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Month

September 2015

Congruence in Triangles

The following link explains the different congruence criteria for triangles:

https://drive.google.com/file/d/0B_5ZswHKMyPDQU9Sc1lFYnk4TWs/view?usp=docslist_api

Presentations related to derivation of these rules will soon be released.

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Cell Cycle and Division

The following link is about Mitosis in animals:

https://drive.google.com/file/d/0B_5ZswHKMyPDeW82Rzk2UFNYTjA/view?usp=sharing

You’ll find a .ppt file by following this link.

Density And Buoyancy

Well this ain’t about density=mass/volume stuffs; every bloke knows that. This is about the deep meaning of it and Why the hell is this happening and…….. forget it, you’re soon gonna find out:

Density

Density is mass upon volume (ρ = m/v). I know what you’re thinking but, you know, it’s the basics.It’s a property of matter.

Well to be frank density is nothing but amount of stuffs in a particular volume. This definition must be much more soothing than the one given above.

Buoyancy

Buoyancy is a simple puny force which works when there is a liquid, an insoluble solid and Gravity.

Look here, everyone is in tough competition in nature, everything. When there is beaker filled with water, it only wants to go as down as possible (all thanks to Gravity!) and will not let anything come in their path until its opponent is really strong.

So when you drop a hollow plastic ball it tries to go deeper into the water but water being denser than the hollow ball manages to defeat it and stops it from drowning whereas pushes it upwards, this upward force is Buoyancy. Yet the ball is not that weak and manages to be partly submerged in water. If you watch closely, you would find the tip of ball is submerged into the water. This means a part of the water has been displaced by the ball.

Well here are few points everyone must know related to Buoyancy:

  • The volume of the part of the ball submerged in water is equal to the volume of water displaced
  • Total mass of the ball equals the mass of the water displaced!
  • The upward force of Buoyancy is only possible when there is a downward Gravitational force
  • The force of Buoyancy depends on the density of both the liquid and the solid.
  • Weight of the  ball equals to the buoyant  force exerted by the displaced liquid
  • Weight of the displaced liquid equals Buoyancy Force

Types of Buoyancy

Density of liquid > Density of solid

  • The Solid floats
  • The buoyancy at the most stable position (i.e if you Leave the apparatus undisturbed) is that of neutral buoyancy[1].
  • Buoyancy force > weight of the object.(continue reading before coming to any conclusion)
  • Well. Didn’t we just read earlier that Bf   (Buoyant  Force) equals the Weight of the object? Then what is this nuisance? I’ll clear your doubt. The above given case is not for neutral buoyancy. It’s when you drop a wooden log from a height and it plunges deep into the water. At that depth, Bf   is greater than the Weight[2]  of the object and the Bf pushes it upwards until it equals the Weight of the object i.e until it attains Neutral Buoyancy.(read the heading-“comparison between the types of Buoyancy” to clearly understand it.)

Density of liquid < Density of solid

  • The whole body gets submerged into the liquid
  • The volume of the entire body equals volume of water displaced.[3]
  • Weight of the body is more than the B.
  • The body drowns to the deepest point possible since change in depth has nothing to do with volume of water displaced (unless and until it’s completely submerged.This comparison cannot be made between buoyancy type 1 and buoyancy type 2)

Density of liquid = Density of Solid

  • The entire body is submerged
  • The volume of the entire body equals volume of water displaced.
  • The body drowns but hovers in any position but completely submerged. If you place it in any position it’d hover in the position you had assigned it, this situation is called Neutral Buoyancy[4]
  • Neutral Buoyancy is observed in fishes and  Hot air balloons.

Comparison between the types of Buoyancy

Type 1

It’s said that the density of liquid is more than that of the solid. But this fact is not acceptable when the apparatus attains ‘stability’  and the solid is floating. This is only acceptable only when the solid is plunged deep into the liquid where the Bf is greater than the solid’s weight. As unbalanced external forces are acting on the solid and the net force being upward. The body moves up until it attains neutral buoyancy.

Type 2

The weight of water displaced = buoyant force and as the density of solid is more when compared to a liquid of same volume it’s weight would eventually be more[5]. So the solid would surely sink. Since at any depth the amount of water displaced would be the same and due to the action of unbalanced force the net force would be a downward movement.

Type 3

Since the density as well as volume is equal for both the solid and the liquid, eventually the mass would be constant. And if mass is constant then the weight and the buoyant force would be the same resulting in balanced forces. So if you submerge the solid completely anywhere inside the water it’d hover in the particular position since the net force is zero.

Calculation of the buoyant force

F=ma

=m/v  * v * a

=ρ*v*g

=ρvg

Where ρ= density of liquid (pronounced as ‘ro’  or ‘rho’) ,  v= volume of liquid displaced,  g=acceleration due to gravity

This can also be said as ρ= density of liquid,  v= volume of solid submerged,  g=acceleration due to gravity (since volume of liquid displaced equals volume of solid submerged) 


Bet you didn’t know 

The density of water is 1g/cm3 and that of ice is 0.9g/cm3. Therefore ice has density 90% that of water. If you observe a floating ice carefully, you’ll find 90% of it submerged in water. This holds good for other liquids and solids.  Want to know why ice floats on water? Check out this link: https://m.youtube.com/watch?v=UukRgqzk-KE

By Aryaman


Footnotes

(1.) Neutral Buoyancy is a situation where the Bf equals Weight of the object.

(2.) You should be knowing that Weight is a force and is entirely different from mass,  rather weight depends on the mass of an object, since W=mg in which g is acceleration due to gravity so it can also be written as W=ma; since F=ma, Weight is a force.

(3.) Since on comparison with point 1 under the subtopic-“important points to know about buoyancy”, Volume of submerged part in this situation is the volume of the complete body since the entire body is submerged.
(4.) Neutral Buoyancy is observed when density of liquid = density of solid. But actually Neutral Buoyancy is when Bf equals Weight of the object.
DO NOT CONFUSE!

(5.) ρ=m/v and volume of both the solid and the liquid are equal (in type 2 volume of solid = volume of displaced liquid), therefore if density increases mass should increase.

If you have any doubt your free to ask in the comment section

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