This text is meant to accompany class discussions. It is not everything there is to know about fluids, hydrostatics, and fluid dynamics. It is meant as a prep for class.
If you put a ball under water it creates a hole where the water has been was.
The bowling ball feels a buoyant force pushing it up. the buoyant force is equal to the weight of the water that would have filled the hole the bowling ball made.
Weight of a fluid is
Since the buoyant force is equal to the weight of the water that would fill the "hole" under water created by the ball
B= Buoyant Force in Newtons [N]
ρ is the fluid's density in [mg/m3]
V is the volume that is under water [m3]
g is the acceleration due to gravity 9.80 m/s2
Some key points to remember
The buoyant force always points up.
The buoyant force can be used to free body diagrams to calculate net forces and accelerations.
The fluid's density provides the buoyant force.
Floating and sinking
There are the possibilities for a body that is not accelerating. It can float, sink, or be neutrally buoyant.
When the density of the body in a fluid is GREATER than the density of the fluid the body will sink. If the fluid provides very little resistance then the body will accelerate downward until the resistance force and buoyancy is matched by the weight of the object.
When the body sinks, it is called "negatively" buoyant.
The body's density is greater than the fluid's density it is in.
When the density of the body is LESS than the density of the fluid the body will rise up.
If the body is held down by some other force, say a hand, and then released, the body will instantly accelerate upwards. This can be calculated with with a free body diagram. (Neglecting water resistance.)
When the body floats, it is called "positively" buoyant.
The body's density is less than the fluid's density it is in.
When the density of the body is EQUAL to the density of the body, the body will either "hover" in water and neither move up or down.
When this situation occurs the body is "neutrally" buoyant.
The body's density is equal to the fluid's density it is in.
If the density of the body is a lot less than the density of the fluid, then the rise up through the fluid until it sits on the surface. It floats above the surface until the the amount of the body that is under water has a weight equal to the amount of water it displaces.
The body's density is less than the fluid's density it is in and the body has had a chance to reach equilibrium at the fluids surface.
When the body is resting on the bottom, such that no water can get between the body and the bottom, the fluid cannot exert an upwards pressure and therefore there will not be a buoyant force pushing up on the block. This is only if the bottom of the body is "perfectly smooth" and the container's bottom also "perfectly smooth." This is not the normal situation when a body rests on the bottom in the real world.
If the body is said to be "resting on the bottom," in a problem, then water will still seep between the body and floor and there will still be an upwards buoyant force. The free body diagram would look like this one with the addition of a buoyant force pointing upwards.
There is a special unit of measure called, "specific gravity." Specific gravity is the ratio of a fluid or body's density to that of water. Water has a density of 1000 kg/m3.
Examples
If a cup of oil has a specific gravity of 0.95, then what is its density?
A piece of very light wood has a specific gravity of 0.400, what is its density?
Example #1
Question
Solution on Paper
Video Solution
Question
Solution on paper
Video Solution
A barge is made from a rectangular box. The bottom of the box is 4.00 m by 3.0 m. How much farther will the barge sink below the surface of the water when a 1500 kg pickup truck is loaded on it?
To lift up a heavy chest of gold, salvage divers will take a large pair of deflated round balloons 1.00 m in diameter and attach them to a small chest of gold with a mass of 1000.0 kg. They will then inflate balloons to a diameter of 1.00m. Will the balloons lift the chest and if so will it accelerate as it is lifted? If instead the chest would sink, then how fast will it accelerate downwards. Neglect friction with the water.
A block of wood measures, 3.81x 8.89 x 20.32 cm. It is placed in still, fresh, water with the orientation shown below. The wood has a density of 444 kg/m3. How many cm of the wood will stick up above the water?
A block of wood measures, 3.81x 8.89 x 20.32 cm. It is placed in still, fresh, water with the orientation shown below. The wood has a density of 444 kg/m3. How many cm of the wood will stick up above the water?
Rules of thumb for buoyancy
Floating bodies (that is not attached to anything else)
It is not accelerating
The weight of the entire floating body is equal to the buoyant force.
The volume of the water that is displaced by the floating body is equal to the weight of the fluid that was displaced.
The percentage of the volume that is under water is equal to the ratio of the densities,
Submerged bodies
It is possible for a body have a net force and a net acceleration.
The volume of the water that is displaced by the floating body is equal to the weight of the fluid that was displaced.
The buoyant force is equal to ρVg where the Volume, V, is the entire volume of the submerged body.
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
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