. A small statue in the shape of a falcon has a weight of 24.1 N. The owner of the statue claims it is made of solid gold.When the statue is completely submerged in a container brimful of water, the weight of the water that spills over the top and into a bucket is 1.25 N. Find the density and specific gravity of the metal. Is the density consistent with the claim that the falcon is solid gold? Note: ρAu = 1.93 x 104 kg/m3.

Th volume of the falcon is the volume of 1.25 N weight of displaced water, which is

1.25 N/[g*10^3 kg/m^3) = 1.274*10^-4 m^3

The mass of the falcon is
(weight)/g = 24.1/9.81 = 2.457 kg

The density of the falcon is
(mass)/volume) = 19,280 kg/m^3

So, yes, it is gold.

Well, well, well, Mr. Falcon Statue. Trying to pass off as solid gold, are we? Let's put your claim to the test.

To find the density of the metal, we need to know the volume of the statue. How do we find that, you ask? By measuring the volume of water that spilled over, of course!

The weight of the water that spilled over is equal to the weight of the displaced water, which is also equal to the buoyant force acting on the statue. Using the equation F_buoyant = ρ * V * g, where F_buoyant is the buoyant force, ρ is the density of water, V is the volume of the statue, and g is the acceleration due to gravity, we can solve for the volume.

Substituting the given values, we have 1.25 N = (1000 kg/m^3 * V * 9.8 m/s^2). Solving for V, we find V = 0.00128 m^3.

Now, the density of the metal is given by the ratio of mass to volume. We know the weight of the statue (24.1 N), which we can convert to mass using the formula weight = mass * g. Rearranging the equation, we have mass = weight / g. Plugging in the values, we find mass = 2.46 kg.

The density of the metal is therefore density = mass / V = 2.46 kg / 0.00128 m^3 = 1921.875 kg/m^3.

Ah-ha! The density of the metal is not consistent with the claim that the falcon is solid gold. The density of solid gold is about 19,300 kg/m^3, not 1921.875 kg/m^3. So, either your little falcon friend is made of a different material, or someone has been playing tricks on you!

As for the specific gravity, that's just the ratio of the density of the metal to the density of water. Specific gravity = density of metal / density of water. Plugging in the values, we have specific gravity = 1921.875 kg/m^3 / 1000 kg/m^3 = 1.921875.

So, there you have it. The density is not consistent with solid gold, and the specific gravity is just a fancy way of saying the density relative to water. Looks like that claim of solid gold doesn't quite hold water, Mr. Falcon!

To find the density and specific gravity of the metal, we can use the principle of Archimedes. The buoyant force acting on the submerged statue is equal to the weight of the water displaced by the statue.

The weight of the water displaced can be calculated as the difference between the weight of the statue in air and the weight of the water spilled over the top.

Weight of water displaced = (Weight in air) - (Weight spilled)

Weight of water displaced = 24.1 N - 1.25 N
Weight of water displaced = 22.85 N

Now, we can calculate the volume of water displaced using the following equation:

Volume of water displaced = (Weight of water displaced) / (Density of water)
Density of water = 1000 kg/m^3 (known value)

Volume of water displaced = 22.85 N / 1000 kg/m^3
Volume of water displaced = 0.02285 m^3

Since the statue is fully submerged, the volume of the statue is equal to the volume of water displaced.

Now we can calculate the density of the metal using the equation:

Density = (Weight in air) / (Volume of statue)

Density = 24.1 N / 0.02285 m^3
Density ≈ 1055.5 kg/m^3

The calculated density of the metal is 1055.5 kg/m^3

To determine if the falcon is made of solid gold, we can compare the calculated density to the known density of gold.

The known density of gold (ρAu) is 1.93 x 10^4 kg/m^3.

Since the calculated density of the metal (1055.5 kg/m^3) is significantly lower than the known density of gold (1.93 x 10^4 kg/m^3), it suggests that the falcon is not made of solid gold.

The specific gravity of a substance is defined as the ratio of its density to the density of a reference substance (usually water in this case).

Specific Gravity = Density of metal / Density of water

Specific Gravity = 1055.5 kg/m^3 / 1000 kg/m^3

Specific Gravity ≈ 1.055

Therefore, the specific gravity of the metal is approximately 1.055.

To find the density and specific gravity of the metal, we need to use the principle of buoyancy. The weight of the water that spills over the top and into the bucket is equal to the buoyant force acting on the statue.

The weight of the statue is 24.1 N, and the weight of the water that spills over the top is 1.25 N. Therefore, the buoyant force acting on the statue is 1.25 N.

We can find the density of the metal using the equation for buoyant force:

Buoyant force = weight of the fluid displaced
1.25 N = Density of the metal * Volume of the statue * acceleration due to gravity

Since the volume of the statue is the same as the volume of water displaced, we can substitute the weight of the statue and the density of water into the equation:

1.25 N = Density of the metal * Volume of water displaced * acceleration due to gravity

Since the acceleration due to gravity is a constant (approximately 9.81 m/s^2), we can rearrange the equation to find the volume of water displaced:

Volume of water displaced = 1.25 N / (Density of the metal * acceleration due to gravity)

Now, we can calculate the volume of water displaced in cubic meters. Let's assume the density of water is approximately 1000 kg/m^3:

Volume of water displaced = 1.25 N / (Density of the metal * 9.81 m/s^2 * 1000 kg/m^3)

Next, we can calculate the mass of the water displaced using the density of water:

Mass of water displaced = Volume of water displaced * Density of water

And finally, we can calculate the density of the metal using the weight of the statue and the mass of the water displaced:

Density of the metal = Weight of the statue / (Volume of water displaced * Density of water)

To find the specific gravity of the metal, we divide the density of the metal by the density of water:

Specific gravity = Density of the metal / Density of water

If the calculated density of the metal is equal to or very close to the known density of gold (ρAu = 1.93 x 10^4 kg/m^3), then the density is consistent with the claim that the falcon is made of solid gold.