How to derive equation 3 and 4 by using a graph? It is simple! imagine a trapezoid on a graph. Since the trapezoid is composed of a right triangle and a rectangle shaped figure, we can actually simply add the area of the right triangle and the rectangle for equation three:

Area for rectangle:  (v1)(t)

Area for right triangle:   (v2-v1)(t)/2

So, after combining these two results, the equation would be: 

d = v1t + ½(v2-v1)t

Because at = v2-v1 the next step would be substituting this equation into the one above. So it becomes:  d = v1t + ½at(t). As we continue, the final equation which is the third equation would be d = v1t + ½at²


Equation Four


This time, we change our steps for finding the area of the trapezoid. We previously used addition to find the area, therefore this time we will be using subtraction. We first calculate the total area of a rectangle which is the trapezoid, but we see it as a rectangle. The equation will be: (v2)(t). In order for us to get the correct area of the trapezoid, we have to subtract the excessive area we included. So the excessive area would be: (v2-v1)(t)/2

Again, since at = v2-v1, we substitute this into the result we got from above and the equation would be like: d = v2t-½(v2-v1)t, then, 

d = v2t-½at(t), continue to d = v2t-½at², and we are done!

Motion

• This is a d->t (distance and time) graph.
• When line is horizontal, it represents immobility, thus stay at one spot.
• When the line has an inclining slope, it means moving backward from the senor in this case.
• When the line has a declining slope, it means moving oppositely of backward, so in this case, move forward towards the sensor.

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

2.Walk 1.5 meter away from the origin in 2 seconds with constant speed.

3. Stand 2.5 meter away from the origin, and stay for 3 seconds.
4. Walk 0.75 meter toward the origin in 1.5 seconds with constant speed.
5. Stand 1.75 meter away from the origin, and stay for 2.5 seconds.

This is a d->t graph

         1. Stand 3 meter away from the origin, and walk 1.5 meter toward the origin in 3 seconds, with constant speed.

           2. Stand 1.5 meter away from the origin, and stay for 1 second.

           3. Walk 1 meter toward the origin in 1 second with constant speed.

           4. Stand 0.5 meter away from the origin, and stay for 2 seconds.

           5. Walk 2 meter away from the origin in 3 seconds.

1. Stand 0.8 meter away from the origin, and walk 1 meter away from the origin in 3.5 seconds with constant speed.
2. Stand 1.8 meter away from the origin, and stay for 3 seconds.

3. Walk 1.3 meter away from the origin in 3 seconds.

This is a v->t (velocity and time) graph

• Postive and constant line represents a constant velocity moving away from the sensor
• Negative and constant line represents a constant velocity moving West (toward the sensor)
• Sudden increase or decrease in the value of the line means a dramatic acceleration or deceleration.

1. Speed up for 4 seconds.

 2. Walk at a speed of 0.5m/s and move away from the origin for 2 seconds.

3. Walk at a speed of 0.4m/s and move toward the origin for 3 seconds.

4. Stay for 1 second.

Translation from Velocity to Acceleration
1. The acceleration is 0.1m/s^2, and the line is on the positive side.
2. There is no acceleration.
3. There is no acceleration.
4. There is no acceleration.

This is a velocity-time graph

1. Stay for 2 seconds.

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

3. Stay for 2 seconds.

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

Translation from Velocity to Acceleration
1. There is no acceleration.
2. There is no acceleration.
3. There is no acceleration.
4. There is no acceleration.

This is an acceleration graph

Translation from Acceleration to Velocity

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

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

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

5. Slow down, toward the origin, for 0.25 second.
6. Stay for 3 seconds.

1. There is no acceleration.
2. The line is on the negative side.
3. The line is on the negative side.
4. There is no acceleration.
5. The line is on the positive side.
6. There is no acceleration.

Motor

Simple Motor

Today, in the physics class, our group learned how to build a simple motor with materials such as cork, wires, wood, thumbtack nails, and aluminum pieces. The motor are basically divided to different components - the commutator, split-ring, conductor, and power supply. The commutator involves two pins that are metal that are fixed in the cork so they can attach to the brushes located at the both sides of the commutator while spinning (aluminum pieces), and the electricity will pass through the metal conductor to the wires wrapped around the cork. While electricity passing through the wires been wrapped around the cork, magnetic field is created which makes a up force at one side and a down force at the other side due to the direction of current flow, so overall the commutator could spin a complete circle. In the process of building a simple motor, there are few details that needs to be further noticed otherwise, the motor will not work at the first time. The brushes made of aluminum pieces from cans are needed to be rubbed by sandpaper until the silver-shiny surface appear, otherwise electricity will not passes through them. The wires are also required to be rubbed at the end and the beginning part which then will wrap around the pin. For building the commutator, wires should be wrapped neatly, and parallel to each other.

Magnetic Force

Right Hand Rule #1

Right Hand Rule #2

• Magnetic Field is the distribution of a magnetic force in the region of a magnet There are two different magnetic characteristics, labelled North and South.
• Similar magnetic poles, north and north or south and south, repel one another. Dissimilar poles, north and south, attract one another with a force at a distance.
• Metals such as iron, nickel, and cobalt, or mixtures of there metals, are called the ferromagnetic metals, which means they could be attracted by magnets.
• Magnets are made of ferromagnetic metals
• Domain Theory states that 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.
• Domains that line up could make the metal be magnetized.
• Oersted's Principle: Charge moving through a conductor produces a circular magnetic field around the conductor.
• Right-hand rules are three rule about magnets fields that involves your right hand. The abbreviation for them are RHR#1, RHR#2, and RHR#3.
• Right-hand rule#1: For conventional current flow, 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. There is a Left-hand rule#1, which is just opposite to RHR#1
• Scientists curve the conductor to strengthen the magnetic field.
• RHR#2: For conventional current flow, 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 tin the direction of the magnetic field within the coil. Outside the coil, the thumb represents the north end of the electromagnet produced by the coil.
• Left-hand rule#2: Opposite to RHR#2, the left-hand thumb grasp the coiled conductor, pointing the direction of the electron (-) current flow through the conductor.
• Electromagnet is a coil of wire around a soft iron core, which uses electric current to produce a magnetic field.
• Important formulas in the chapter are B2 = B1(I2/I1), and B2 = B1(n2/n1) - both of them are for calculating the strength of an electromagnet (B).

Resistance - Ohm's Law and Kirchhoff's Laws

• The amount of energy transferred to a load depends on two things: 1. the potential difference of the power supply and 2. the resistance of the pathway through the loads that are using the lectir potential energy.
• Resistance directly affect the amount of current passes through the load. Low resistance makes current to pass through the load much more easily.
• The measure of the opposition to flow is called electrical resistane.
• R = V/I is the formula for calculating resistance. R is the resistance in volts/ampere and unit is Ω. V is the potential difference in volts and I is the current in amperes.
• The Ohm's law states that the V/I ratio is constant for a particular resistor.
• The amount of current flowing through a resistor varies directly as the amount of poetential difference applied across the resistor. The higher the potential difference, the more the current flows through the resistor.
• The resistance on a conductor depends on many properties such as Length, corss-sectional area, the material it is made of, and its temperture.
• The formula for calculating the resistance of  conductors in difference length  R1/R2 = L1/L2.  
• Cross-sectional area that affects the resistance, the larger the area or thicker the conductor, the less resistant it has to current flow. It is represented as R1/R2 = A2/A1
• Some materials are better conductors than other materials. The measure of the resistance of a substance is called resistivity. It has units Ω m. It is represented as R1/R2 = p1/p2
• Temperature also works as one factor that changes resistance of a substance. Unsually the higher the temperature the higher the resistance, however, not for all substances.

Prelab: Using Voltmeter and Ammepter

Name	Symbol	Unit	Definition
Voltage	V	V	Potential difference for each coulomb of charge in a circuit.
Current	A	A	The flow of charge
Resistance	R	Ω	The opposition to current flow
Power	P	W	The rate at which work is performed or energy is converted

Qustion 1 - 12

1. Touch two metal contacts to make the ball flash.
2. To create a complete electric circuit
3. The ball will not flash. It needs a conductor, and it will flash only when the two materials that works as the conductor connects forming a complete circuit. 
4. The materials we tested are metal, and human body. Both of them could work as conductor.
5. When the body is not attached to the metal contacts which means covered by something such as clothing.
6. We can make the energy ball work with all people as long as a complete circuit is established.
7. A series circuit
8. We could make both ball light up in either a series circuit or a parallel circuit.
9. If two balls are in one circuit when on person disconnects with the other, the balls will not light up. If there are two circuits when on person disconnects in a circuit, the other circuit still operates.
10. In a series circuit, no.
12. 4 people.