An iron piece of mass 360g and a density of 6g/cm^3 is suspended by a rope so that is partially (halfway)in oil of density 0.9 g/cm^3.Find the tension (force) in the string.

find volume submerged:

1/2 * mass/density=1/2 * 360*1/6=30cm^3 check that.

Now mass loss due to submerged:
volumesuberged*densitywater=30cm^3*.9=27g

tension= mg-mg ofdisplaced fluid
= .06*9.8 -.027*9.8 N= .323 Newtons

check that

Well, let's analyze the situation here. We have an iron piece that is partially submerged in oil and hanging by a rope. So, basically, we have a "weighty" situation on our hands, literally.

Now, to find the tension in the string, let's start by determining the volume of the iron piece that is submerged in the oil. Since the iron has a density of 6g/cm^3 and is half-submerged, we can calculate the volume using the mass and the density.

Volume of iron in oil = (mass of iron) / (density of iron)
= 360g / 6g/cm^3
= 60cm^3

Now, since the density of the oil is 0.9g/cm^3, we can calculate the weight of the oil displaced by the submerged iron piece.

Weight of oil displaced = (volume of iron in oil) * (density of oil)
= 60cm^3 * 0.9g/cm^3
= 54g

To find the tension in the string, we need to consider the equilibrium of forces. The tension in the string will be equal to the weight of the iron piece minus the weight of the oil displaced.

Tension in the string = (weight of iron) - (weight of oil displaced)
= (mass of iron) * (gravity) - (weight of oil displaced)
= 360g * 9.8m/s^2 - 54g * 9.8m/s^2
= 3528N

So, the tension in the string is 3528N (Newtons). That should be enough to keep everything hanging in balance!

To find the tension in the string, we need to consider the forces acting on the iron piece.

1. Weight of the iron piece:
The weight of an object is given by the formula: weight = mass * gravitational acceleration.
The mass of the iron piece is given as 360g. To convert grams to kilograms, we divide by 1000: mass = 360g ÷ 1000 = 0.36 kg.
The weight of the iron piece can be calculated as weight = mass * gravitational acceleration = 0.36 kg * 9.8 m/s^2 = 3.528 N.

2. Buoyant force exerted by oil:
The buoyant force experienced by an object submerged partially or fully in a fluid can be calculated as follows:
buoyant force = volume of fluid displaced * density of fluid * gravitational acceleration.

Since the iron piece is submerged halfway in the oil, it will displace a certain volume of oil. We can calculate the volume of the iron piece using its density and mass:
volume of iron piece = mass of iron piece ÷ density of iron = 0.36 kg ÷ 6 g/cm^3 = 0.36 kg ÷ 6000 kg/m^3 = 6 * 10^(-5) m^3.

The volume of oil displaced will be half of the volume of the iron piece, as it is partially submerged. Thus,
volume of oil displaced = (1/2) * volume of iron piece = (1/2) * 6 * 10^(-5) m^3 = 3 * 10^(-5) m^3.

Now, let's calculate the buoyant force:
buoyant force = volume of oil displaced * density of oil * gravitational acceleration = 3 * 10^(-5) m^3 * 0.9 * 10^3 kg/m^3 * 9.8 m/s^2 = 2.646 N.

3. Tension in the string:
The tension in the string can be found by considering the equilibrium of forces acting on the iron piece. The upward force due to the buoyant force should be equal to the downward force due to the weight of the iron piece.
Therefore, the tension in the string is the sum of the weight of the iron piece and the buoyant force:
tension in the string = weight of iron + buoyant force = 3.528 N + 2.646 N = 6.174 N.

Therefore, the tension in the string is approximately 6.174 N.

To find the tension in the string, we need to consider the forces acting on the iron piece.

First, let's calculate the volume of the iron piece:
Given that the mass of the iron piece is 360g and its density is 6g/cm^3, we can use the formula:
Volume = Mass / Density
Volume = 360g / 6g/cm^3
Volume = 60 cm^3

Since the iron piece is partially submerged in oil, we need to consider the part of the iron's volume submerged in the oil.

Let's assume the height of the iron piece submerged in the oil is "h" cm. Since the iron piece is halfway submerged, the height is equal to half of the total height.
Therefore, h = 60 cm / 2
h = 30 cm

Now, let's calculate the volume of the part submerged in the oil.
Volume_submerged = Area_base * Height_submerged
In this case, the base area is the same as the cross-sectional area, which is constant throughout the piece. So we can write:
Volume_submerged = Area * Height_submerged

Now, we need to consider the buoyancy force acting on the submerged part of the iron. The buoyancy force is equal to the weight of the displaced fluid.

Let's calculate the weight of the oil displaced by the submerged part:
Weight_displaced = Volume_submerged * Density_oil
Weight_displaced = (Area * Height_submerged) * Density_oil

Next, we need to calculate the weight of the iron piece:
Weight_iron = Mass * g
Weight_iron = 360g * 9.8 m/s^2 (where g is the acceleration due to gravity)

Now, let's consider the forces acting on the iron piece:
1. Tension in the string (upward force)
2. Weight of the iron (downward force)
3. Weight of the displaced oil (upward force)

The tension in the string is equal to the sum of the weight of the iron and the weight of the displaced oil, as these two forces balance each other out:
Tension = Weight_iron + Weight_displaced

Substituting the previously calculated values:
Tension = (360g * 9.8 m/s^2) + (Area * Height_submerged * Density_oil).

Please note that to find the tension in the string, we still need to know the cross-sectional area of the iron piece. If the area is provided, substitute that value into the formula mentioned above to calculate the tension.