Saturday, August 30, 2008

Work and Energy

Hey there,
Since you should be enjoying your last days of holiday ( I'm enjoying them anyway), I'll just be adding a short post today. It's about work and energy. Maybe better: Work or Energy.

All objects contain energy. This energy makes them capable to perform "work". So, for energy, we use the same unit as for work: the joule. The energy in an object can be divided in 2 categories:
  • Potential energy: The energie an object contains because it's located in a gravitational field.
  • Kinetic energy: the energy an object contains because it has a certain speed
  • (All matter also contains energy. Because trough out the entire universe, matter and energy can be converted, and the total stays constant, according to Einsteins formula: E=mc²)
The total of these tree energy types in an object always stays constant. And because in the early exercises, we won't be using the mass-energy, we can say that the 'total energy', consisting of kinetic and potential energy, remains constant. More about this later.

Oké, this was just an 'Intermezzo'. Next topics will be about potential and kinetic energy.

Thursday, August 28, 2008

Work: A force on the move

It was a difficult decision, but I thought it would be better to see "work" before pressure, although I find it more difficult. But let's give it a go.

Work in physics isn't the same as work as we know it. In physics, we say work is done by a force on an object only if:
  • The object displaces.
  • the direction of the displacement isn't at right angles with the direction of the force.
We define this 'work' as the product of the force acting on the object and the distance through which the object moves. Or

W = F. d(x)

If we insert the units Force and Distance, we get the unit of Work, the Joule:

J = N . m

Sometimes, the direction of the force isn't the same as the direction of the movement. For example, if a boat is pulled by boatman with a rope:

Here, we have a pulling force, F, which pulls in the movement direction. If we want to determine the part of the force that moves the boat, we have to project the force on the direction of the movement. If we do so, we get Fm = F . cos(a). So, the work done by the force F, with regard only to the direction of the movement, is:

W = Fm . d(x) => W = F . cos(a) . d(x)

These are the basics to work. It's probably verry abstract, but it will become clearer in the next posts about work to move objects etc.

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Saturday, August 23, 2008

2nd common force: 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.
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Monday, August 18, 2008

1st common force: 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:

In stead of

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

Saturday, August 16, 2008

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.