An iron piece of mass 360g and a density of 6g/cm if suspended by a rope so that is partially submerged in oil of density 0.9g/cm find the tension (force) in the string
To find the tension (force) in the string, we need to determine the buoyant force acting on the iron piece.
Step 1: Calculate the volume of the iron piece.
Given: Mass of iron piece = 360g; Density of iron = 6g/cm³
We can use the formula: Mass = Density x Volume
Rearranging the formula, Volume = Mass / Density
Volume of iron piece = 360g / 6g/cm³ = 60 cm³
Step 2: Calculate the volume of the submerged portion of the iron piece.
Given: Density of oil = 0.9g/cm³
Since the iron piece is partially submerged, we'll need to find the volume of the submerged portion.
Submerged volume = Total volume x Submerged height / Total height
Submerged height = Volume of iron piece / (Area of cross-section)
The area of the cross-section is the same as the area of the iron piece since it is uniform.
Submerged height = 60 cm³ / (60 cm²) = 1 cm
Step 3: Calculate the buoyant force.
Buoyant force = Density of fluid x Volume of fluid displaced x Acceleration due to gravity
The volume of fluid displaced is the volume of the submerged portion.
Buoyant force = 0.9g/cm³ x 1 cm³ x 9.8 m/s² (since 1 g = 9.8 m/s²)
Buoyant force = 8.82 N
Step 4: Calculate the tension in the string.
The tension in the string is equal to the weight of the iron piece plus the buoyant force.
Weight of the iron piece = Mass x Acceleration due to gravity
Weight of the iron piece = 360g x 9.8 m/s² = 3.528 N
Tension in the string = Weight of the iron piece + Buoyant force
Tension in the string = 3.528 N + 8.82 N
Tension in the string = 12.348 N
Therefore, the tension (force) in the string is approximately 12.348 N.
To find the tension (force) in the string, we need to consider the forces acting on the iron piece.
1. Weight of the iron piece:
The weight of the iron piece can be calculated using the formula: weight = mass × gravitational acceleration (W = m × g).
In this case, the mass of the iron piece is given as 360g (0.36kg) and the gravitational acceleration is approximately 9.8 m/s².
So, the weight of the iron piece = 0.36kg × 9.8 m/s² = 3.528 N.
2. Buoyant force:
The buoyant force acting on the iron piece is equal to the weight of the liquid displaced by it. In this case, the liquid is oil, and the density of the oil is given as 0.9g/cm³.
The volume of the submerged part of the iron piece can be calculated using the formula: volume = mass / density (V = m / ρ).
For the iron piece, the mass is given as 360g (0.36kg) and the density is 6g/cm³.
So, the volume of the submerged part = 0.36kg / 6g/cm³ = 0.06 cm³.
The buoyant force can be calculated using the formula: buoyant force = density of the liquid × volume of the submerged part × gravitational acceleration (B = ρ × V × g).
In this case, the density of the liquid is 0.9g/cm³, the volume of the submerged part is 0.06 cm³, and the gravitational acceleration is approximately 9.8 m/s².
So, the buoyant force = 0.9g/cm³ × 0.06 cm³ × 9.8 m/s² = 0.5292 N.
3. Tension in the string:
The tension in the string can be calculated by considering the net force acting on the iron piece. The net force is the difference between the weight of the iron piece and the buoyant force acting on it.
Tension in the string = Weight of the iron piece - Buoyant force
Tension in the string = 3.528 N - 0.5292 N = 2.9988 N.
Therefore, the tension (force) in the string is approximately 2.9988 N.
You have to know how far it is submerged
m = 0.360 kg
g = 9.81 m/s^2
tension = m g - buoyant force
buoyant force = submersed volume * 900 kg/m^3 * g