Solving a Hydrostatic Problem: Cylinder Height in Water and Oil

[brykz]

Homework Statement

A Cylinder got ratio of 15 cm, and h=15. Their mass=7kg. This is floating in water. After we put oil on it (density=725kg/m^3), on the water.
Calculate what's the height of cylinder when its in oil.


Answer=7.6cm

Homework Equations

F=D x V x g

The Attempt at a Solution

I tried everything


Help please...

Sorry for my english.

 

[Shooting Star]

Hi, welcome to PF.

A Cylinder got ratio of 15 cm,

I think you mean "radius"...

So now that you know the volume and the height, and also the mass, you can calculate the density.

Homework Equations

F=D x V x g

F is the weight of the cylinder. Now it is surrounded by oil, which is exerting a buoyant force on it.

The Attempt at a Solution

I tried everything

Did you try Archimedes' principle? Do that now.

 

[nlightner]

I would approach this problem by first understanding the concept of hydrostatics and how it applies to this situation. Hydrostatics is the study of fluids at rest and the forces acting on them. In this case, we have a cylinder floating in water, which means that the upward force of buoyancy is equal to the downward force of gravity.

To solve this problem, we need to use the equation of buoyancy, which states that the buoyant force (F) is equal to the density (D) of the fluid, the volume (V) of the object submerged in the fluid, and the acceleration due to gravity (g). Mathematically, this can be represented as F = D x V x g.

We are given the mass of the cylinder (7kg) and the ratio of its height (15cm), but we need to find its volume in order to use the buoyancy equation. To find the volume, we can use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the cylinder and h is its height. Since we are given the ratio of the cylinder's height, we can assume that h is equal to 15cm. Therefore, we can rewrite the equation as V = π(15/2)^2 x 15 = 1767.15 cm^3.

Now, we can plug in the values into the buoyancy equation: F = 1000 kg/m^3 x 1767.15 cm^3 x 9.8 m/s^2 = 1.73 x 10^7 N. This is the buoyant force acting on the cylinder when it is submerged in water.

Next, we need to consider what happens when we add the oil on top of the water. The oil has a density of 725 kg/m^3, which means that it is less dense than water. This means that the cylinder will displace less oil than it did water, resulting in a smaller buoyant force. To find the height of the cylinder in the oil, we need to find the volume of oil that is displaced by the cylinder. This can be done by dividing the buoyant force by the density of the oil and the acceleration due to gravity: V = F/(D x g) = 1.73 x 10^7 N/ (725 kg/m^3 x 9.8 m/s