what is the likely identity of a metal if a sample has a mass of 63.5kg when submerged in air and an apparent mass of 55.4kg when submerged in water?
the metal displaces 63.5 - 55.4 liters of water
... the volume is 8.1 liters
the density is ... 63.5 kg / 8.1 L = 7.8 g/cm^3
probably steel
Well, if I were to take a wild guess, I'd say the metal in question might be "Lead-balloonium!" I mean, who wouldn't be surprised if a metal magically lost weight when submerged in water? But in all seriousness, based on the difference in apparent weight, it suggests that the metal has a density less than that of water, and that could indicate the presence of a metal like aluminum or titanium.
To determine the identity of the metal, we can use Archimedes' principle, 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.
Step 1: Calculate the buoyant force:
The buoyant force is the difference between the weight of the object in air and the weight of the object in water. The weight of the object in air can be calculated using the formula:
Weight in air = Mass × Gravitational acceleration
Weight in air = 63.5 kg × 9.8 m/s² = 623.3 N
Step 2: Calculate the weight of the object in water:
The weight of the object in water can be calculated using the formula:
Weight in water = Weight in air - Buoyant force
Weight in water = 623.3 N - Buoyant force
Step 3: Calculate the apparent mass of the object in water:
We know that the apparent mass of the object in water is 55.4 kg.
Apparent mass = Weight in water / Gravitational acceleration
55.4 kg = (Weight in air - Buoyant force) / 9.8 m/s²
From this equation, we can solve for the buoyant force:
Buoyant force = Weight in air - (55.4 kg × 9.8 m/s²)
Step 4: Calculate the volume of the object:
The volume of the object can be calculated using the formula:
Volume = Buoyant force / Density of water
Density of water = 1000 kg/m³ (assuming standard conditions)
Volume = Buoyant force / (Density of water × Gravitational acceleration)
Step 5: Calculate the density of the object:
The density of the object can be calculated using the formula:
Density of object = Mass / Volume
Density of object = 63.5 kg / Volume
Therefore, with the given information and these calculations, you can determine the density of the object, which can help identify the likely metal.
To determine the likely identity of the metal, we need to use the concept of buoyancy and Archimedes' principle. Archimedes' principle 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.
First, let's calculate the weight of the water displaced by the metal sample:
Weight of water displaced = Mass of water displaced × Acceleration due to gravity
We know the mass of the water displaced by the metal, as it is equal to the apparent mass of the sample in water:
Mass of water displaced = 55.4 kg
Next, we need to determine the weight of the metal sample in air:
Weight of metal in air = Mass of metal × Acceleration due to gravity
We know the mass of the metal sample, which is given as 63.5 kg.
Now, the buoyant force acting on the metal when submerged in water is equal to the weight of water displaced. According to Archimedes' principle, this buoyant force is also equal to the weight difference between the metal in air and the metal in water:
Buoyant force = Weight of metal in air - Weight of metal in water
We can rearrange this equation to solve for the weight of water displaced:
Weight of water displaced = Weight of metal in air - Buoyant force
Substituting the known values:
Weight of water displaced = 63.5 kg × Acceleration due to gravity - (63.5 kg - 55.4 kg) × Acceleration due to gravity
Simplifying the equation gives:
Weight of water displaced = 8.1 kg × Acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s².
Using the value of 9.8 m/s² for acceleration due to gravity, we can calculate the weight of water displaced:
Weight of water displaced = 8.1 kg × 9.8 m/s² = 79.38 N
By using the density formula, the volume of the metal can be determined:
Density = Mass / Volume
We already know the mass of the metal sample (63.5 kg), so we rearrange the formula to solve for volume:
Volume = Mass / Density
To find the density, we need the volume of the water displaced. Dividing the weight of water displaced by the density of water will give us the volume:
Volume of water displaced = Weight of water displaced / Density of water
The density of water is approximately 1000 kg/m³.
Volume of water displaced = 79.38 N / 1000 kg/m³ = 0.07938 m³
Now, we can find the volume of the metal sample:
Volume of metal = Volume of water displaced
Finally, by comparing the volume and mass of the metal sample, we can determine the likely identity of the metal. Different metals have different densities, so we need to find a metal with a density that matches the volume-to-mass relationship of the sample.