How equation #3 translates into the v/t graph

                               
Equation #3  ────   d = V1Δt + 1/2 aΔt²
                                          ↓             ↓
                                   rectangle   triangle

As the graph above, we know that we have to calculate the area of the trapezoid to find out the displacement. But, in Equation #3, only V1 is usable. We would break down the trapezoid into a triangle and rectangle.

To determine the area of the rectangle, we would multiple V1 (as symbol "a" shown in the graph《Width》) to t2 - t1, which known as Δt. (as symbol "h" shown in the graph《Height》)

It will give us a equation of  Area of rectangle = V1Δt

To determine the area of the triangle, we would multiple (V2 - V1) 《Base》to  Δt 《Height》divided by 2

According to Equation #1 aΔt = V2 - V1, so, as we sub this equation,
Area of triangle = ½(V2 - V1)(Δt)
Area of triangle = ½aΔt(Δt)
                        
Displacement = Total Area

Displacement = Area of rectangle + Area of triangle  (As we sub the equations in,)

Displacement = ½V1Δt + aΔt²
                                      

Translation of Graph

Graph B)
There are five sections in this graph:

Velocity →↓
Section 1) Time (in second) 0 ~ 1  : The Velocity starts at the x-axis, a horizontal line which lies on the x-axis is created.
Section 2) Time (in second) 1 ~ 3  : A horizontal line is created in the positive area at  0.75 as the walking speed is 0.75m/s [E]     Slope: 1.5(m)/2(s)
Section 3) Time (in second) 3 ~ 6  : No change in distance, so there's a horizontal line on the x-axis.
Section 4) Time (in seond) 6 ~ 7.5  : A horizontal line is created in the negative area at -0.53 as the walking speed is 0.53m/s [W]c or -0.53m/s [E]    Slope: -0.8(m)/1.5(s)
Section 5) Time (in second) 7.5 ~ 10  : No change in distance, so there's a horizontal line on the x-axis.

Acceleration →↓
 There's no acceleration in this graph. The line lies on the x-axis.

Graph C)
There are 5 sections in this graph
Velocity →↓
Section 1) Time (in second) 0 ~ 3  : A horizontal line is created in the negative area at -0.5 as the walking speed is 0.5m/s [W] or -0.5m/s[E]   Slope: -1.5(m)/3(s)
Section 2) Time (in second) 3 ~ 4  : No change in distance, so there's a horizontal line on the x-axis.
Section 3) Time (in second) 4 ~ 5  : A horizontal line is created in the negative area at 1 as the walking speed is 1m/s [W] or -1m/s [E]    Slope: -1(m)/1(s)
Section 4) Time (in second) 5 ~ 7  : No change in distance, so there's a horizontal line on the x-axis.
Section 5) Time (in second) 7 ~ 10  : A horizontal line is created in the positive area at 0.83 as the walking speed is 0.83m/s    Slope: 2.5(m)/3(s)

Acceleration →↓
There's no accelerationin this graph. The line lies on the x-axis.


Graph D)
There are 4 sections is this graph:

Distance →↓
Section 1) Time (in second) 0 ~ 2  : The distance start from 0m, and stay for 2 seconds therefore a horizontal line lies on the x-axis.
Section 2) Time (in second) 2 ~ 5  : The line goes up with a positive direction and stop at 1.5m away the origin.  Distance: 0.5(m/s)*3(s)
Section 3) Time (in second) 5 ~ 7  : The velocity is 0, that causes a horizontal line is drawn at 1.5m.
Section 4) Time (in second) 7 ~10  : The line decreases with a negative direction and stop at 0. Distance : -0.5(m/s)*3(s)
Acceleration →↓There's no acceleration in this graph. The line lies on the x-axis.


Graph E)
There are 4 sections in this graph:

Distance →↓
Section 1)
 Time (in second) 1 ~ 4  : The speed increases in a speed of 0.125m/s Slope: 0.5(m/s)/4(s), so it will become a curve, a cureve which has a smaller slope at first and become gather and the line stop at 1m away the origin.
Section 2) Time (in second) 4 ~ 6  : The line goes up with a positive direction and stop at 2m away the origin.   Distance: 0.5(m/s)*2(s)
Section 3) Time (in second) 6 ~ 9  : The line decreases with a negative direction and stop at 0.8m away thre origin.  Distance: -0.4(m/s)*3(s)
Section 4) Time (in second) 9 ~ 10  : The velocity is 0, that causes a horizontal line is drawn at 0.8m

Acceleration →↓Section 1) Time (in second) 1 ~ 4  : A horizontal line is created at 0.125(m/s2) Slope: 0.5(m/s)/4(s).
Section 2 ~ 4) There're no acceleration in section 2 to 4. The line from 4 to 10 second is on the x-axis.

Graph F)
There are 3 sections in this graph:

Velocity →↓
Section 1) Time (in second) 1 ~ 4  : A horizontal line is created in the positive area at 0.26m as the walking speed is 0.26m/s  Slope: 0.9(m)/3.5(s)
Section 2) Time (in second) 4 ~ 6.5  : No change in the distance, so there's a horizontal line on the x-axis.
Section 3) Time (in second) 6.5 ~ 10  : A horizontal line is created in the positive area at 0.43 as the walking speed is 0.43m/s  Slope: 1.5(m)/3.5(s)
Acceleration →↓There's no acceleration in this graph. The line lies on the x-axis.

Motion prelab

Distance (m) VS. Time (s)

1. Stay at 1m away from the origin for 1 second.

2. Walk 1.5m in 2 seconds away from the origin. [0.75m/s]

3. Stay at 2.5m away the origin for 3 seconds.

4. Walk 0.75m in 1.5 seconds towards the origin. [0.5m/s]
5. Stay at  1.75m away teh origin for 2.5 s.

                                             Distance (m) VS. Time (s)

1. Start from 3m away the origin, walk 1.5m for 3s towards the origin. [0.5 m/s]

2. Stay at 1.5m away the origin for 1 s.

3. Run 1m in 1 second toward the origin. [1 m/s]

4. Stay at  0.5m away the origin for 2 s.

5. Run 2.5m away the origin in 3 seconds. [0.83 m/s]

                                Velocity

1. Stay for 2 seconds.
2. Walk at 0.5 m/s away the origin for 3 seconds.
3. Stay for 2 seconds.
4. Walk at 0.5 m/s toward the origin for 3 seconds.








                                                                                  Velocity

 

1. Speeds up  to 0.5 m/s away the origin in 4 seconds.

2. Walk in constant speed [0.5m/s] away the origin for 2 seconds.

3. Walk at [0.4 m/s] towards the origin  for 3 seconds.

4. Stop walking and stay for 1 second.



                    Distance (m) VS. Time (s)

1. Start from 0.9m away the origin, walk  0.9m away the away in 3.5 s [0.26 m/s]

2. Stay at 1.8m away the origin for 3 s.

3. Walk 1.5m away the origin in 3.5 s (0.43 m/s)







                                                                                        Velocity

1. Walk  at 0.35 m/s away the origin for 3 seconds.

2. Walk at 0.35 m/s toward the origin for 3.5 seconds.

3. Stand  for 3.5 seconds.

MOTOR PRINCIPLE

 1.     In this motor model, the power (conventional
current flow) flow though the brushes and connect to
the commutator pin. It causes it to become a DC motor.
According to the RHR #2, the direction of conventional
current flow is shown in the picture which located at the
middle. After using the RHR #2, we could predict the
direction of the force by using the RHR #3. The direction
of the force at the left side is different from the right
side’s, so the cork could spin.

.

 2.     Then, after the motor spins half way of a circle, the
commutator pins touched another brush (not the brush
 that has been touched before the motor spins) that
changed the direction if the current and also the direction
of forces changed, too.

 
3.     After the forces changed when the motor reached
the half way point, the motor continues to spin and
it changed its forces while it meets another half way
point, and it spins more and more that forms a loop.

 

Now， the loop has been formed and the cork can spin
nicely until there is no power anymore.

RHR 1&2

The right hand rule helps demonstrate the relationship between conductor current and the direction of force. The first right hand rule for convertional current flow is used to determine the direction of current flow in a conductor. The conductor where you right hand's thumb is pointing at, is the direction of convertional. (positive current flow).

In the second right hand rule, the propose is to determine the direction of the magnetic field. The thumb point at the North -Pole.  

Notes - Magnetism p.582~589

● Magnetic Field is the repartion of a magnetic force in a region of a magnet.

●We use test compass to measure the magnetic forces within an area or object, instead of the test charge we used in electrostatics.

●Magnet attracts ferrous objects such as, pieces of iron, steel, nickel and cobalt.

●The magnet repel one another if both magnetic poles are north and north, or south and south ; The magnet attract one another if magnectic poles are difference(dissimilar). <North and South>

●The Domin Theory tells us that all large magnet are constitute by many smaller and rotatable magnet. Those small and rotatable magents are called dipoles. Dipoles can interact with other dipoles to close by.

● Magnetic Domin is created if dipoles are lined up.

●Oersted’s Principle is an important discovery made by Hans Christian Oersted. Oersted’s Principle tells that a circular magnetic field around the conductor is produced when charge moving through a conductor.

●There are two right- hand rules that help us to predict how magnetic force act. Right- hand rules are like physical formula because they allow us to take certain known factors and predict one unknown factor.

●The first right hand rule for convertional current flow is used to determine the direction of current flow in a conductor. The conductor where you right hand's thumb is pointing at, is the direction of convertional. (positive current flow).


●The second Right hand rule is to determine the direction of current flow within a coiled. The thumb point at the direction of the magnetic field within thr coil.

Notes from p.553~563

◎Electrical resistance is a material's opposition to the flow of electric current and it's measured in Ohms (Ω)

◎ Circuit with a boarder pathway and narrow pathway is different by the current flow, there're more current pass though a circuit with a boarder pathway than a circuit with a narrow pathway

◎The resistance of a conductor depends on things such as, its length, cross-sectional area, the material it is made of , and its temperature.

◎Series circuit is the circuit which the loads are connected one after another in a single path.

◎If two or more components are connected in parallel they have the same potential difference across their ends, that's parallel circuit and they are side by side.

←◎Georg Simon Ohm is the person  who discovered that V/I ratio was constant for a particular resistor. (Known as the Ohm's law)

◎ Kirchhoff's Current Flow us the total amount of current into a  junction point of a circuit equals the total current that flows out of that same junction.
 
             I(1) + I(2) + I(3) = I(T) = I(4) + I(5)

◎    Kirchhoff's Voltage Law is the total of all electrical potential decreases in any complete loop is equal to any potential increases in that circuit loop.                                             
                                                             Gustav Robert Kirchhoff →↑

◎There is no net gain or loss of electric charge or energy in any circuit with the laws of conservation of electric charge and the conservation of energy, these laws are corresponding to the Kichhoff's laws too.

※ R = Resistance   V = Volts (The potential Difference)  I = Amperes (Current flow)

The equation of calculating electrical resistance is                        

R = V/I                                                            

               

The equation of calculating voltage (volt) is
                                                                                                    V = IR


The equation of calculating Current flow (Amperes) is
                             I = V/R