Destructive Interference & Constructive Interference

Wave interference is when two or more waves interact at the same time and a combined, stronger wave is formed. Destructive interference and constructive interference are two types of wave interference. During any wave interference the shape of the medium is determined by the sum of the separate amplitudes of each wave. i.e. when waves interfere, amplitudes add. 



In destructive interference, the positive amplitude of one crest is added to the negative amplitude of the other trough. The two waves combined interfere with each other, weakening the wave.

In constructive interference, the positive amplitude of one crest is added to the positive amplitude of the other crest. The two waves combined will be stronger.

Energy

The three laws of thermodynamics state that:

1. Conservation of Energy: Energy cannot be created or destroyed
2. Law of Entropy: Randomness (disorder) always increases
3.Absolute Zero: All things stop moving

               Energy is all around us. Every task that we complete in our day to day life uses up energy. It is important to note that thought energy cannot be destroyed (first law) it can be transformed. There many different types and forms of energy we encounter. Some of these are:

Potential Energy
Chemical Energy
Mechanical Energy
Kinetic Energy
Electric Energy
Sound Energy
Light Energy
Mechanical Energy
Thermal Energy
Nuclear Energy
Radial Energy
Elastic energy

All About Cannons

               A cannon is a piece of artillery than uses explosive- based propellants to launch a projectile. There are various types of cannons specialized in a task they are used for: range, mobility, rate of fire etc. The earliest known cannon was used as early as the 3rd century BC. Ever since, cannons have become more and more advanced and efficient in its design.

               Our latest project is to build a cannon using just 5 pop cans, duct tape, and 2 styrofoam cups. The goal is to maximize horizontal distance travelled by the cannon.

               The optimal angle to fire the cannon is 45 degrees. A 45 degree angle will ensure that there is a perfect balance between height and horizontal distance for maximum hang time and range. The base of the cannon should be stable so as not to backfire when the cannon-ball is launched. The mass of the cannon-ball should be minimal to maximize acceleration (F=ma). Something that is also important is that the cannon needs to build up as much pressure as possible within it before the fluid within it is lit. This can be achieved by increasing the surface area of the baffles and shaking the cannon well to achieve an even coating of ethanol over the entire surface area of the cannon. The cannon-ball should be tightly sealed to the cannon so none of the gas will be expelled before the lighting.

Solving Newton's Problems

Newton's laws of motion are as such:

1. 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.

2. The acceleration of an object depends inversely on its mass and directly on the unbalanced force applied to it (F=ma)

3. Every action has an equal and opposite reaction.

There are four types of problems that incorporate Newton's second law in its solution: Equilibrium, Inclines, Pulleys, and Trains. In order to solve such questions, some assumptions must be made about the conditions surrounding it. The assumptions for each type of question are listed below:


Equilibrium:
-no friction or air resistance
- a=o (y and x)


Inclines (static)
- no air resistance
-a=o (y and x)
-Fn is perpendicular to surface
-+ve axes is direction of a
-μ= tanθ


Inclines (kinetic)
- no air resistance
-a=o (y)
-Fn is perpendicular to surface
-+ve axes in direction of a


Pulleys 
-no friction or air resistance
-+ve axes in direction of a
-a of the system is the same
-2 FBDs 
-T1= T2


Trains
-No air resistance
-a=0 (y)
-a is constant
-+ve axes in direction of a 
-1 FBD to find a
-3 FBDs to find T1 or T2




After listin assumptions, draw the appropriate free body diagrams. Next use the formula F=ma and split the data from the FBDs into x and y components. Sub in values accordingly to find the desired variable.

The first and most important step in solving a projectile motion problem is to split the givens into x and y components. 

X components	Y components
a= 0	a=-9.8m/s^2
v= constant	v= changing
d=range	d=height
t= same for both values

knowing that the time elapsed on both axes are the same, we can incorporate the big 5 equations to find the time for whichever axis is possible.
for x:   dx= (vx)(tx)
for y:   Δdy= vy Δt + ½ ayΔt²


Now this value can be used along with other available values to solve for any missing values.

The Physics Behind Rollercoasters

            Something most people do not realize is that rollercoasters do not have an engine. After the car has been pulled to the top of the first drop by a mechanical belt, the rest of the ride is completed through the conversion of potential energy (stored energy) to kinetic energy (motion energy). This is why as hills shorten and the angle of curves become more shallow as the ride progresses.
             When you descend that first hill, different types of wheels keep the ride interesting and safe. Running wheels guide the coaster on the track, friction wheels control lateral motion, etc. The compressed air brakes stop the car as the ride ends.

              As for my favorite rollercoasters, I would say they are The Behemoth and The Mighty Canadian Minebuster, both at Canada's Wonderland. Behemoth, with a 230 feet drop and reaching speeds of 125 km/h is definitely the favorite of many. The Minebuster however only reaches speeds of 90km/h, but the old wooden design and rickety tracks make it one of my favorites.

How To Add Vectors

• If the givens are collinear, set a reference direction and solve by addition/ subtraction.
• If givens are not collinear, draw head-to-tail arrows in the direction of travel.
• Draw and label the resultant vector. From start of first to end of last component vector.

• Label your positive axis, for example North and East are positive, therefore South and West are negative.
• Group and add all the X components. Do the same for Y components. (N and S are Y components, E and W are X components)
• Using c²= a²+b² ( Pythagorean theorem), find magnitude (c²).
• Now use SOH CAH TOA to find the angle of direction. 

Therefore, the final hypoteneuse is the resultant vector and the final angle is the angle of direction.