Interference of waves

Constructive interference is 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 this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses. Constructive interference is observed at any location where the two interfering waves are displaced upward. But it is also observed when both interfering waves are displaced downward. This is shown in the diagram below for two downward displaced pulses.
Destructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine pulse with a maximum displacement of +1 unit meets a sine pulse with a maximum displacement of -1 unit, destructive interference occurs. This is depicted in the diagram below.

ENERGYYY !!@!@!@#!@#!@#!@#

What Is Energy?

Energy makes change possible. We use it to do things for us. It moves cars along the road and boats over the water. It bakes a cake in the oven and keeps ice frozen in the freezer. It plays our favorite songs on the radio and lights our homes. Energy is needed for our bodies to grow and it allows our minds to think.
Scientists define energy as the ability to do work. Modern civilization is possible because we have learned how to change energy from one form to another and use it to do work for us and to live more comfortably.

Energy can be classified as either stored (potential) energy and working (kinetic) energy. All energy can be measured in “Joules”.

Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. Sound is produced when a force causes an object or substance to vibrate — the energy is transferred through the substance in a wave. Typically, the energy in sound is far less than other forms of energy.

Radiant Energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Light is one type of radiant energy. Sunshine is radiant energy, which provides the fuel and warmth that make life on Earth possible.

Thermal Energy, or heat, is the vibration and movement of the atoms and molecules within substances. As an object is heated up, its atoms and molecules move and collide faster. Geothermal energy is the thermal energy in the Earth.

Motion Energy is energy stored in the movement of objects. The faster they move, the more energy is stored. It takes energy to get an object moving and energy is released when an object slows down. Wind is an example of motion energy. A dramatic example of motion is a car crash, when the car comes to a total stop and releases all its motion energy at once in an uncontrolled instant.

Chemical Energy is energy stored in the bonds of atoms and molecules. Biomass, petroleum, natural gas, and coal are examples of stored chemical energy. Chemical energy is converted to thermal energy when we burn wood in a fireplace or burn gasoline in a car's engine.

Mechanical Energy is energy stored in objects by tension. Compressed springs and stretched rubber bands are examples of stored mechanical energy.

Nuclear Energy is energy stored in the nucleus of an atom — the energy that holds the nucleus together. Very large amounts of energy can be released when the nuclei are combined or split apart. Nuclear power plants split the nuclei of uranium atoms in a process called fission. The sun combines the nuclei of hydrogen atoms in a process called fusion.

Gravitational Energy is energy stored in an object's height. The higher and heavier the object, the more gravitational energy is stored. When you ride a bicycle down a steep hill and pick up speed, the gravitational energy is being converted to motion energy. Hydropower is another example of gravitational energy, where the dam "piles" up water from a river into a reservoir.


Electrical Energy is what is stored in a battery, and can be used to power a cell phone or start a car. Electrical energy is delivered by tiny charged particles called electrons, typically moving through a wire. Lightning is an example of electrical energy in nature, so powerful that it is not confined to a wire.

Potential Energy
Potential energy is stored energy and the    energy of position — gravitational energy. There are several forms of potential energy.

Kinetic Energy

Kinetic energy is motion — of waves, molecules, objects, substances, and objects.

Cannons?

 

How To Maximize a Cannon's Horizontal Range

In order to maximize a cannon's horizontal range, the angle of the barrel must be set to 45 degrees above the horizontal (assuming all other things like the size of the projectile and the power of the propellant are equal, level ground, and no air resistance). This optimal angle can be proven using the formula for the range of a projectile:

R = V²sin(2θ)/g

Using this formula, we can determine the value of θ that will maximize the value of sin(2θ), which will maximize the range of the projectile since v and g do not change. The maximum value of sin(2θ) is 1, which occurs at sin(90). Therefore the value of θ must be 45 degrees above the horizontal. 

4 NEWTONS PROBLEM Equilibrium , inclines , pulleys , trains.

Equilibrium and Inclines

pulleys

train

ROLLERCOASTER

Roller Coaster For many people, there is only one reason to go to an amusement park: the roller coaster. Some people call it the "scream machine," with good reason. The history of this ride reflects a constant search for greater and more death-defying thrills. How does a roller coaster work? What you may not realize as you're cruising down the track at 60 miles an hour is that the coaster has no engine. The car is pulled to the top of the first hill at the beginning of the ride, but after that the coaster must complete the ride on its own. You aren't being propelled around the track by a motor or pulled by a hitch. The conversion of potential energy to kinetic energy is what drives the roller coaster, and all of the kinetic energy you need for the ride is present once the coaster descends the first hill.. Once you're underway, different types of wheels help keep the ride smooth. Running wheels guide the coaster on the track. Friction wheels control lateral motion (movement to either side of the track). A final set of wheels keeps the coaster on the track even if it's inverted. Compressed air brakes stop the car as the ride ends. Wooden or steel coaster: Does it make a difference? Roller coasters can be wooden or steel, and can be looping or nonlooping. You'll notice a big difference in the ride depending on the type of material used. In general, wooden coasters are nonlooping. They're also not as tall and not as fast, and they don't feature very steep hills or as long a track as steel ones do. Wooden coasters do offer one advantage over steel coasters, assuming you're looking for palm-sweating thrills: they sway a lot more. Tubular steel coasters allow more looping, higher and steeper hills, greater drops and rolls, and faster speeds.

Projectile motion

Falling

At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. Thus, two objects of different sizes and weights, dropped from the same height, will hit the ground at the same time.
Drop

An object is controlled by two independant motions. So an object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

Here are the formulas that describe projectile motion:

Once the object leaves the table, it experiences a downward acceleration equal to gravity. Thus the vertical velocity(Vy) is continually increasing. The horizontal velocity(Vx) remains constant and is equal to Vxo.The two vectors Vx and Vy are added together to get the velocity at each point on the path.	If an object is pointed at an angle, the motion is essentially the same except that there is now an initial vertical velocity(Vyo). Because of the downward acceleration of gravity, Vy continually decreases until it reaches its highest point, at which it begins to fall downward.

ADDING VECTORS

Vector Addition

A variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors. Two vectors can be added together to determine the result (or resultant). This process of adding two or more vectors has already been discussed in an earlier unit. Recall in our discussion of Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. That is the net force was the result (or resultant) of adding up all the force vectors. During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. Observe the following summations of two force vectors:

Then use Pythagorean Theory to measure the resultant of the vectors.

EXAMPLE:

To get the Angle of the Resultant:

http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/Vectors/Add3Vectors.html