A Scientific Report on the Physics of a Situation

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In relation to physics, buoyancy is a term used to refer to the force a fluid may exert to oppose the object’s weight. Due to the overlying fluid’s weight in a column of fluid, the pressure will increase as depth increases. For this reason, a fluid, or an object that has been submerged in the fluid, will experience less pressure at the top of that column while the bottom column will have greater pressure. The outcome of this pressure differences is what accelerates the object to move upwards in what is termed as buoyancy. The difference in pressure between the top of the column and that at the bottom will have some proportionality to the magnitude of its force.

Archimedes Principle

According to this principle that was coined by Archimedes of Syracause, a floating object displaces its weight of the fluid. This a principle of floating bodies only. In reference to general objects, whether floating or sinking in a fluid, this principle may be stated in terms of forces as follows: An object, whether immersed wholly or partially, will be pushed up by a force equal to the fluid weight the object displaces. He came to the realization that objects which have been submerged in fluids tend to displace the fluids upwards. He came across this realization while he was taking a bath and the water level in the bath tub rose when he got in. from this observation, he concluded that an object’s buoyant force was equivalent to fluid weight that was displaced by that object. An object will, for this reason, sink if it is submerged in a fluid whose density is less than the object’s density.

An object will only float if it is less dense than the fluid or if it assumes an appropriate shape such as that of a boat. The magnitude of fluid weight a body displaces is thus equivalent to its upward force of buoyancy.

According to Archimedes Principle

Weight of the displaced fluid = force of buoyancy

Example:

A basketball with a mass of 0.5 kg and a diameter of 22 cm floats in a bathtub of water. Calculate:

a)      The force of buoyancy

b)      The volume of water displaced by the ball

c)      The ball’s average density

To calculate the force of buoyancy, the following formula is applied:

FB = mg

(Mg = weight) where M is mass and g is the force of gravity

= 0.5 x 9.8 = 4.9 N

Force of buoyancy is equal to the weight of the displaced fluid. To calculate the volume of the water displaced by the ball

Buoyancy force = weight of water displaced

Weight of water displaced = density of water x volume of water displaced x g

So,

Volume of water displaced = force of buoyancy / (density x gravitational force)

= 4.9 / (1000 x 9.8)

= 5.0 x 10 -4 m3

To calculate the density of the ball, we first determine the volume of the ball. The following formula may be applied:

Volume of ball = 4/3 πr3 (where radius of the ball is 0.11)

= 5.58 x 10-3 m3

To get the density, the mass is divided by the volume

0.5 / 5.58 X 10-3 = 89.6 kg/m3                     

Stability

If a floating object has the ability to bring itself back to its position of equilibrium upon a small displacement, the object is considered to be stable. The floating object tends to create a greater force of buoyancy when it is slightly pushed down. This signifies that the object possesses vertical stability. A floating vessel upon being given a slight angular displacement may resume its original position, to show stability, deviate from its original position, to show instability, or maintain its position and not move at all to show neutrality. An object’s upward force of buoyancy tends to act through the centre of buoyancy. Similarly, the force of weight applied on the object will act through its centre of gravity.
In this logic, a buoyant object will achieve stability if the centre of gravity is below the centre of buoyancy. Ideally, the centre of gravity in a ship should be aligned vertically to its centre of buoyancy.

Also, a ship must uphold a delicate balance between its stability and buoyancy for it to be considered seaworthy. A light vessel with little density and too much volume ma bobble on the surface of the water. For this reason, it is required to bear a certain amount of weight to be stable.

The density of the atmosphere is greatly dependent on its altitude. The buoyancy of an airship will decrease as an airship rises higher into the atmosphere. This is because there is an increase in the surrounding air’s density. In disparity, a submarine rises as its buoyancy tanks expel water. This is because the volume remains constant even as the mass decreases.

Compressible Objects and Fluids

Since buoyancy is dependent on volume, if an object is expanded, its buoyancy will increase and if it is compressed, its buoyancy will decrease.

An object’s equilibrium will remain stable if its compressibility happens to be less than the surrounding fluid. The object’s equilibrium will, however, be unstable if its compressibility is much greater than the surrounding fluid. As such, a slight upward perturbation will cause it to rise and expand whereas a slight downward perturbation will cause it to fall and compress.

Submarines rise and submerge by expelling and filling its tanks with large volumes of sea water. To submerge, water is allowed to flow into the tanks which are opened up. To obtain neutral buoyancy, the density of the submarine needs to be the same as the surrounding water. This will allow the submarine to remain at the required depth.

Fish present an example of applying volume change to bring about buoyancy change. They have an internal swim bladder occupied with gas. The fish changes the volume of the swimming bladder when it needs to ascend or descend

Density                     

An object with less density than the surrounding fluid will experience a greater buoyancy force than the force of its own weight when submerged fully in that fluid. As a result, the object will float and displace the same fluid weight as that of itself. The object will consequently rise once it has been immersed in the fluid. An example of this would be a block of wood immersed in water.

An object with the same density as that of the fluid will have a buoyancy force equal to its weight.
It will not sink, neither will it float but will remain submerged in that fluid. A commotion may, however, cause it to drift away from its location.

An object having a higher density than the surrounding fluid will sink because it will experience less buoyancy than its own weight. An example of this would be a steel ball immersed in water.

The density of air in comparison to a number of solids and liquids is negligible. An object’s weight while in the air is almost the same as its weight when it is placed in a vacuum. Air buoyancy of most objects is thus often rejected because its error is not of significance. The exception is in objects with low density such as balloons.

Swimmers demonstrate the principle that the force of buoyancy is much dependent on density. They experience a greater force when swimming in salty water than in fresh water.

 Icebergs are also a good example of the principle of density in relation to buoyancy. Water has an anomalous nature in that it becomes less dense when it is nearing its freezing point. Upon turning into ice, it freezes. This is the reason why icebergs and ice cubes are able to float.

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