You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads 35.4 N. If you then lower the statue into a tub of water, so that it is completely submerged, the scale reads 12.4 N. What is the density?

To determine the density of the ceramic statue, you can use the principle of buoyancy.

Step 1: Determine the weight of the statue in air.
The weight of the statue in air is equal to the reading on the spring scale, which is 35.4 N.

Step 2: Determine the weight of the statue in water.
The weight of the statue in water is equal to the difference between the weight of the statue in air and the scale reading when it is completely submerged. So, weight in water = weight in air - scale reading in water
Weight in water = 35.4 N - 12.4 N = 23 N

Step 3: Calculate the buoyant force on the statue.
The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The buoyant force is equal to the weight of the statue in air minus the weight of the statue in water.
Buoyant force = weight in air - weight in water = 35.4 N - 23 N = 12.4 N

Step 4: Calculate the volume of the statue.
The volume of the statue is equal to the volume of water displaced by the statue when it is submerged. With the help of Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object, we can relate the buoyant force to the volume of the statue.
Buoyant force = weight of the fluid displaced
Buoyant force = density of water * volume of the statue * acceleration due to gravity (density of water = 1000 kg/m^3, acceleration due to gravity = 9.8 m/s^2)
12.4 N = 1000 kg/m^3 * volume of the statue * 9.8 m/s^2

Step 5: Solve for the volume of the statue.
To find the volume of the statue, isolate the variable.
volume of the statue = 12.4 N / (1000 kg/m^3 * 9.8 m/s^2)
volume of the statue = 0.00127 m^3

Step 6: Calculate the density of the statue.
Density is defined as mass per unit volume. Rearrange the formula to solve for density.
Density = mass of the statue / volume of the statue

To calculate the mass of the statue, we need to use the weight of the statue in air and the acceleration due to gravity.
weight in air = mass of the statue * acceleration due to gravity
mass of the statue = weight in air / acceleration due to gravity = 35.4 N / 9.8 m/s^2 = 3.61 kg

Now, substitute the values into the density formula.
Density = 3.61 kg / 0.00127 m^3
Density ≈ 2847 kg/m^3

Therefore, the density of the ceramic statue is approximately 2847 kg/m^3.

To determine the density of the ceramic statue, 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.

First, let's calculate the weight of the ceramic statue. The scale reads 35.4 N when the statue is suspended. This is the weight of the statue in air.

Next, let's calculate the weight of the statue when it is completely submerged in water. The scale reads 12.4 N. This reading includes both the weight of the statue and the buoyant force acting on it.

The change in weight between the two readings is due to the buoyant force. So, the buoyant force acting on the statue is given by the difference between the weight in air and the weight in water:

Buoyant force = Weight in air - Weight in water

Substituting the given values, we get:

Buoyant force = 35.4 N - 12.4 N
Buoyant force = 23 N

Now, we can calculate the weight of the water displaced by the statue, which is equal to the buoyant force.

Weight of water displaced = Buoyant force = 23 N

Finally, let's calculate the density of the statue using the formula:

Density = Mass / Volume

Since density is mass per unit volume, we can calculate the density by dividing the weight of the statue by the weight of water displaced:

Density = Weight of statue / Weight of water displaced

To find the weight of the statue, we need to convert the given values into mass using the formula:

Weight = Mass x Acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s².

Weight of statue in air = 35.4 N
Mass of statue in air = 35.4 N / 9.8 m/s²

Weight of statue in water = 12.4 N
Mass of statue in water = 12.4 N / 9.8 m/s²

Substituting the calculated masses into the density formula, we get:

Density = (Mass of statue in air) / (Mass of statue in air - Mass of statue in water)

Simplifying the equation, we can calculate the density.