Constructive vs. destructive Wave interfearence (i think im the first to post this) -.-"

Constructive Waves- constructive waves are when two separate waves are on the same surface and they are moving towards each other in an attempt to collide. The name "Constructive" gives it away due to the fact that when the waves collide, they construct into a higher and different wave height. They are added together to create a wave with larger amplitude. Of course, the amplitude and wavelength can be different, but when they are added, the smaller one is forced up onto the larger one. If the wavelength and amplitude are the same, they are just twice the height as the original one. After the mere second of collision, the wavelengths and amplitude of the two different waves remain the same as they go the opposite direction they were originally traveling towards.

Destructive Waves- destructive waves are when two separate waves on the opposite surfaces and they are still moving towards each other in a desperate attempt to collide. The name "Destructive" also gives it away, when the waves collide, they will cause either deformed shapes or the top of the larger shape sinking the same width as the smaller shape into the larger shape's structure. Now, it can (in some cases) move the opposite directions into the below section of a wave. Thus, if the two amplitudes have opposite signs, they will subtract to form a combined wave with a lower amplitude.

types of energy? :P

 well... i found these 5 major energies which I'm going to describe. we learned about potential energy and kinetic energy already in class... so I'm not going to describe that.

Gravitational Potential Energy
 well, based on the name, i think one can already guess that this is the type of energy that gravity generates. since gravity is the forcing pushing us down, the gravitational potential energy is related to pushing the objects down. since work is done when something is lifted, the force times gravity will equal to gravitational potential energy.


Mechanical Kinetic Energy
 Well, it is actually difficult to define this one... Mechanical energy is the energy required to do work. and kinetic energy is the energy of motion. both of them combined is basically the energy required to do work such as motion. Walking and running is considered motion.

Chemical Potential Energy
This type of energy is the type of energy the food that human eats transfers into energy. the human body's acid in our stomach dissolve the food then it is transformed into Chemical Potential energy to have energy to work for the day, do the homework and finish the tests with enough energy for the next class! :)

Thermal Energy
 This type of energy is the energy which heat generates. the heat all stocked up will create energy. the amount of energy can be measured by the equation Q=MC∆T  where the amount of heat transfer (J) which is equal to mass (kg) x heat capacity (J/kg ◦C) x change in temperature (◦C).  Thermal energy can be transferred using one of these three methods: conduction, convection and radiation. 


Sound Energy   
Sound energy is caused by the vibration of the sound waves. The sound vibrations create waves of pressure which leads to compression of the sound waves. then the pressure causes the vibration to cause sound waves. but this type of energy is usually too small to cause electricity. 

the canon report

Well, first, in order to maximize the canon's shooting range, we will need it to be in a 45 degree angle. that will make the canon shoot the furthest. however, that is if there is no air resistance and wind affecting the light light canon ball we were FORCED TO USE STYROFOAM TO BUILD >:( sigh, so anyways, without wind patterns there should be no problem with the ball shooting its maximum range.

Also we use this equation: R = V²sin(2θ)/g to calculate it. We determine the value of θ to be sin(2θ) since we are assuming v and g do not change... Well, we need it to be sin 90 which means they need it to be a 45 degree angle.

Newton's problems... well not his problems but his problems to the world- ehhhh you know what i mean >:(

First of all, The 4 problems are Equilibrium, Inclines, Pulleys and Trains(not the band, actual trains :))

- They all need assumptions
For Equilibrium- No Friction and a=0
For Inclines- positive direction of motion, a=0, no resistance
For Pulleys- No friction, no resistance, 2 FBDs
For Trains- 3 FBDs, No resistance, a=0 and constant, horizontal and positive motion

Example from my notes!-(sorry about it being sideways, its the only way to take the picture :( )
Equilibrium-

 Inclines-

 

Pulleys-

 Lastly, Trains-

Two in one- Vector addition AND physics of a Roller Coaster

 Physics of a Roller Coaster

Well a roller coaster works because of two principles, Kinematics and Dynamics. First of all we have to understand Newtons three laws:

Newton's first law- law of inertia : All objects will remain in a state of rest or continue to move with a constant velocity unless acted upon by an unbalanced force.

Newton's second law : The acceleration of an object depends inversely on its mass and directly on the unbalanced force applied to it.

Newton's third law : For every action force, there is an equal and opposite reaction force.


 Those laws would prove that Roller coasters have force applied on them in order for them to move. With a force of gravity acting against and along with it, the roller coaster is able to gain speed to fulfill the entrainment which people require for amusement. So we see Newton's first law applied as the roller coaster does not move unless there is a chain dragging it against gravity, and gravity acting on it as it goes down. Then we see Newton's second law as the weight of the people on the coaster and the coaster itself will affect the free fall or the fall of a roller coaster. Lastly, we see Newton's third law as for the against gravity movement, there is a along gravity movement.

Vector Addition

Vector addition is the addition of vectors. You basically need to understand that you are adding the directions along with the length. So first, before we move on to an example, you need to recall the Pythagorean Theorem which is A^2 + B^2 = C^2

 The vector addition is similar to that, because it is just one unknown side (usually the hypotenuse) then two known sides, which then will lead to the square of the two known numbers followed by the addition of both known numbers.

whoops almost forgot :P. deriving equations 3 and 4!

So Equations 3 and 4 are basically what Mr.Chung calls "Twins" so they are basically the same except that one is  V_{1 and the other is} V₂


How to transform from Equations 1 and 2 to Equations 3 and 4:
Equation 1: V₂₌ V_1+at
Equation 2: d= ^1/₂  (V₂ -V₁ )t

3:

Sub (at) for (V₂ -V₁ ) from equation 2_: d= ^1/₂  (V₂ -V₁ )t   +    V₁ t

 d= ^1/₂  (at)t   +    V₁ t

  d= ^1/₂   a t²   +    V₁ t

 d=  V₁ t  +   ^1/₂   a t² 

4:

d= V₂ t - ^1/₂  (V₂ -V₁ )t
Sub (at) for (V₂ -V₁ ) from equation 2
d= V₂ t - ^1/₂  (at )t
d= V₂ t - ^1/₂  a t²

The graphs but switched....i drew them...