Interference of Waves

Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium.
The principle of superposition says  that the resulting wave is the sum of the two individual wave functions.

Two types of wave interference:

CONSTRUCTIVE INFERENCE:

a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction. In other words, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the beginning waves.

For example, if the crests (or troughs) of two lwaves are in the same direction,

they combine together to create an amplified wave.

DESTRUCTIVE INFERENCE:  

a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. In other words, when two waves with
opposite displacements (one wave displaced up and the other down) meet at a given location, the upward pull of one wave is balanced (canceled or destroyed) by the downward pull of the other wave.

In the opposite scenario, where the crests of one wave are aligned with the troughs of another,

they cancel each other out.

ENERGY in Various Forms

Energy comes in many different forms.

The two main forms of energy are KINETIC ENERGY and POTENTIAL ENERGY.

KINETIC ENERGY: ENERGY OF MOTION.
We know that there is kinetic energy when the matter is moving. The faster an object moves, the more kinetic energy it has.

- THERMAL or HEAT ENERGY: ENERGY THAT MAKES OBJECTS HOT.
It is a form of kinetic energy at the molecular level.
It is caused by the increase in activity or velocity of molecules in a substance, which causes the temperature to rise.

Example: When we boil water in a kettle,
we are increasing the kinetic energy of every particle of water.
The collective kinetic energy of all these particles is thermal energy.

POTENTIAL ENERGY: STORED ENERGY.
Due to its position, an object can store energy which is called potential energy.

- GRAVITIONAL POTENTIAL ENERGY: STORED ENERGY IN OBJECT DUE TO ITS HEIGHT WHERE THE FORCE OF GRAVITY CAN ACT ON IT TO MAKE IT FALL.
This type of energy depends on the mass and the height.
There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the gravitational potential energy.

Example: Water at the top of Niagara falls can be said
to have this type of energy that can be used to do work as it "falls".

- ELASTIC POTENTIAL ENERGY: ENERGY STORED BY BENDING, STRETCHING, OR COMPRESSING OF MATTER.
Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, etc. The amount of elastic potential energy stored in such a device is related to the amount of stretch of the device - the more stretch, the more stored energy.

Example: Stretching an elastic band infront of someone's face,
will cause that person to make it clear that he/she is aware of
the energy that might be released from the band.

- CHEMICAL POTENTIAL ENERGY: ENERGY STORED IN THE CHEMICAL BONDS OF MATTER AND CAN BE RELEASED BY WAY OF CHEMICAL REACTION.
Chemical potential energy can be stored in unlit matches, batteries, food, and gasoline.

Example: When food is digested and metabolized (often with oxygen),
chemical energy is released, which can in turn be
transformed into heat, or by muscles into kinetic energy.

- SOUND ENERGY: ENERGY PRODUCED BY SOUND VIBRATIONS AS THEY TRAVEL THROUGH A SPECFIC MEDIUM.

Sound vibrations cause waves of pressure which lead to some level of compression and rarefaction in the mediums through which the sound waves travel.
Sound travels at different speeds depending on the material it is travelling through.  (Fastest through solids because they are so dense, slower through liquids and gases because they're not as dense).  Sound energy is typically not used for electrical power or for other human energy needs because the amount of energy that can be gained from sound is quite small. Sound Energy is measured in terms of pressure and intensity using units such as pascals and decibels.


MECHANICAL POTENTIAL ENERGY : MECHANICAL ENERGY IS THE SUM OF ENERGY IN A MECHANICAL SYSTEM. THIS ENERGY INCLUDES BOTH KINEMATIC ENERGY AND POTENTIAL ENERGY.

Mechanical energy is the energy that is possessed by an object due to its motion or due to its position.

Example: A moving baseball possesses mechanical energy
due to both its high speed (kinetic energy) and its vertical position
above the ground (gravitational potential energy).

and

MECHANICAL POTENTIAL ENERGY: ABILITY TO WORK.
Any object that possesses mechanical energy - whether it is in the form of potential energy or kinetic energy - is able to do work. That is, its mechanical energy enables that object to apply a force to another object in order to cause it to be displaced.

CANNONS!

Jaivan Cannon - Worlds largest Cannon on wheels



An important aspect of how successful a cannon can be in shooting its object out to its maxium distance would be the projectile degree.

According to various sources:

"We know from theory and experiment that you get the most distance with the least effort by firing a projectile at 45 degrees, exactly midway between vertical and horizontal."

So from this we learn that launching a projectile at 45 degrees from the ground will allow it to reach it's optimum distance (in the x axis).

Of course, I think that they're are many variables can alter this:

1) Weight of projectile: If the object is heavier, it would most likely reach the ground faster.

2) Air resistance: Our cannons are not launched in a vacuum where there is no drag forces such as air resistance. The horizontal component of the cannon's porjectile's velocity would decrease steadily as it moves through the air.

3) Power behind projectile: We can assume that since the cannons cannot be pushed against the floor for power or as Mr. Chung said we can't add wings on it or anything, the fastest and easiest angle would seem to be 45 degrees.

4 Newton Problems!



Sir Isaac Newton





So it all started

out with Newton

sitting under an

apple tree .......  

Newton's three laws of motion:

1. INERTIA: "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

(Inertia is the tendency of an object to resist changes in its state of motion.)

2. F = MA: "The acceleration of an object depends directly upon the force acting upon the object, and indirectly upon the mass of the object."

As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

3. For every action, there is an equal and opposite reaction.


 

There are four types of Newton's problems:
Equilibrium, inclines, pulleys, and trains.

EQUILIBRIUM When forces are balanced.

Assumptions:
- no friction

- positive axes
- a = 0 (ax = 0 and ay =0, there is no movement in the x axis or y axis)

INCLINES

STATIC:When the object is not moving while on an incline. Static friction is preventing motion on a stationary object.

Assumptions:
- a = 0
- Fn is perpindicular to surface
- positive axes in the direction of acceleration
- no air resistance
- static friction = coefficient of static friction x normal force
- μ = tanΘ

KINEMATIC:
When the object is moving down an incline. The kinematic friction is working against the moving motion.

Assumptions:

- ax ≠ 0, ay = 0 (because it is moving in the x axis)
- positive axes in direction of acceleration
- Fn is perpindicular to surface
- no air resistance
- kinetic friction = coefficient of kinetic friction times normal force

PULLEYS
When objects are held by pulleys.

Assumptions:
- frictionless pulleys + rope
- no air resistance
- multiple FBDs
- positive axes in direction of acceleration
- T1 = T2
- acceleration of system is the same

TRAINS
When the problem deals with a train.

Assumptions:
- 1 FBD for acceleration
- 3 FBDs for T1 & T2

- no air resistance
- weightless cables
- positive axes in direction of acceleration
- ay = 0
- a is consistent

And remember that for each problem,
BREAK DOWN THE X and Y COMPONENTS and SET YOUR POSITIVE AXES.  

PROJECTILE MOTION

 CLICK HERE!!! CHECK THIS VIDEO. IT'S REALLY GOOD. It's a really simple explanation of projectile motion.

PROJECTIVE MOTION:
events where object moves under the influence of gravity and is not self powered.

A horizontal constant motion plus an accelerating vertical motion = parabolic motion (curved motion).



This diagram shows a ball that is thrown in a parabolic motion.

  As you can see from the above illustration, the velocity components are at different positions.

Vx, the velocity for the x component is constant because it's displacement is the same everytime and there is no acceleration, since it goes on in a continueous speed. Due to no air resistance, the velocity in the horizontal direction is constant.

The Vy factor that represents the y component is not constant. Vy1 is 0 because it is clearly shown when the ball is at it's peak height the Vy1 is 0 because there is a x vector which means there will not be a y vector. As the ball goes higher in the first half of the projectile, the Vy magnitude decreases and soon after it starts coming down on the second half of the projectile motion, it increases in magnitude in a negative direction. The change in Vy is due to gravity.


Solving projectile problems:

Look at the given values and split into x and y components.

X: ax = 0
     Vx = constant
     Dx = range/ horizontal displacement

Y: ay = -9.8 m/s2
    Vy = changing
    Dy = height/ vertical displacement

Remember that x and y component share only ONE same component which is TIME.
Tx = Ty

For X:
Dx = VxTx

For Y:
Use BIG 5 EQUATIONS ... Dy = Vyt + 1/2 at²