An ore sample weighs 15.00 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 9.00 N. Find the total volume and the density of the sample.
hints:
1. conversion from weight to mass:
mass (in kg)
= weight (in N) / g (in m/s²)
= weight (in N) / 9.81
2. Archimedes principle
The upthrust on an immersed object equals the weight of liquid displaced (i.e. weight of liquid of net volume equal to object)
3. Density of water is 1 kg/L
Well, it seems you want me to do some math. I apologize in advance if my calculations turn out to be more clown-like than accurate, but I'm always up for a challenge! Let's give it a shot.
To find the total volume and density of the sample, we can use Archimedes' principle. According to Archimedes, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by that object.
First, let's find the weight of the water displaced by the sample. Since the tension in the cord is 9.00 N and the weight of the sample in air is 15.00 N, we can subtract 9.00 N from 15.00 N to get the weight of the water displaced, which is 6.00 N.
Now, we can use the density formula to find the total volume and density. Density is defined as the mass of an object divided by its volume.
Since we don't know the mass of the sample, let's assume the density of water is 1 g/cm³ (an approximation), which means the density of the sample will be less than that since it floats. Please keep in mind that this is a simplification, and real-life situations might be more complex.
To find the volume, we can use the formula:
Volume = Weight of the water displaced / Density of water.
Since we already found the weight of the water displaced is 6.00 N and we assumed the density of water is 1 g/cm³, we can say:
Volume = 6.00 N / 1 g/cm³.
Using my trusty calculator to convert units, it turns out the volume of the sample is 6.00 cm³. Keep in mind that this value might not be 100% accurate, but we're doing our best here!
Now, we can find the density of the sample:
Density = Mass / Volume.
Since we don't know the mass of the sample, we can rearrange the formula:
Density = Weight of the sample / Volume.
Since we know the weight of the sample in air is 15.00 N and the volume is 6.00 cm³, we can say:
Density = 15.00 N / 6.00 cm³.
Using my calculations, the density of the sample is approximately 2.5 N/cm³. Please keep in mind that this value is just an approximation, so don't go writing it down in your science textbook just yet.
So, based on my clown-like calculations, the total volume of the sample is 6.00 cm³, and the density is approximately 2.5 N/cm³. I hope that satisfies your curiosity, and if not, at least I provided some entertainment along the way!
To find the total volume and density of the sample, we need to use the concept of buoyancy. The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Step 1: Find the weight of the fluid displaced by the sample.
In this case, the weight of the fluid displaced by the sample is equal to the difference between the weight of the sample in air and the tension in the cord when the sample is immersed in water.
Weight of the displaced fluid = Weight of the sample in air - Tension in the cord
Weight of the displaced fluid = 15.00 N - 9.00 N
Weight of the displaced fluid = 6.00 N
Step 2: Find the volume of the sample.
Since the weight of the displaced fluid is equal to the weight of the sample, we can say that the volume of the sample is equal to the volume of the fluid displaced.
Volume of the sample = Volume of the fluid displaced
Step 3: Find the density of the sample.
The density of the sample can be calculated using the formula:
Density = Mass / Volume
Since we have the weight of the sample and the weight of the fluid displaced, we can use the relationship between weight, mass, and acceleration due to gravity.
Weight = Mass × Acceleration due to gravity
Mass = Weight / Acceleration due to gravity
Density = (Weight of the sample / Acceleration due to gravity) / Volume
Step 4: Calculate the density of the sample.
Substitute the values into the formula:
Density = (6.00 N / 9.8 m/s²) / Volume
Now, we need to find the value of the volume.
Step 5: Calculate the volume of the sample.
To find the volume of the sample, we can use the ideal gas law.
Density = Mass / Volume
Mass = Density × Volume
Since the weight of the sample is equal to the mass × acceleration due to gravity, we can write:
Weight of the sample = (Density × Volume) × Acceleration due to gravity
Now, substitute the known values:
15.00 N = (Density × Volume) × 9.8 m/s²
Step 6: Solve for the volume.
Divide both sides of the equation by (Density × 9.8 m/s²):
15.00 N / (Density × 9.8 m/s²) = Volume
Step 7: Calculate the volume.
Substitute the known weight (15.00 N) and the calculated Density (as calculated in step 4) into the equation:
Volume = 15.00 N / (Density × 9.8 m/s²)
This will give you the total volume of the sample.
To find the total volume and density of the ore sample, we need to make use of Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's break down the problem step by step:
Step 1: Find the weight of the ore sample in air.
Given that the weight of the ore sample in air is 15.00 N, this means that when the sample is not submerged in water, it experiences a gravitational force of 15.00 N.
Step 2: Find the weight of the ore sample in water.
When the sample is completely submerged in water, it experiences a buoyant force that reduces its weight. In this case, the tension in the cord is 9.00 N. This tension represents the weight of the sample minus the buoyant force acting on it:
Weight in water = Weight in air - Buoyant force
Weight in water = 15.00 N - 9.00 N
Weight in water = 6.00 N
Step 3: Calculate the buoyant force acting on the ore sample.
The buoyant force is equal to the weight of the water displaced by the sample. Since the sample is fully submerged, its weight in water is equal to the buoyant force:
Buoyant force = Weight in water = 6.00 N
Step 4: Determine the volume of the ore sample.
To find the volume of the sample, we need to divide the buoyant force by the density of water:
Buoyant force = Density of water × Volume of sample × Acceleration due to gravity
6.00 N = (1000 kg/m^3) × Volume of sample × (9.8 m/s^2)
Rearranging the equation to solve for the volume of the sample:
Volume of sample = 6.00 N / [(1000 kg/m^3) × (9.8 m/s^2)]
Volume of sample ≈ 0.000612 m^3
Step 5: Calculate the density of the ore sample.
The density of the sample can be determined using the formula:
Density = Mass / Volume
Since the mass is not given, we can use the weight in air to find it. By using the formula:
Weight = Mass × Acceleration due to gravity
15.00 N = Mass × 9.8 m/s^2
Solving for the mass of the sample:
Mass = 15.00 N / 9.8 m/s^2
Mass ≈ 1.53 kg
Finally, substituting the values into the density formula:
Density = 1.53 kg / 0.000612 m^3
Density ≈ 2500 kg/m^3
Therefore, the total volume of the ore sample is approximately 0.000612 m^3, and its density is approximately 2500 kg/m^3.