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.

Deriving the Big 5 Equations

Equations are used as they are more versatile and easier to manipulate than graphs. In total there is a set of 5 equations which can be derived from a velocity vs. time graph. 


The first equation: constructed by taking the slope of the graph
a= rise/ run
a= v2-v1/ Δt       rearrange it:
v2= v1+ aΔt


Equation two: found by calculating the area under the graph (displacement)
Δd= ½ (v2+ v1)Δt


Now we can manipulate these two equations to create three more equations.


Substitute the expression for v2 into equation 2 to find equation 3:
Δd=½ (v1+aΔt+v1)Δt
Δd=½Δt (2v1+ aΔt)
Δd= v1Δt+½aΔt²


To find equation 4: first isolate v1 in equation 1, then substitute this in equation 2:
v1=v2-aΔt      subs. in equation 2:
Δd= ½ (v2+v2-aΔt) Δt
Δd= ½Δt(2v2-aΔt)
Δd= v2Δt- ½aΔt²


To find the final equation 5, isolate Δt in equation 1 and substitute it into equation 2:

Δt= v2-v1/a      subs. in equation 2:

Δd= ½ (v2+ v1) v2-v1/a

Δd= ½ (v2²- v1²) /a

2aΔd= v2²- v1²

v2²= v1²+ 2aΔd


These are the five fundamental equations in kinematics. They are applicable only in problems that have constant acceleration.

Motion Graphs

Graph 1: Distance vs. Time

Starting at 1m from the origin

Rest for 1sec

Walk 1.5m away from the origin in 2secs

Rest for 3secs

Walk 0.5m towards the origin in 1sec

Rest 3secs

Graph 2: Distance vs. Time

Starting 3m away from the origin 

Walk 1.5m towards the origin in 3secs

Rest for 1sec

Walk 1m towards the origin in 1sec

Rest for 2secs

Walk 2.5m away from the origin in 3secs

Graph 3: Velocity vs. Time

Rest 2secs

Walk away from place of origin and speed up to 0.5m/s for 3secs

Rest 2secs

Walk towards the place of origin at a speed of 0.5m/s for 3secs

Graph 4: Velocity vs. Time

Speed up slowly away from the origin until reaching 0.5m/s at 4secs

Walk at 0.5m/s for 2secs

Walk towards the origin at 0.4m/s for 3secs

Rest 1sec

Graph 5: Distance vs. Time

Start 0.8m away from the origin

Walk away 1m in 3.5secs

Rest for 3secs

Walk away 1.5m in 3.5secs

Graph 6: Velocity vs. Time

Walk away from point of origin at 0.35 m/s for 3secs

Walk towards point of origin at 0.35m/s for 3.5secs

Rest for 3.5secs

Building an Electric Motor

On Thursday, our class was given the task of building an electric motor. We had previously decided to work in either pairs or to work alone. In preparation, my partner (Bojana) and I collected all the materials we would need for the task at hand: a piece of non compressed wood, 4x 4inch nails, smaller nails, thumb tacks, sand paper, a soda can, paper clips, a kebab stick and a cork. We were provided the power supply, magnets, copper wire, and tools. Another member was added to our group the day of (Emily).

We started by hammering the 4 4inch nails into the piece of non compressed wood, while other members hammered the two commutator pins on either side of the cork and slid the kebab stick through the centre. We twisted two paper clips into loops having to change the shape many times in order to allow the kebab stick enough space to freely spin when place with these loops. the paper clips were thumb- tacked to the wood. Then we cut our pop can to get two thin strips which we sanded on both sides, this would be our brush. 

                     

Next we took the copper wire we were provided and wrapped it in the same direction around the cork and the two commutator pins. the two ends of the wire were well sanded previously. Now that everything was in place, the brushes were thumb-tacked so that they would touch the commutator pins when spun. Our model was ready to be tested.

Unfortunately, our model could not be tested because of several factors, the nails happened to be two far apart and the brushes did not reach the pins when the axel was spun. The design overall was very unstable. My group decided to take our model home and fix it. 

Later that day, my partner and I met in hopes of fixing our model. We took out the 4inch nails and carefully hammered them back in according to the given measurements. We remodeled the paper clip bearings we had made so that they were equal and the axel could lay parallel. We hammered the commutator pins so that they were in not too far that the brushes couldn't reach them. The hardest part was getting the brushes just right. We cut and bent it many times before it finally appeared as if our model was perfect.

The next day, we were excited to test our model again. When the power supply was turned on... it did not work! we were surprised and didn't know what we had done wrong our how to fix it. Fortunately Mr. Chung figured out that it could be a problem with the wire and not the model. When he tested it again, our motor began to spin smoothly and continuously. We were so relieved! Our hard work the night before definitely payed off.

Magnetism and Electromagnetism Notes (Pages 582-9)

17.1 The Magnetic Force- Another Force at a Distance

• A magnetic field is the distribution of a magnetic force in the region of a magnet. 
• There are two magnetic characteristics, lebelled north and south, that are responsible for magnetic forces. Similar magnetic poles repel one another while dissimilar poles attract one another.
• Magnets attract certain metals such as iron, nickel, and cobalt, which are not magnetic. These are called ferromagnetic metals.
• 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.

17.2 Electromagnets

• Oersted's Principle- Charge moving through a conductor produces a circular field around the conductor.
• Scientists have developed several hand signals to predict how magnetic forces act, known as right hand rules because they involve using your right hand.

• RHR#1: Grasp the conductor with the thumb 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: Grasp the coiled conductor with the right hand such that 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.
  

Notes: Textbook pages 553-63

16.5 Resistance- Ohm's Law

• The amount of energy transferred to a device depends on both the potential difference of the power supply and the nature of the pathway using the electrical potential energy.
• Resistance is a measure of the opposition to current flow. the formula is:
  
  R=V/I
• The amount of current flowing through a resistor varies directly as the amount of potential difference applied across the resistor.
• Properties such as length, cross-sectional area, material, and temperature also affect the resistance of a conductor.
  

16.6 Series and Parallel Circuits

• In a series circuit, the loads are connected one after another in a single path. In a parallel circuit, they are side by side.
• 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.
• Kirchoff'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.
• There is no net gain or loss of electric charge or energy in a circuit.

Pre Lab: Using Voltmeter and Ammeter

NAME	SYMBOL	UNIT	DEFINITION
Electrical Potential Difference	V	Volt (V)	Electrical Potential energy for each coulomb of charge.
Current	I	Ampere (A)	Rate of charge flow.
Resistance	R	Ohm  (Ω)	The opposition to current flow.
Power	P	Watt (W)	The rate at which electrical energy is passed on the various circuit loads.

In Class Assignment- Circuits

In Today's class we worked in groups of 4 to learn more about circuits. We played around with a "special" ping-pong ball that would light up and hum if its circuit was completed. Here is what we found out:

     1.Can you make the energy ball work? What do you think makes it flash and hum?

Yes, we could make the ball flash and hum by completing the gap in the circuit using our hands.

     2.Why do you have to touch both metal contacts to make the ball work?

As mentioned in the previous question, touching both metal contacts bridges the gap in the circuit. Since humans do conduct electricity, the flow is able to resume, thus completing the circuit.

     3. Will the ball light up if you connect the contacts with any material?

No. Only electrical conductors will make the ball light up.

     4. What materials will make the energy ball work? 

When tested, the materials that make the energy ball work were all conductors of electricity, such as metal and the human body.

     5. This ball does not work on certain individuals, what could cause this to happen?

This question had the whole class thinking. We were unsure because the ball worked on everyone in our class. The only reason I could think of was that some people's bodies may not conduct electricity as well as the rest of ours. With further research I have found that water and salt in our bodies cause the conduction of electricity. Maybe some people have a condition where they don't have as much salt/ water in their bodies?

     6. Can you make the energy ball work with 5-6 individuals in your group? Will it work with the entire class?

We experimented with this question and found that it did work with 5-6 people, as long as we were all connected to each other. We also tried this out with the entire class and once again, the ball began to flash and hum. However I do think the strength is weakened when more people stand between the completed circuit.

     7. What kind of circuit can you form with one energy ball?

A series circuit.

     8. Given two balls can you create a circuit where both balls light up?

Yes, to complete this we simply connected our hands as before except the people who had a ball beside them touched a metal connector.

     9. What do you think will happen if one person lets go of the other person's hand and why?

The energy ball stops working. The gap in the circuit now makes this an open circuit.

     10. Does it matter who lets go?

It does not because everyone in the group played a part in the completed circuit.

     11. Can you create a circuit where only one ball lights up? Use both.

This can be attained by forming a parallel circuit. Much like the ones we have in our homes (if one system fails everything else still works). creating a break in the circuit wouldn't affect both balls, just one.

     12. What is the minimum number of people needed to complete this?

A minimum of five people would be needed. 

In conclusion, what is the difference between a series and parallel circuit?

In a series circuit, all the loads are connected one after another in a single path. It is possible for some of the loads to be supplied with current while others are not.

In a parallel circuit, the loads are connected side by side. Thus, any break in the circuit would cause a loss of current to all the loads.

 

Challenge 1: Physics of Tall Structures

Yesterday in class we accomplished a mini challenge. In small groups we were told to build the tallest, free- standing structure we could with 5 sheets of newspaper and a length of tape. The class immediately started planning and got to work on their structures. Within the given period of about 25 minutes many of the groups had completed their challenge. However not all of the structures worked. Some collapsed while some were unable to stand freely. Many of the structures were extremely unstable. So, what was the best way to build the structure? How much height has to be compromised in order to make the structure stable?

Physics of Tall Structures

Several aspects can contribute to a stable tall structure. Mainly, having most of the mass located at the base would help the construction to stand. Other ways to make sure of an effective structure would be to: have a wider base and/ or attaching tripod- like extensions to distribute the mass.

What Makes a Tall Structure Stable?

Obviously the most important thing to consider when building a tall structure is the base. It must be wider, and able to support the weight of the rest of the building.It is also better that the base is as flat as possible

Center of Gravity

The center of gravity is a point where the total weight of a structure is thought to be concentrated.  A structure should be built with the lowest center of gravity possible, this means that it is most stable at this point.

Overall, i think my group did a good job building our structure. We stacked our newspapers pyramid- like so that the base was the widest part. In addition, we incorporated the tripod design for additional stability.

Our Structure

Notes: Current Electricity

Current

·         In an electric circuit, an energy source provides electrons with energy.

·         Conductors transport the electrons to where the electron energy is transferred, then back to the source to be re-energized.

·         Current can be defined as the rate of charge flow and is given the symbol I. The formula for current is the total amount of charge moving past a point in a conductor divided by the time taken.

I=Q/T

I is the current in amperes (A), Q is the charge in coulombs (C), and t is the time in seconds.

·         Current is a flow of negatively charged electrons repelling one another.

·         On the subject of measuring current, an ammeter must be used. It must be rewired so that all current runs serially through the ammeter.

·         In direct current (DC) the current flows in a single direction from the power supply through the conductor to a load, while in alternating current (AC), the electrons periodically reverse the direction of their flow.

·         A path for the electric current to flow to and from the power supply is called a circuit and is required for any electrical device to work properly.

Example of an electrical circuit (This is the familiar circuit of a torch battery

Electrical Potential

·         An electric charge has a certain amount of electrical potential energy because of the electric field set up by the power supply. The power supply has to increase the electrical potential energy of each coulomb of charge from a low to a high value. As the charge flows through the load, its energy decreases.

·         The electrical potential energy for each coulomb of charge in a circuit is called electric potential difference (Voltage)

V=E/Q

E is the energy required to increase the electric potential of a charge, Q. 

·         A volt (V) is the electrical potential difference between two points if one joule of work (J) is required to move one coulomb (C) of charge between the points.

·         Potential difference between any two points can be measured using a voltmeter.

Example of a voltmeter