Thursday, September 3, 2009

VECTORS

Vectors are measurements that have both magnitude and direction. Vector quantities are used frequently in both math and physics; vector usage has both basic and complex applications. Vectors are represented by straight lines with a head on one end (denoted by an arrow,) and a tail (denoted by a “flat” end) on the other. As might have been assumed, the arrow represents the direction of the vector, and the length of the line represents the distance of the vector.
Basic Vectors(www.physics.brocku.ca)
[The meaning of the word "vector" itself has a definition that lends itself to desciribing many other phyics related terms (each that complys with having both a direction and a magnitude) such as velocity as opposed to speed, which connotes only magnitude and not direction.]

CENTRIFUGAL FORCE

We can find the equation for centrifugal force by finding the equation for centripetal force because we know that the two forces are equal in magnitude.
We have already derived the formula for centripetal acceleration([[1]]) and know that ac=v2/r or centripetal acceleration=velocity squared divided by the radius (in meters). We also know that f=ma or force=mass times acceleration (for derivation click [[2]]).
When we combine these two equations we end up with
Fc=mv2/r or
centripetal force=mass times velocity squared divided by radius (in meters)
Now that we have the equation for centripetal force we almost have the equation for centrifugal force as well. The acceleration for centripetal force is aimed into the center of the circle but the acceleration for centrifugal force is aimed away from the circle. Therefor, because centripetal acceleration is positive and centrifugal acceleration is going in the oposite direction, it is negative. Image:Wiki3.jpg


[edit] FINAL EQUATION FOR CENTRIFUGAL FORCE

The final equation for centrifugal force is
f=-mv2/r
where...
f= force (in newtons)
m= mass (in kilograms)
v= velocity (in meters per second)
r= radius (in meters)

QUADRATIC RELATIONSHIP IN PHYSICS

Quadratic relationships describe the relationship of two variables vary, directly or inversely, while one of the variables are squared. The word quadratic describes something of or relating to the second power. When it is a directly relationship will result to the shape of half of a parabola. In such a case, the two variables vary directly because they increase/decrease in conjunction. But they are described differently from a linear relationship because process of raising one of the variables to the second degree changes the rate of change every time.

[edit] Quadratic Relationships in Physics

Not all formulas in physics are linear; there are many that are quadratic as well. Just to name a few:
  • Centripetal Acceleration: ac = v2/r
    Centripetal Acceleration
  • Kinetic Energy: KE = ½ mv2
    Kinetic Energy
  • Law of Universal Gravitation:
    Law of Universal Gravitation
Let’s explore with the Law of Universal Gravitation. In the equation, d is the distance between the centers of the masses and G is the universal constant—one that is the same everywhere. According to Newton’s equation, if the mass of a planet near the sun were doubled, the force of attraction would be doubled. Similarly, if the planet were near a star having twice the mass of the sun, the force between the two bodies would be twice as great. In addition, if the planet were distance from the sun, the gravitational force would be only one quarter stronger.
Force vs Location
In this law, the distance varies inversely quadratic to the gravitational force and varies directly quadratic to G and the two masses.

IMPULSE-MOMENTUM THEOREM

Newton's Second Law of Motion: F = ma


Since acceleration (a) is equal to Δv/Δt you can replace the acceleration (a) in Newton's Second Law of Motion with Δv/Δt to get
F = (mΔv)/Δt
To get rid of the fraction (or division), you can multiply both side with Δt and then the equation will become
FΔt = mΔv
mΔv = m(v2 - v1) = mv2 - mv1, and since {mv2 = P2} and {mv1 = P1}
then FΔt = mΔv = P2 - P1
we can now conclude that
J = FΔt, J = mΔv, or J = P2 - P1 !!!
F = Force, m = mass, a = acceleration v = velocity/speed P = momentum

newton's third law of motion

The third law states that for every force there is an equal and opposite force. For example, if you push on a wall, it will push back on you as hard as you are pushing on it.


NEWTON'S SECOND LAW OF MOTION

Newton's second law of motion explains how an object will change velocity if it is pushed or pulled upon.
Firstly, this law states that if you do place a force on an object, it will accelerate, i.e., change its velocity, and it will change its velocity in the direction of the force.


Secondly, this acceleration is directly proportional to the force. For example, if you are pushing on an object, causing it to accelerate, and then you push, say, three times harder, the acceleration will be three times greater.


Thirdly, this acceleration is inversely proportional to the mass of the object. For example, if you are pushing equally on two objects, and one of the objects has five times more mass than the other, it will accelerate at one fifth the acceleration of the other.


PHYSICS-LAWS OF MOTION

NEWTON'S FIRST LAW OF MOTION
Isaac Newton stated three laws of motion.
The first law deals with forces and changes in velocity. For just a moment, let us imagine that you can apply only one force to an object. That is, you could choose push the object to the right or you could choose to push it to the left, but not to the left and right at the same time, and also not up and to the right at the same time, and so on.
Under these conditions the first law says that if an object is not pushed or pulled upon, its velocity will naturally remain constant. This means that if an object is moving along, untouched by a force of any kind, it will continue to move along in a perfectly straight line at a constant speed.





This also means that if an object is standing still and is not contacted by any forces, it will continue to remain motionless. Actually, a motionless object is just a special case of an object that is maintaining constant velocity. Its velocity is constantly 0 m/s.


Now, what about if there is more than one force on the object? You really can push an object, say, to the left and down at the same time, so, what happens then?
Under these conditions we must realize that a group of forces on an object adds up so that all the forces appear to the object as one force. This one force that is the sum of all the forces is called the net force. The word net in this context means total. It is this net force that may change the velocity of the object. Let us look at some examples.
Imagine that two forces act at the same time on an object. One is a very strong force to the left, and the other is a weaker force to the right. These two forces add up to one net force. Since the force to the left is stronger, the net force is to the left. This net force to the left will cause the velocity of the object to change. The object experiences this one net force as if this was the only force pushing it, although, actually, there are two separate forces present. Next let us see what happens when two forces act, but they are equal in strength.
Imagine that two forces, one up and one down, push on an object, and imagine that the two forces are the same size. These two forces add up as before, but this time one of them does not overpower the other. They cancel each other out. So, in this example the net force is zero. It is as though no forces were really acting on the object. Under these conditions the velocity of the object would not change. If it was moving in a straight line at constant speed before the two forces were applied, then it would continue to move in a straight line at constant speed after these two equal and opposite forces were applied. If it was standing still before the application of these forces, it would continue to stand still afterwards.
The net force is the total force. It could be the sum of two forces or more than two forces. If only one force acts upon an object, then this one force would be the net force. If the net force on an object is zero, then the object experiences no velocity change. If the net force on an object is not zero, then the object will show a change in velocity.
Lastly, this net force must be external to the object. The net force can not come from the object itself. You could not, for example, put on ice skates, stand on a frozen pond, push on your back by reaching around with your arms, and expect to get going. Although if someone else came up from behind and gave a you a shove, then your velocity would change.
But skaters do get going all by themselves, so, how does that happen? Well, that answer is in Newton's third law of motion.
Newton's first law of motion contains the same information as Galileo's explanation of inertia.
To see this law in action go to the following VRML 2.0 world.
You will find an object there upon which you can apply a force. You can apply only one force on the object at a time. The object's velocity will only change while this one force is being applied. The VRML world looks like this picture:
The object to be moved floats in the center of the world. There are six dark arrows touching it. Each arrow represents a force that can be activated upon the object. One arrow points in the positive x direction (to the right), another points in the positive y direction (upward), and so on. Click and hold down the mouse on one of the boxes in the foreground to activate the force that is described by the label on the box. The corresponding arrow on the object will turn white, and a force in its direction will be applied.
Notice that with no net force on the object, its velocity does not change. The only way to change the velocity is to apply a non-zero net force. If the object drifts away, either use your browser viewpoint options to get a better look or hit the Reset button. That button will bring the object back to its original position.