a 1.0kg beaker containgin 2.00kg of oil with a density of 916kg/m3 rests on a scale. a 2.0kg block of iron is suspended from a spring scale and completly submerged in the oil, find the euilibrium readings of both scales.density of iron 7860.
To find the equilibrium readings of both scales, we need to consider the buoyant forces acting on the beaker and the iron block.
1. Let's start with the beaker and the oil:
- The weight of the beaker (1.0 kg) acts downward.
- The buoyant force on the beaker is equal to the weight of the oil displaced by the beaker.
- The volume of the beaker is the same as the volume of the oil it contains (using the fact that density = mass/volume).
- The volume of the oil is 2.00 kg / 916 kg/m^3 = 0.0021837 m^3.
- The buoyant force on the beaker is 0.0021837 m^3 * (9.8 m/s^2) * (916 kg/m^3) = 20.13 N (upward).
- So, the equilibrium reading on the scale under the beaker is 20.13 N.
2. Now, let's consider the iron block:
- The weight of the iron block (2.0 kg) acts downward.
- The buoyant force on the iron block is equal to the weight of the oil displaced by the block.
- The volume of the iron block is 2.0 kg / 7860 kg/m^3 = 0.0002543 m^3.
- The buoyant force on the iron block is 0.0002543 m^3 * (9.8 m/s^2) * (916 kg/m^3) = 2.221 N (upward).
- So, the equilibrium reading on the spring scale with the iron block is 2.221 N.
Therefore, the equilibrium readings of both scales are:
- The beaker scale: 20.13 N
- The spring scale with the iron block: 2.221 N
To find the equilibrium readings of both scales, we need to consider the buoyancy force acting on the block of iron.
First, let's calculate the volume of the block of iron. We can use the formula:
Volume = Mass / Density
Given that the mass of the iron block is 2.0 kg and the density of iron is 7860 kg/m³, we can calculate the volume of the block as:
Volume = 2.0 kg / 7860 kg/m³ ≈ 0.0002543 m³
Now, let's calculate the buoyant force acting on the iron block. The buoyant force is equal to the weight of the fluid displaced by the block, which is oil in this case. The weight of the oil can be calculated using the formula:
Weight = Volume × Density × gravitational acceleration
Given that the density of the oil is 916 kg/m³ and the gravitational acceleration is approximately 9.8 m/s², we can calculate the weight of the oil as:
Weight = 0.0002543 m³ × 916 kg/m³ × 9.8 m/s² ≈ 2.189 N
Since the block of iron is completely submerged in the oil, the buoyant force acting on it will be equal to the weight of the oil, which we just calculated.
So, the equilibrium reading of the spring scale, which is supporting the iron block, will be:
Equilibrium reading of spring scale = Weight of iron block + Buoyant force
Equilibrium reading of spring scale = 2.0 kg × 9.8 m/s² + 2.189 N ≈ 21.96 N
Therefore, the equilibrium reading of the spring scale supporting the iron block is approximately 21.96 N.
To find the equilibrium reading of the scale supporting the beaker with oil, we need to consider the weight of the beaker and the weight of the oil inside it.
The weight of the beaker can be calculated as:
Weight of beaker = Mass of beaker × gravitational acceleration
Given that the mass of the beaker is 1.0 kg and the gravitational acceleration is approximately 9.8 m/s², the weight of the beaker will be:
Weight of beaker = 1.0 kg × 9.8 m/s² ≈ 9.8 N
The weight of the oil can be calculated using the formula:
Weight = Volume × Density × gravitational acceleration
Given that the volume of the oil is 2.00 kg and the density of oil is 916 kg/m³, we can calculate the weight of the oil as:
Weight = 2.00 kg × 916 kg/m³ × 9.8 m/s² ≈ 17.864 N
The equilibrium reading of the scale supporting the beaker with oil will be:
Equilibrium reading of scale = Weight of beaker + Weight of oil
Equilibrium reading of scale = 9.8 N + 17.864 N ≈ 27.664 N
Therefore, the equilibrium reading of the scale supporting the beaker with oil is approximately 27.664 N.