2nd common force: Buoyancy

Buoyancy

My last topic about forces (but don't be scared, there is more to life than just that) is about buoyancy.

One day, Archimedes was taking a bath. He had already spent some years on finding out why an object in water experiences a lower gravitational force. Suddenly, he noticed he kept floating in the water, and that hes bath had overflowed when he stepped in it. He found the explanation, and completely naked, he ran on to the streets screaming "eureka" (I found it) (running naked on the streets wasn't such a big deal back then).

What was he so happy about? He had discovered that an object immersed in a fluid, experiences an upward force, equal to the gravitation on the displaced mass of water.

Knowing that, we can easily producea formula for the so called buoyancy.
All matter has a density, P (The Greek letter 'rho'). This is the ratio of the mass to the volume (for water, this is 1000kg/m³ ). So, the mass of an amount of fluid is the product of P and the volume of the fluid. But since the volume of the displaced fluid equals the volume of the object in the water, we can say:

m = V . P

So the gravitation on this mass of displaced fluid is:

FA = m . g => FA = P . g . V

If the buoyancy on an object is bigger than the gravitation on the object, the object will rise and come out of the water, until the gravitation and the buoyancy are equal. The opposite happens when the gravitation is bigger than the buoyancy. Then the object will keep on sinking until it hits the bottom. When the gravitation equals the buoyancy, the object floats on or in the water.

Now, we can calculate we whether a small submarine of 10 kg with a volume of 0,05 m³ (under water) will sink, float or rise out of the water.

FG = 10kg. 9,81N/kg = 9,81. 10 N

FA = P.g.V => FA = 0,05m³ . 9,81N/kg . 1000kg/m³ = 50. 9,81N

Since FA = 5 . FG => FA > FG. So, the object will rise (disregarding atmospheric pressure).

We can also calculate how much of the sub will remain under water. To do this, we'll need an equitation, since the sub will only stop rising when it is in rest. This is, when the resultant force ( = the sum of all force vectors) equals zero. In this case:

FG + FA = 0 <=> FG = FA
=> m.g = V.g.P

We know almost everything, so, same as before:

10kg . g = V . g . 1000kg/m³
=> V = (10kg . m³)/1000kg = 0,001 m³ = 10 dm³

So, the sub will keep rising until only 10 dm³ is still under water and 40dm³ is above (disregarding atmospheric pressure).

So, that's what I have to say about buoyancy. Hope you understand it. I think next, I'll start with pressure or work, we'll see.
Bye.
Technorati labels: Buoyancy

1st common force: Gravitation

Gravitation

You may already know that the weight of an object depends on its location in a specific gravitational field. Your weight is not the same on earth as it is on the moon. "Weight" is a force acting on an object because the force is in a gravitational field which pulls the object towards its center.

Since "weight" is a force, it's expressed in "N". It has a point in which the force starts, a direction (from the center of gravity from the object, to the center of gravity of the earth), and a size.

This size can easily be measured with the formula:

FG=m.g (or F=m.a *)

Here, "FG" is the force of the gravitational force, m is the mass of an object (while the weight of an object depends on its place, its mass (in kg) stays constant), and "g" is the gravitational constant, which is (on sea level) 9,81 N/kg.

So, a bag of 10 kg, on sea level, is pulled towards the center of the earth by a force of 10kg.9,81N/kg=98,1N.

* Some schools start by teaching "acceleration". When an object falls in free fall (on sea level), it accelerates with 9,81m/s². And, according to Isaac Newton's definition of force, a N is the force that accelerates a mass of one kg by 1 m/s². But I thought it would be easyer just to say:

g=9,81N/kg
In stead of
a=9,81m/s²

and then having to convert kg.m/s² at the end.
So, i'll be using "g".

So, that's gravitation. I'll add more on gravitation fields in the future, but meanwhile, this should do.
The next toppic will be buoyancy

Back to basics: What's a force?

I don't think it's a bad idea to start with repeating the basics of the basics. Especially because we're holiday now. And so I dedicate my first post to " forces", in its wide, physical meaning.

"A force is a cause of a transformation or of a velocity change of an object." and this means a force can give an object a different form (like when you go sit on a pillow), or it can accelerate, slow down, or completely stop an object (like you can do by kicking a football). All other reactions of a force acting on an object are derived from these 4 effects.

That, you just have to keep in mind. More important in physics, is being able to measure that force and perform calculations with it. Therefore, we have unit of force: the "Newton", or simply "N". For example, if you have a bag of 1 kg on your hands, on sea level, there is a force of 9.81N pushing your hands down.

This is still very abstract, but it will become more clear overtime, after it you have performed some calculations with it. The "Newton" is also one of the only new units you have to know. Many other units are derived from it.

By the way, a force is a vector, while the size of the force (in Newton) is a scalar. So, to name a force, we use an "F" with "->" on top of it. If we talk about the size of the force, we simply use "F" (if there is more then one force, we use indexes, like F1, F2, FA(buoyancy), FG (Gravitational force), etc.)

Since a force is a vector, it also has all the characteristics of it. In maths, you might have learned, a vector is completely determined by 3 things: the point in which the vector starts, its size and its direction.
For example
In this case, the point where the force starts is "A", the size is 15N and the direction is horizontal.

These are the basics, and you should understand them. If they are not clear to you, please mail me, and I'll add more.