Friday, January 7, 2011

Constructive and Destructive Interference

Sound waves are fluctuations in a medium's pressure that move away from their source.

Interference is the result of two or more waves meating each other at a praticular point in space at the same time. The net waves that forms at the point of interference has an amplitude that is equal to the vector sum of all wave amplitudes at this point. This concept of the sum of all amplitudes is called the principle of the superposition.

When two wave  pulses interfere with each other they can form pulses of larger amplitude, or, if they have  oposite orientation they can destroy each other. The increase of the waves amplitude is called constructive interference and the decrease of the amplitude is called destructive interference. The destructive and constructive intereference are shown in the diagrams below.

Did you know?

The  Tacoma Narrows Bridge (USA) collapsed in 1940  because the winds blowing across it matched its natural resonant frequency.

Saturday, December 11, 2010


1. Conservation of Energy
2. Law of Entropy
3.Absolute Zero

The first law of thermodynamics says that energy cannot be created or destroyed. Energy can be transformed and transferred.

Many different types of energy exist:

  • kinetic energy
  • gravitational potential energy
  • mechanical energy
  • chemical energy
  • electrical energy
  • light energy
  • heat energy
  • sound energy
  • elastic energy
  • nuclear energy

Kinetic energy describes movement.  
On the other hand, gravitational potential energy is energy due to an object's distance from the ground. This is usually measured when the object is static.  
Gravitational potential energy and kinetic energy combine to form mechanical energy. Mechanical energy is energy produced due to the movement of objects. Mechanical energy assists many machines.Some simple machines aided by mechanical energy are are incline plains and levers. Other machines that make use of mechanical energy are pulleys and screws.

Chemical energy is caused by chemical reactions. It  can be called chemical potential energy because there is energy stored in the molecular bonds ready to be used.

Electrical energy is caused by charged particles that produce an electrical current. The particles are always moving. On a molecular level this type of energy is kinetic.

Light energy is a form of kinetic energy that emits light (visible or non visible to the naked eye).  Sometimes, light energy goes hand in hand with heat energy. 
Heat energy is energy stored in objects above absolute zero. This would comprise of all objects. Heat energy can be either potential or kinetic.When an object is heated, the particles in the object contain more energy and bounce off each other faster. On a molecular level heat energy is kinetic.

Sound energy is energy caused by vibrating object. Vibrations are movements of waves in the air. In this sense sound energy is kinetic.
Elastic energy (i.e. spring energy) is potential energy.  It is shown whenever and object is stretched. Springs get either compressed and pulled. Elastics can be stretched out. When someone points a stretched elastic at you , it is an instinct to pull away. This is because people are aware of potential of the elastic to hit you.

Nuclear energy energy that is stored in atoms. Nuclear energy is a form of potential energy. Nuclear fusion and nuclear fission are the two types of nuclear energy. Nuclear fusion is a combining of atoms. Nuclear fusion releases a certain amount of energy.  Nuclear fission is the opposite; atoms are split instead.

Energy is essential to our lives and well being. Without it, we cannot form chemical bonds in our stomachs and digest the food we eat. Likely without energy we would not exist due to absolute zero. It is important to remember that energy is never lost. It is transformed into different types of energy.


The third class assignment we completed was building a cannon.

This is what we built, kind of. Except that we made it out of popcans.
Cannons are capable of creating a lot of destruction by shooting out cannon balls or simply investing more energy into making much noise. Either way, a real cannon might seem intimidating, which is probably why many ancient battle tactics involved cannons. They had a wide variety of purposes, some of the most common ones involving sinking enemies ships or conquering strongholds.
By analyzing the reason why cannons were so popular we must look at the the way they achieve theirr parabolic motion. Cannons make use of projectile motion. Cannons make use of parabolic motion (due to a vertically shot cannon ball which is brought down by gravity.) Cannons also display the transformation of chemical potential energy into sound energy, kinetic energy, heat energy and work done.

In Kinematics we learned a formula that calculates the range of a projectile.
The velocity in the x-axis is constant because of negligible air resistance. We cannot assume there is no air resistance, however it is low enough not to make a difference in the long run.

The initial height of the projectile is from the ground, thus 0 metres in displacement in the y component. This is not exactly how our cannon operated however, because we raised up the opening where the cannon ball was shot out by about 25 cm.  As well, the optimum angle to shoot the cannon ball at is 45°. This is explained due to the parabolic motion of the cannon ball. The cannon ball will not be shot too low (resulting in a short flying time) nor will it be shot too far up, resulting in a short distance traveled horizontally. If the cannon is shot at a great angle up (e.x. 80°  the range might just be close to 0 metres.) The projectile will be in a parabolic motion, therefore the maximum range might be obtained if the cannon makes a 45° with the ground.

Other factors can contribute to a greater range.  The cannon ball should be as light as possible. The force applied on the cannonball is constant. The mass of the cannon ball is inversely proportional to the acceleration. If the mass of the cannon ball is lighter, a higher acceleration will be achieved. Lastly, the projectile should launched from a longer barrel of the cannon, with more baffles.  more energy will be stored before the cannon is launched. The ethanol will have more surface area to spread over, and therefore it will have the ability to make more connections with air. By increasing the action force acting on the cannon, the reaction force will also increase (equal and opposite reaction force.) This exemplifies Newton's Third Law.


Newton's Three Laws are:

  1. The law of Inertia.  Objects will continue to be in motion or stationary unless it is affected by another force against it.
  2. Force=mass . acceleration.  Force is directly proportional to mass times acceleration. Mass and acceleration however share an inverse relationship.
  3. For every action force, there is and equal and opposite reaction force. (However it is possible for the reaction force to act in the same direction as the action force. For example if a person with skates is standing constant on ice, and another person skating bumps into the stationary person, the reaction force will send the stationary person in the same direction as the skating person was traveling.)
Four types of problems involving Newton's Three Laws:
1. Equilibrium
Equilibrium is when the object remains static.  These are the assumptions made when solving equilibrium problems:
  • there is no friction
  • there is no acceleration
  • the net force is 0
2. Inclined Planes
There are incline problems can be solved in two ways. (Those involving a static Mk and those involving a  kinetic Mk.) Incline plane problems involves friction because the object is sliding down a slope (hence the name inclined plane). The object has a friction because since the surface is slanted there is a force applied in the x-axis. Friction resists the force. Assumptions to be made when solving incline plane problems are:
For static:
  • there is no acceleration
  • the positive axes is the direction of acceleration on the surface
  • there is no air resistance
  • Mu is static if the object is not moving at first
  • the normal force is perpendicular to the surface
For kinetic:
  • The normal force is perpendicular to the surface
  • there is acceleration
  • there is no air resistance
  • Positive axes are in the direction of acceleration and surface
  • Mu is kinetic if the object is moving
When solving incline questions FBDs can be really helpful.  Gravity is always pointing down.  Gravity should be broken down using x and y components.
3. Pulleys
The assumptions when solving pulley problems are:
  • the pulley has no friction
  • the rope is frictionless
  • there is no air resistance
  • there are 2 FBDs (one for each load)
  • tension for both systems is equal
  • Acceleration of the 2 systems is the same
  • Positive axes are the direction of the acceleration of each load
4. Trains
Assumptions for train questions:
  • there is no air resistance
  • there is the same acceleration throughout the whole system
  • the y component is in equilibrium (no acceleration) 
  • FBDs one for each of the masses
  • The cables that connect the masses are weightless
  • Positive axis is in the direction of  the acceleration
There are also tension forces connecting the carts. For example the tension force pulling cart 3 forwards is the same as the tension force pulling cart 2 backwards.

Assumptions are very important to include when solving the four types of problems, because it is necessary to specify the conditions concerning a problem in order to find a way to solve it.

Sunday, November 7, 2010

Projectile Motion

The key to solving two-dimensional problems is to break them up into two one-dimensional parts, then recombine them to produce a final answer. You will have a set of givens in the x-direction and another set in the y-direction.

Projecto shot horizontally:

ax =0                                          ay =  - 9.8 m/s2
vx = constant                              vy changing
Δdx = range                                Δdx = height

Use the formulas:

Δdx= vx Δt                                  Δdy= vy Δt + ½ ay Δt2

If you can find the Δt in x direction, then transfer it in the y direction and find the height.

If you can’t find Δt in the x-direction calculate it in the y-drection, and then transfer it to y-direction to find the range.

Friday, October 29, 2010

The Physics Behind Roller Coasters

The roller coaster is driven almost entirely by inertial, gravitational and centripetal forces.
The train is moved by gravity and momentum. When a coaster has reached the highest point along its course, normally a tall hill at the beginning of the circuit, gravity is what provides the force that controls the speed of the ride.  Inertia is the reluctance of a body ( for example, a coaster train) to change its direction of motion. A coaster train that is accelerating down a steep hill will resist the change in direction and head up the next hill.

But before the train can gain momentum and take advantage of gravitational forces, it needs an initial push to get up the hill.
A chain loop can be used to move the train up. This can consist of a gear at the bottom attached to a motor that moves the roller coaster up.
A catapult launch can build up a great amount of kinetic energy over a short time.

The potential energy the roller coaster builds going up the hill is released as kinetic energy, the energy of motion that takes the coaster down the hill.

The coaster tracksare important in channeling the force. They control the way the coaster cars fall. If the tracks slope down, gravity pulls the front of the car toward the ground. The coaster therefore accelerates. If the tracks tilt up gravity applies a downward force on the back of the coaster. The coaster decelerates.

An object in motion tends to stay in motion (Newton's first law of motion.) The roller coaster car will maintain a forward velocity even when it is moving up the track. This movement is opposite the force of gravity. When the coaster ascends one of the smaller hills that follows the initial lift hill, its kinetic energy changes back to potential energy. It is back at the top. The course of the track is constantly converting energy from kinetic to potential vice versa again.

In most roller coasters, the hills decrease in height as they progress along the track. Thsi happens because the total energy reservoir built up in the lift hill is gradually lost to friction.There is friction between the train and the track and between the train and the air. When the train reaches the end of the track the energy reservoir is almost completely empty.

Roller coasters have brake systems. Those brake systems however, are not situated on the coaster itself, but on the tracks. There are a series of clamps built into the track of the train. There is a central computer system which operates the hydraulic system and closes the clamps for the train to stop.

To sum it all up , when a coaster is at the highest point of its track, there is a high potential energy This can be referd to as energy of position. When the coaster accelerates down the hill the potential energy changes into kinetic energy (or energy of motion). Each time the coaster goes up another hill, the kinetic energy turns into potential energy again. The cycle continues. Ideally, the total amount of energy would remain the same. However some is lost to friction between the wheels and the rails. There is wind drag along the train, and also friction applied by the brakes. Due to this energy loss, each successive hill along a coaster track needs to be smaller than the previous hill to allow the train to continue along the course.

Safety Features
By the nature of the laws of physics a roller coaster wants to fly off the track. Any accidents are prevented by the wheel design and the track.
The weight of the train is supported by running wheels (the largest wheels.)
On the sides of the coaster train guide wheels are arranged to provide stability during tight turns and to keep the coaster train from rubbing the structure of the ride.
Upstop wheels are smaller wheels. They are on the underside of the rails that keep the train locked to the track and allow the train more airtime because they eliminate the danger of the train leaving the track.
A rollback can occur when a coaster fails to crest a hill. Instead, it begins to move backward. Coaster trains are equipped with anti-rollbacks paired with the chain dogs. A rollback can be caused from too much gravity.

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Monday, October 25, 2010

How To Add Vectors

For scalar quantities there is no question about the final result of adding two quantities. For vector quantities the value depends on the direction and angle between the two vectors. The resultant vector of the addition needs to be specified by a magnitude and direction. It is called total displacement.
The vector direction needs to be shown in relation to North and South.
If you know the angle from North or South to the direction, use trigonometry to solve for vertical and horizontal displacement.
Use sin and cos to find the horizontal and vertical distance.
Record the distance in a table with a positive sign if N or E and a negative sign if S or W.
Add up the total displacement horizontally and the total displacement for each vector. (This is similar to collecting like terms in math.)
Once you have the total horizontal and vertical displacement you can find the length of the distance and direction.
Use Pythagoras' theorem for length and the tan function for direction and angle compared to N or S.

If you know the length of a bunch of vectors and directions in relevance to North and South it is possible to find the total displacement horizontally and vertically. This can be done using cosine and sine function of an angle, and the hypotenuse. When the total horizontal and vertical displacement of all the vectors are found, they need to be added up. This will give us the two legs of the triangle. Knowing the two legs' length will make it possible to fine the hypotenuse using Phythagoras' theorem. The angle of the final displacement, in relevance to North and South can be found by using the tangent function.
It is important to split up vectors in horizontal and vertical displacement when adding the total of the vectors, because that way all of the directions are the same. It is possible to add them together. Otherwise the vectors would be going in different directions, and when added up would give a not accurate result. By splitting up vectors into horizontal and vertical it is also possible to assign a positive and negative direction.