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

Let's take a ride on a ROLLERCOASTER



Canadian Mind Buster

 Okay, I'm going to admit that I'm not too crazy about rollercoasters. I dread waiting in line for them but right after I just  can't wait to get back on them. But still, I hate that stomachy feeling you get when you're falling down and it feels like you're going to die. I really don't have a favourite rollercoaster but the one that I've rode on a lot would have to be the wooden Canadian Mindbuster at Canada's Wonderland. Yeah, it's old, wooden and doesn't look like a lot of fun, but I like it. It's tame and controllable and I love the riggity sounds it makes.


Let's first take a look at energy:

Potential Energy

Potential energy is the same as stored energy. When you lift a heavy object you exert energy which later will become kinetic energy when the object is dropped. A lift motor from a roller coaster exerts potential energy when lifting the train to the top of the hill. The higher the train is lifted by the motor the more potential energy is produced; thus, forming a greater amount if kinetic energy when the train is dropped. At the top of the hills the train has a huge amount of potential energy, but it has very little kinetic energy.

Kinetic Energy

"Kinetic energy" is the energy of motion - it's ability to do work. The faster the body moves the more kinetic energy is produced. As the train accelerates down the hill the potential energy is converted into kinetic energy. There is very little potential energy at the bottom of the hill, but there is a great amount of kinetic energy.


How roller coasters work:

A motorized chain pulls the roller coaster to the top of the first hill (that's why you hear that click, click, click sound). The first hill is always the tallest one unless the coaster has more motorized chains later on (more clicking), which means that the first hill has the largest large amount of gravitational potential energy. We know from our previous unit, that this is the amount of work an object will be able to do with the energy it builds up from falling. The energy the roller coaster builds up from falling down that first hill will be enough to take you all the way to the end of the ride.


This diagram demonstrates the force of gravity
on the rider's weight while on a roller coaster

  

The physics of roller coasters:

Now that the roller coaster has made it to the top of the first hill, gravity takes over. When the roller coaster goes down the hill, it speeds up. As it accelerates down the hill, the potential energy gets converted to kinetic energy.The weight of the roller coaster is pulled down by gravity (which means it's falling).

Newton's Law of Roller Coasters:

Sir Isaac Newton (the dude who explained gravity) figured out the concept of inertia.
It's the law of physics that says that any object in motion will stay in motion until acted on by an equal but opposite force. When the roller coaster is at the bottom of the first hill, the kinetic energy is at it's biggest. Now that the coaster is whipping around loops and other hills, its energy is being lost to other forces like friction (energy created by two things being rubbed together) and air resistance. By the time the roller coaster gets to the end of the ride it has lost enough energy to come to a stop (usually with a little help from the brakes).

Adding Vectors

VECTORS: magnitude AND direction.

These are the simple steps for adding vectors by components:

1. First, set your positive axes.

2. Break the vectors down into two components: X and Y.

For example the question is A - 3D. (Vector A minus three times vector D)

A chart would help to organize and visualize the X and Y components easier.

3. Solve for the sum of X and the sum of Y.

4. Using the Pythagorean theorem, the two sums can be added to get the resultant.

R = √ A2 + B2
R = √ (65.5)2 + (-14.4)2
R =  67

5. Use trigonometry to solve for the angle.

tanθ = opposite/adjacent

tanθ= 65.5/-14.4

       = -77

Therfore the completed answer is: 67 [ S 77° E]

The Big 5 KINEMATIC EQUATIONS

Formula 1:


This formula comes directly from the graph.
To find acceleration on a v -> t graph, you find the slope.

a = rise/run
a = ∆v / ∆t
a = (v2 - v1) / ∆t
a∆t = v2 - v1


Formula 2:


To find d on a v-> t graph, you find the area.

Area of a trapezoid: A = (a+b)h /2
d = (v1 + v2)∆t / 2
2d= (v1 + v2)∆t d = 1/2(v1 + v2)∆t


 Formula 3:


A and d must be included because they were already proven.

From Formula (1), isolate v2.v2 = a∆t + v1 =☺
Sub ☺ into Formula (2).
d = 1/2(v1 + ☺)∆t
d = 1/2(v1 + a∆t + v1)∆t
d = 1/2∆t(2v1 + 2∆t)d = v1∆t + 1/2a∆t²

Formula 4:


From Formula (1), isolate v1.v1 = a∆t - v2 =☻
d = 1/2(☻+ v2)∆t
d = 1/2(-a∆t + v2 + v2)∆t
d = 1/2∆t(-a∆t +2v2)
d = v2∆t - 1/2a∆t²

Formula 5:


Isolate ∆t from Formula 1.
a∆t = v2-v1
∆t = v2 - v1/a = A
sub A into Formula (2).
d = 1/2(v1 + v2)(v2 - v1/a)
ad = 1/2(v2 + v1)(v2 - v1)
2ad = v2² - v1²v2² = v1² + 2ad

There is another method of doing Formula 5, but I prefer this method.

Motion Sensor Graphs

D-t Graphs

This stimulation helps with understanding the displacement, velocity and acceleration graphs.

 Click here, it's fun :)

In a d-t graph, if you are walking at a constant rate away, then the line would slope upward away from the origin. If you walk at a constant rate forward, then the line would slope downward away from the origin. If the line is horizontal, there is no movement at that particular point.


A. Stand 1 m away from the origin, and stay for 1 second.

B. Walk 1.5 m away from the origin for 2 seconds.

C. Stand 2.5 m away from the origin, and stay for 3 seconds.
D. Walk 0.75 m toward the origin for 1.5 seconds.
E. Stand 1.75 m away from the origin, and stay for 2.5 seconds.

A. Stand 3 m away from the origin, and walk 1.5 m toward the origin for 3 seconds.

 B. Stand 1.5 m away from the origin, and stay for 1 second.

 C. Walk 1 m toward the origin for 1 second.
 D. Stand 0.5 m away from the origin, and stay for 2 seconds.
 E. Walk 2 m away from the origin for 3 seconds.

A. Stand about 0.8m away from the origin, and walk 1 m away from the origin for 3.5 seconds.
B. Stand 1.8 m away from the origin, and stay for 3 seconds.
C. Walk 1.3 m away from the origin for 3 seconds.

 

V-t Graphs

In a v-t graph, a straight horizontal line represents walking at a constant speed, therefore the speed doesn't change. If the line slopes upward or downward depending on the direction, the speed has changed. When the line is at 0, there is no movement.

A. Speed up for 4 seconds.

B. Walk at a velocity of 0.5 m/s away from the origin for 2 seconds.

C. Walk at a velocity of 0.4 m/s toward the origin for 3 seconds.

D. Stay for 1 second.

A. Stay for 2 seconds.

B. Walk at a velocity of 0.5 m/s away from the origin for 3 seconds.

C. Stay for 2 seconds.

D. Walk at a velocity of 0.5 m/s toward the origin for 3 seconds.

A. Walk at a velocity of 0.35 m/s away from the origin for 3 seconds.

B. Speed up, still away from the origin, for 0.25 second.
C. Slow down, now toward the origin, for 0.25 second.

D. Walk at a velocity of 0.35 m/s toward the origin for 3 seconds.

E. Slow down, toward the origin, for 0.25 second.
F. Stay for 3 seconds.

Building a Motor

Our physics class had the wonderful opportunity this thursday to build electric motors.
I love building things do this was going to be real fun ... except for the fact that it was way harder than I imagined.

The materials we needed for this project was one piece of wood, four nails, pop can to use as brushes, a stick for the axel of the motor, cork, wire, and paper clips to support the axel. And of course a power supply and magnets are needed for the motor to work.

Starting off, my partner and I had a limited time to hammer in the nails to the wood. At first, it seemd like an easy task but soon we found out the nails had to be hammered in correctly to stand up straight as well as the length between each nail was important. Soon afterwards, we began vigrously sanding the pop can and screwing the stick into the cork. Next, the paper clips were bent in a shape that would support the axel. Our motor was very near to completion with just the coiling of the wires left to do. The direction of the wire coiling was significant in the way it should be in one direction and parallel to the commutator pins.

Excited with our finished product we rushed over to test it out but were soon dissapointed with the fact that it did not work. The motor was not spinning around, or causing any spark. It stayed the same as if no current was passing through it.

With some minor changes such as baring the wires at the end, or making sure that the commutator pins touch the brushes, and even recoiling the wire on the cork about 4969693451 times ................. our motor still didn't work.

It's okay though, just getting the experience of building the motor made the motor principle and other concepts of this project more clearer. :)

Our beautiful motor :)

Right Hand Rules #1 & #2

OERSTED'S PRINCIPLE: Charge moving through a conductor produces a circular magnetic field around the conductor

RHR#1



RIGHT-HAND RULE #1 (RHR#1) for conventional current flow: Grasp the conductor with the humb of the right hand pointing in the direction of conventional, or positive (+), current flow. The curved fingers point in the direction of the magnetic field around the conductor.



RHR#2



RIGHT-HAND RULE #2 (RHR#2) for conventional current flow: Grasp the coiled conductor with the right hand so that the curved fingers point in the direction of conventional, or positive (+), current flow. The thumb points in the direction of the magnetic field within the coil. Outside the coil, the thumb represents the north (N) end of the electromagnet produced by the coil.

Check out this awesome video:

Magnetic Force /Electromagnets

MAGNETIC FIELD: distribution of a magnetic force in the region of a magnet.
- Two different magnetic characteristics labelled North and South

- Similar magnetic poles, north and north or south and south REPEL one another with force
- Dissimilar poles, north and south, ATTRACT one another with a force

The law of magnetic forces

TEST COMPASS: a compass used to check for the presence of a magnetic field

FERROMAGNETIC METALS: metals such as iron, nickel, cobalt or mixtures of these three that attract magnets

DOMAIN THEORY: All large magnets are made up of many smaller and rotatable magnets, called dipoles, which can interact with other dipoles close by. If dipoles line up, then a small magnetic domain is produced.

Dipoles: the small and flexable magnets that make up a large magnet

Magnetic domain: the effect produced when dipoles of a magnet line up

Resistance/Ohm's Law/Kirchhoff's Law

RESISTANCE:  a measure of the opposition to current flow  

•  the amount of current flow in a circuit depends on two things: 

1)  the potential difference of the power supply
2) the nature of the pathway through the loads 

OHM'S LAW:

• Graphing the Linear Equation for Ohm's Law from Data:

• Factors that Affect Resistance:

- Length: longer the conductor, the greater the resistance
- Cross-sectional area: the larger/thicker conductor, less resistant it has to charge flow
- Type of material: resistivity is measure of resistance of a substance
- Temperature: greater molecular motion at higher temperature increases the resistance

• SUPERCONDUCTIVITY: ability of a material to conduct electricity without heat loss due to electrical resistance.

KIRCHHOFF'S CURRENT LAW:
The total amount of current into a junction point of a circuit equals the total current that flows out of that same junction.

KIRCHHOFF'S VOLTAGE LAW:
The total of all electrical potential decreases in any complete circuit loop is equal to any potential increases in that circuit loop.

• In other words, there is no net gain or loss of elecric charge or energy

Kirchhoff's laws in a SERIES circuit:
VOLTAGE: Voltage must be distributed so that the sum of all voltage drops must equal this value.

VT= V1 + V2 + V3

CURRENT: The circuit only has one path to flow.

IT= I1 = I2 = I3

Kirchhoff's laws in a PARALLEL circuit:
VOLTAGE: Voltage drops have to remain the same no matter what.

VT= V1 + V2 + V3

CURRENT: the sum of the current entering junctions must equal the sum of the current exiting them.

IT= I1 + I2 + I3

RESISTANCE IN SERIES:

RT = R1 + R2 + R3 .... + RN

(N is the total number of series resistors in the circuit)

RESISTANCE IN PARALLEL:

1/RT = 1/R1 + 1/R2 + 1/R3 .... + 1/RN

You can rewatch the video on RESISTANCE :)

Prelab Table

Completing the Circuit

What is the difference between a series and parallel circuit?

( A circuit is the path that electricity follows. )

All of the electricity
follows path #1

SERIES CIRCUIT: In a series circuit, the parts of the circuit (such as the battery, a switch, and the electric device) are connected one after another (in series) in a single closed loop. A series circuit allows electrons to follow only one path. The loads in a series circuit must share the available voltage. In other words, each load in a series circuit will use up some portion of the voltage, leaving less for the next load in the circuit. This means that the light, heat, or sound given off by the device will be reduced. If one device (e.g. bulb) in series burns out, the circuit is broken and there is no other path for the flow of charges therefore the other devices no longer work.

Some current follows path #1,
while the remainder splits
off from #1 and follows path #2

PARALLEL CIRCUIT: In parallel circuits, all the devices share a common connection to the voltage source. Different devices are on separate "parallel" branches. In parallel circuits, the electric current can follow more than one path to return to the source, so it splits up among all the available paths. Across all the paths in a parallel circuit the voltage is the same, so each device will produce its full output. There are different paths for currents such that a break in the flow of charges in one path does not interrupt the flow along other paths.

 

“To give an analogy of each circuit, in a series circuit, a postman has something to deliver to only one house; and in a parallel circuit, the postman has things to deliver to two houses. In a series circuit, if a part of the route gets destroyed, the postman cannot deliver whatever has to be delivered; in a parallel circuit, if one route becomes impassable for whatever reason, the postman can still reach one house.” - EC

Check out this awesome video on this topic.