1. Fluids and Buoyant Force
Physics
Section 8-1
Fluids and Buoyant Force

2. Fluids
A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid.
Both liquids and gases are fluids.

3. Gases and Liquids Both liquids and gases have a definite mass.
Both will conform to the shape of their container. Therefore, neither has a definite fixed shape, as the molecules they are made of can move and flow.
Liquids have a definite volume. They tend to expand and contract very little.
Gases have no definite volume. They can expand to fill and container.

4. Fluid density
The density of a fluid, like all materials, is the mass divided by the volume.
ρ = m/V
ρ is the Greek letter rho (r) and is a common symbol for density in science.
The standard SI unit is kg/m3.

5. The buoyant force B
When an object or substance is put into a fluid (liquid or gas) an upward force is created. This force vector is opposite to the gravity vector. This upward force is called the buoyant force. CM mg

6. Archimedes’s Principle
Archimedes’s Principle gives the size of the buoyant force.
The magnitude of the buoyant force is exactly equal to the weight of the fluid displaced by the object. N
“Any floating object displaces its own weight of fluid.”
— Archimedes of Syracuse (“On Floating Bodies”) N
Overflowed when object was submerged. N N

7. Calculating the buoyant force
To calculate the value of the buoyant force, we must find the weight in newtons of the fluid displaced by the object. If the object is floating, not all the object will be submerged. In that case, the amount of fluid displaced will equal the volume of the submerged part of the object.
Weight equals mg. We might be able to find the fluids mass, but it’s often easier to find the volume displaced. If we know the identity of the fluid, we can use its volume and density to find mass. m = ρV. Therefore, the buoyant force is:
FB = ρfVfg
f = fluid

8. Will it sink or float?
If the weight of the object is more than the weight of the fluid displaced, the object will sink.
If the weight of the object is less that the weight of the fluid displaced, the object will rise and float upward.
If the weights are equal, the object will be suspended in the fluid, and will neither rise nor sink.
Since the object’s volume is equal to the volume of the fluid displaced, we can compare the overall density of the object to the density of the fluid. If the density of the object is less that the density of the fluid, it will float. If its density is greater, the object will sink.

9. Floating objects Net force
Objects that are floating, such as a boat in water, are in equilibrium. In that case the buoyant force equals the weight of the object that is floating.
FB = Fg (object) = ρoVog
o = floating object
Net force
Finding the net force is useful to see if an object will rise, sink, or remain suspended. It is especially useful for submarine problems.
Fnet = FB – Fg (object) = mfg – mog
Fnet = FB – Fg (object) = ρfVfg – ρoVog

10. Solving buoyancy problems
Many buoyancy problems can be solved easily by looking at the ratio of the weight of the object and the buoyant force (weight of fluid displaced).
Fg (object) = ρoVog
Fg (object) ρoVog =
FB ρfVfg
Since the volumes are equal for a submerged object, we can cancel V and g.
Fg (object) ρo =
FB ρf