Relationship Between Work, Energy, and Power

Power is the rate at which work is done and to do work you require energy.

P = E (Joules)
      -----------
       t (time)

W= FD ( force x distance)

Suppose there is a force  F acting on an object, causing it to move in a particular direction. Then the work done by the force is the component of F in the direction of motion × the distance the object moves as a result. Work done is measured in joules (J). 

However, if this force is at an angle of a to the horizontal and the body moves a distance of s metres along the ground, then the work done is F cosa × s (since F cosa is the component of the force in the direction of motion).

** If energy is conserved, no work is done. if it is not conserved, it is used to do work.

There are two main types of energy: kinetic and potential

The kinetic energy (K.E.) of a body is the energy an object has as a result of its motion. An object which has no motion will have zero kinetic energy, therefore.

                          K.E. = ½ mv²
   where m is the mass and v is the velocity

Potential energy (P.E.) is the energy an object using height to its advantage

                         G.P.E. = mgh
where h is the height of the body above the ground.

Basically, the total potential energy measures the energy of the body due to its position.

All three variables are dependent on one another and if one was missing, the others wouldnt exist.

Ready, Set, Fire!!!

From watching many movies of the past, we have observed a weird device when loaded with gunpowder would shoot up and cause objects at far distance to explode. KABOOOMMM.. Now what is this device called?  Wait, wait! I'll tell you ;) : a cannon. A cannon is any piece of artillery that uses gunpowder or other usually explosive-based propellants to launch a projectile. They were very popular weapons in the 18th and 19th centuries. However we have newer technology which can also be referred to as cannons today such as guns, howitzers, mortars, etc.. One of the tips to making a successful cannon is following the general rule which is the longer the barrel, the longer the range of the cannon. To shoot the cannonballs to a great distance, large amounts of gun powder would be required as well. The Tsar Cannon is the largest Howitzer made weighing at 39.312 tonnes and has a length of 5.34 m

A view of the Tsar Pushka, showing its massive bore and cannonballs,
 and the Lion's head cast into the carriage.

Results from Newton's Lab... who says getting hit in the head can't help you?

After a long time I was able to have fun with pulleys and loads. We were to differentiate between mass and force with acceleration. There were 5 different cases we were to follow and produce results. These are the results that I collected with my group :) 

Data collected from the 5 cases

The tower is falling down... falling down

So last week we did another fun activity: constructing a tower. I should mention its not as easy as it sounds with limited tape and newspaper, yet again. That was all we received with even less time! My group and I started with cylinders for the base and for the top we rolled the rest of the papers and stuck it on the top. However, the top was ending up with more weight. Thus, it kept bending :(  We tried repeatedly to fix the problem but it's not like we had any more materials to strengthen the base. Then out came Mr.Chung and said time out. We tried to improve it even after time was up :P well until Mr.Chung was judging our (if you can even call it that) tower... So now it is evident that we were unsuccessful. But all creators fail at some point or the other right? I take this in the positive way and I know what I would have to do to produce better results next time :)

How it all started...

so yeah it won't stay down :P

How High Can You Go?

Ever wondered if there are structures taller than our own CN Tower? Well in reality the CN tower is ranked around the 100's for tallest structure. At number 1 we have Burj Khalifa with an enormous height of 828 m (2717 ft.) What has enabled this structure to maintain such a grand height? Usually when designing a building the main considerations to create a successful building is:

1. The use of strong, unbreakable materials
2. The shape. Usually we see buildings decrease in width from top to bottom. This increases stability. Of course we can't forget the triangles. It had been put into our heads since grade two that it is the strongest shape out there!
3.Weight can be another factor. We can't have a heavier top than bottom... The base should have the most mass.
4. Having a low centre of gravity which minimizes risks and difficulties

Burj Khalifa - Tallest Structure in the World!

What Goes Up Must Come Down!

   We have now started a new section in our unit in kinematics : projectile motion. It seems very complicated at first but eventually you get the hang of it. These are the answers from 1-9 in the projectile motion worksheet.

Egglander or Egg Failure?

Today we were given a new project which would begin on wednesday; it is a gliding egg lander. Let's start by defining aerodynamics. It is the study of forces and the resulting motion of objects through the air. Now what does this have to do with eggs? Well as I mentioned, the egg does have to somewhat fly and to be successful in doing so, we have to know some information about aerodynamics: the study of air and its motion. For this project we will be given 25 straws, one sheet of newspaper, and a limited amount of tape. Learning that was all we had to work with, my group and I got really depressed. However, as Mr.Chung always says: never get freaked out by problems; just slowly and intelligently work it out (changed into my own words of course haha)... To do well on this project, the best thing would be to determine what kind of shape we should use to protect the egg. Obviously the first thing that came into my mind is the structure of a hang glider. Therefore to make our egg glide well enough, making wings for it would be a good idea and making a cushion is good for a safe landing. More brainstorming will be needed evidently but hopefully we can make a good egglander :)

A design I liked made by well some kids in college :P

A design of a hang glider

Word Problems pg 72

answers to word problems from friday on pg 72 :)

If At First You Don't Succeed, Try, Try Again

Today was basically the first day we started kinematics or in other words the motion unit. Mr.Chung had divided us in 7 groups and I was chosen as the leader. My job was to setup the equipment and explain to my group members what we were suppose to do and how. They got the hang of it pretty fast! The objective of the activity was to match our walking patterns to the pattern of the distance-time graphs or velocity-time graphs using a motion detector.

The result for graph B

  A. Stand at 1m away from the origin and stay at rest for 1s
  B. Jog 1.5 m [E] away from the origin in 2s at a constant speed
  C. Stand 2.5 m away from the origin for 3s
  D. Jog 0.75 m [W] toward the origin in 1.5s at a constant speed
  E. Stand at 1.75 m away from the origin and stay at rest for 2.5 s

The result for graph C

A. Start at a distance of 3 m away from the origin and jogs 1.5 m [W] toward the origin in 3s at a constant speed
B. Stand 1.5 m away from the origin and stay at rest for 1s
C. Jog 1 m [W] toward the origin in 1s
D. Stand 0.5 m away from the origin and stay at rest for 2s
E. Jog 2.5 m [E] away from the origin in 3s 

The result for graph D

A. Stay at a velocity of 0 (rest) for 2s
B. Speed is increased to 0.5 m/s [E] during 0.1 s
C. Speed of 0.5 m/s [E] is maintained for 2.9 s
D. Object quickly speeds up in 0.1 s at 0.5 m/s [W]
E. Stay at a velocity of 0 (rest) for 1.9 s
F. Speed is increased to 0.5 m/s [W] during 0.1 s
G. Speed of 0.5 m/s [W] is maintained for 2.9 s

The result for Graph E

A. Increase to a speed of 0.5 m/s [E] going away from the origin for 4s
B. Maintain speed of 0.5 m/s [E] for 2s
C. Speed is at 0 m/s [W] during the 0.1 s
D. Maintain a speed of 0.4 m/s [E] for 3.9 s
E. Speed up for 0.1 s at a speed of 0.4 m/s [E]
F. Stay at a velocity of 0 (rest) for 0.9 s

The result for Graph F

A. Stand about 0.8 m [E] away from the origin and jog 1m away from the origin for 3.5 s
B. Stand 1.8 m [E] away from the origin and stay at rest for 3 s
C. Jog 1.5 m [E] away from the origin in 3.5 s

Some things to know:

D-T Graphs (B,C, F)
-If the slope is inclining, walk away from the origin
-If there is no change in the line (slope of 0), stay still
-If the slope is declining, walk toward the origin
-The speed at which you have to walk depends on the time you have to walk it in

V-T Graphs (D, E)
-If there is no change in the line (slope of 0), the speed is constant
-If the velocity is at 0, there is no movement
-If the line inclines or declines, there is an indication that the speed is changing

Reading D-T or V-T graphs can be quite confusing. Therefore, you should carefully analyze the graphs.

Opposites Attract Creating A Force...

We recently started our new unit on magnetism. Starting from elementary school, we all have played with magnets; knowing that like poles (same charge) repel and unlike poles (opposite poles) attract. To test this theory we used a compass to detect the direction of north and south using a magnet. It was not showing expected results; the north was attracting to the north and south to the south. So we learnt that the earth's actual north pole is not in the arctic it is in the antarctic and the south is actually in the arctic. This concept can be more clearly observed in the below diagram.

                This constant change in the magnetic fields is causing animals who have natural sense of direction to lose their way and eventually leads to their death.

Scientists in the early days were trying to research force at a distance which was the common element between electrostatics and magnetism. Among one of them was Hans Christian Oersted. While conducting his research, he discovered something very significant which came to be known as Oersted's Principle.

Oersted's Principle: Charge moving through a conductor produces a circular magnetic field around the conductor

Using this knowledge from Oersted, scientists were able to develop right-hand rules (called right hand because the use of the right hand is involved).

Right Hand Rule # 1: If the right hand is placed around the conductor with the thumb pointing in the direction of conventional current flow, or positive (+) current flow, the fingers will curl in the same direction as the magnetic field.

               In this case the thumb is pointing upwards and the fingers are curled pointing to the right. This indicates that the magnetic fields will go to the right in other words counter clockwise.

Right Hand Rule # 2: The fingers curl in the direction of conventional current, or positive (+) current flow and 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.

                    In this case the fingers are curled upwards, making the thumb point to the left. This indicates that the  north (N) pole is on the left side of the coil.

Later we can learn how these two rules strengthen our knowledge of magnetism and can enable us to make things move using electricity such as a motor!

The Art of Concept Maps

Today we learnt about concept mapping. It may sound easy, but it is quite the opposite. First of all it is necessary to understand clearly all the topics you are dealing with in order to determine their relationships with each other. As if it wasn't already difficult, we were told to create a concept map with our group without any forms of written or verbal communication i.e no speaking, writing, etc... The concepts we were trying to link and describe was current, voltage, power, and circuit laws.

This is a picture of the end result of our concept map:

10 things to remember when dealing with electricity:

1) First of all what is electricity?
   Electricity is a flow of electrons around a circuit.

2) Current is the rate of charge flow between two points measured in coulombs per second. This unit for current is amperes which is symbolized by I. Current can be measured by a device known as an ammeter. The general formula for current is as follows:

I = charge (Q)
     -----------
      time (t)

3) Voltage is known as electric potential difference which is measured in volts. The voltage between two points can be measured by a device known as a voltmeter. Voltage is defined by energy/charge :

V = E (in joules)
     --------------
      Q (charge)

4) Difference between series and parallel circuits
A series circuit is an electric circuit arranged so that the current passes through all of the loads in one unbranched pathway 
and...
in a parallel circuit the electric circuit is arranged with parallel loads that are connected side by side where electric current can flow through multiple pathways  

5) Circuit Laws
Resistance in Series:
From Kirchhoff's Law:     VT = V₁ + V₂ + V_{3  =} VN

                                                    IT = I₁  = I₂  = I_{3   =}   I_{N
 
From Ohm's Law :}          R_{T =} R₁ + R₂ + R_{3   =}  RN

<sub>Resistances in Parallel: 

From Kirchhoff's Law:</sub>            I_{T  =}  I₁ + I₂ + I_{3  + IN}

                                                   V_{T =}  V₁  = V₂  = V<sub>3  = VN

From Ohm's Law :</sub>         1         1         1          1
                                      --   =   --    =   --    =   --  
                                     R_T         R₁          R₂          R₃ 

6) Power is the rate at which work is done which can be defined by:

P = IV   OR       V²
                        -----
                        R
The unit for power is watts or (w).

7) Energy is work done in joules which can be measured by :
    E= VIT

8) The unit of charge is coulombs which can be defined as a group of electrons. 1 C= 6.24 X 10^18 and the charge of one electron is 1.60 X 10^-19 C.

9) Resistance is the opposition to current flow which can be defined by using the following equation:

R = V
       --
       I

The unit for resistance is ohms (Ω).

10) Two theories describing energy transfer:
Conventional Current - This theory was developed by Benjamin Franklin. This is the model of positive current flow which states that electrons move from the positive (+) terminal, through the circuit, to the negative (-) terminal. 

However, we know today that this theory is wrong but use it anyway because it is too late to change the way we regard energy flow. The correct theory is known as electron flow.

Electron Flow- states that electrons move from the negative (-) terminal, through the circuit, to the positive (+) terminal.


Look how the whole unit of electricity can be briefly summed up in just about 10 points!

Two Great Minds Think Alike

Lately, I have learnt about two physicists that are considered noteworthy. The two people are Georg Simon Ohm and Gustav Robert Kirchhoff.

Ohm discovered that there was a proportional relationship between the voltage and the current that always calculated the same value for resistance (separate from other variables i.e temperature, calculation error). He came up with a general formula to represent the resistance and this was named the Ohm's Law.
 
Ohm's Law : R = V
                           --
                            I
where R is the resistance in volts/ ampere

Kirchhoff studied the way current and voltage was affected in series and parallel circuits respectively. He came up with two laws that we know as today:


Kirchhoff's Current Law: The total amount of current into a junction point of a circuit equals the total current that  flows out of the same junction

The current entering any junction is equal to the current leaving that junction. i₁ + i₄ = i₂ + i₃

        Kirchhoff's Voltage Law: The total of all electric potential decreases in any complete circuit loop is equal to any potential increases in that circuit loop. 

The sum of all the voltages around the loop is equal to zero. v₁ + v₂ + v₃ - v₄ = 0

Kirchoff's laws are improvements made on two other laws:

Conservation of Electric Charge: a law stating that the quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved

Conservation of Energy: a law stating that the total amount of energy in an isolated system remains constant over time, in other words conserved over time


Here are some important formulas to know to calculate current, voltage, or resistance in series circuits using the Ohm or Kirchhoff laws.

Resistance In Series:


From Kirchhoff's Law:     VT = V₁ + V₂ + V_{3  =} VN

                                                     IT = I₁  = I₂  = I_{3   =}   I_{N
 
From Ohm's Law :}     R_{T =} R₁ + R₂ + R_{3   =}  RN


_{In addition, if all the values of all the resistors in a series circuit are the same, the overall resistance can be determined by} 

R<sub>T = NR 
 where the total resistance is calculated by multiplying the total number of resistors (N) by the resistance of each individual resistor (R)

Resistances in Parallel: 

From Kirchhoff's Law:</sub>  I_{T  =}  I₁ + I₂ + I_{3  + IN}

                                                 V_{T =}  V₁  = V₂  = V<sub>3  = VN

From Ohm's Law :</sub>  1         1         1          1
                                      --   =   --    =   --    =   --  
                                     R_T         R₁      R₂        R₃ 

 In addition, if all the values of all the resistors in a parallel circuit are the same, the overall resistance can be determined by 
R_{T = R
         ---
         N
where the total resistance is calculated by divided the resistance of each individual resistor (R) by the total number of resistors (N)}

You spin my head right round :)

I skimmed through some of the roller coasters made in the past few years. There were a few that caught my eye quickly and I really admired the creativity and the hard work put into it. You can see these below !!!

Well since I have grown up playing Mario, I found this one cute :)

I think the ship idea was different!

I like how complex this team made their coaster.. quite nice!!

I've always had an interest in greek mythology ;)

                               This one was my favourite one! All of the wonders of the world are beautiful and creative and I found this coaster to fit both of the categories :D

Go with the flow ;)

Today we learnt about energy flow in circuits. The flow of charge is referred to as electric current.

Electricity is demonstrated by a steady flow of electrons. As electrons move around a circuit, they transfer electric charge with them too.

The current can be measured by using this general formula :

I = charge (Q)
      -----------
      time (t)
I= Current in amperes

Because the size of an electron is very minute (2.82 x 10¹⁵ m )
scientists decided to measure electron in groups referred to as couloumbs. One coulomb is 6.25 x 10¹⁸
electrons.

Lets looks at batteries. You start off with chemical energy which separates the electrons from the atoms. As they continue to separate, there is a charge that builds up between them. This is known as electric potential energy. This energy has the potential to be transferred. There are two theories that describe the transformation. One such theory is the conventional current which was created by Benjamin Franklin. This is the model of positive current flow which states that electrons move from the positive (+) terminal, through the circuit, to the negative (-) terminal. However, we know today that this theory is wrong but use it anyway because it is too late to change the way we regard energy flow. The correct theory is known as electron flow which accurately states that electrons move from the negative (-) terminal, through the circuit, to the positive (+) terminal. In a battery the current flows in a single direction from the power supply through the conductor to the load (which uses the energy) and back to the power supply defined as direct current as opposed to the current continually changing directions defined as alternating current. Anyway in the end all this electric energy that is constantly flowing is converted into electrical energy. 

Current Flow Theory

Electron Flow Theory

Lets get the humming started !

On Friday, our class was able to do a very interesting experiment , which was a good review on the topics we have learnt in the past about physics. We were given a ball that resembled a ping pong, but in fact it was an energy ball. Every time we contacted our fingers to the two metal points the ball would flash and hum. Now how was it able to do so? I was able to conclude that my hands were transferring some type of energy to make the ball work. This energy was electrical energy. We build up this energy through static electricity.  I observed that a few people were not able to make the ball light up and hum. I believe that this was because they were less charged than others. That is why they can light up the ball for shorter amounts of time or none at all. Additionally, I think another factor can be how dehydrated or moisturized their hands were because dehydrated hands can act as insulators, preventing the transfer of electricity. There are also other elements in your body that can contribute to how much charge your body emits like iron and copper. These individuals might be low on these substances; therefore they give off less electric charge than others.

With the ball, the class made two different circuits : series and parallel. Lets review what they are.

Current passage in a series circuit

 series circuit - an electric circuit arranged so that the current passes through all of the loads in one unbranched pathway  
An example of a series circuit system can be Christmas lights. If one of the bulbs burn out, they all go out. 

Current passage in a parallel circuit

parallel circuit - an electric circuit arranged with parallel loads that are connected side by side where electric current can flow through multiple pathways 
An example of a parallel circuit system can be your house. If the lights in your room have a fuse,  it doesn’t mean all of the lights in your house will have a fuse.  

We were told to make a series circuit by linking our pinkys' together. This way the current would be able to flow through us to light the ball. We observed that when one of us would let go (independent of their location in the circuit) the energy ball would stop working. This allowed us to confirm the statement that when one of the devices connected to the circuit stops functioning, the whole system fails to function as well.

Next we made a parallel circuit using two balls, linking to the whole class. Here we observed, that when one person would let go, only one of the balls would continue to work. This allowed us to confirm that in a parallel circuit ,when one device stops functioning, the current can use an alternative path to be transferred.

In most situations we can say that a parallel circuit system would prove to hold more advantages. However, in situations like fire, a series circuit would be safer. If electricity is cut off all at once, it prevents rapid spreading of the fire and would alert nearby people of danger. So we can conclude that both circuit systems have equal disadvantages and advantages. Furthermore, I think this activity proved to be a great learning experience for everyone in the class. It was a great start to our new physics class!