.

Therefore, the density of the object is 1698.2 kg/m³.