Deriving equation 3 and 4 from the v-t graph

The standard velocity-time graph.

Equation 3 is written as d = V1Δt + ½aΔt².

On a v-t graph, when we are looking for distance, we find the area of the trapezoid shape.

We can do that by dividing the trapezoid into a square and triangle.

The formula to find the area of the triangle is ½(V2-V1)t. Equation 1 states that at= V2-V1. Sub equation 1 into the formula. ½at²

The formula to find the area of the rectangle is V1*t, also known as V1Δt.

Combine these 2 formulas to create equation 3, d = V1Δt + ½aΔt².

Equation 4 is written as d = V2Δt - ½aΔt².

On the v-t graph, we can derive equation 4 by making the graph look like this big rectangle.

First, find the area of the rectangle as a whole. V2*t, or V2Δt.

Then find the area of the triangle within the rectangle. ½(V2-V1)t. We know from equation 1 at = V2-V1.
½aΔt².

Combine the two formulas to create V2Δt - ½aΔt².

Motion in Graphs

Last week, we did a lab on distance/time graphs and velocity/time graphs. Here are the 6 graphs we made:

In this Distance/Time graph, the motion is first not moving at 1 m away from the detector. Then walking away from the detector at a constant speed. Next walk towards the detector at a constant speed. Finally, stop moving for the last couple of seconds.

In this Distance/Time graph, The motion is walking towards the detector at a constant speed. Then one stops for a few seconds. Next, walk towards the detector again in a faster constant speed. Then stop for a few seconds. Finally, Walk away from the detector in a constant speed.

In this Distance/Time graph, The motion is walking away from the detector at a constant speed. Then stop moving for a few seconds. Finally, walk away from the detector at a faster constant speed.

In this Velocity/Time graph, The motion is walking away from the detector at a slow speed, but then quickly pick up speed. Then, continuing walking at a constant speed. Next, start walking in towards the detector at a constant speed. Then keep that speed for a few seconds. Finally, stop moving.

In this Velocity/Time graph, the motion is not moving for the first few seconds. Next, start walking away from the detector at a constant speed. Then stop moving again for a few seconds. Finally walk towards the detector at a constant speed.

In this Velocity/Time graph, The motion is to be already moving at a constant speed going away from the detector once it starts recording. Then one will change directions and start moving back toward the detector at a constant speed. Finally one will stop moving all together.

Motor Lab

We were asked to build motors the other day. We had one day to gather up all the materials needed to build a motor. Luckily, we were able to gather all the materials even though some of them were hard to get.
When we started building the motor, we were given 30 minutes to hammer the 4 four-inch nails into the wood. The nails had to be 2-3cm apart in width and 5-6 cm apart in length. We then sanded the pop can all the way to the point where both sides were silver. Our first problem popped up when we were trying to fit the axel into the cork. Our cork was a bit bigger than the other corks other people had so it took longer to get the axel in. The cork was also a bit rubbery which didn't help us. The second problem with the cork came up right after the first. the copper coil wasn't holding onto the cork tightly enough, and we spent a long time trying to get it to stick. In the end, our motor ended up as a fail. D=

Right-hand rule #1: Hold the conductor with your right hand. Your thumb should be pointed in the direction of the conventional, or positive current flow. Your fingers should be pointing in the direction of the magnetic field around the conductor.

Right-hand rule #2(for coils): Hold the coiled conductor with the right hand such 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 north end of the electromagnet produced by the coil.

Magnetism

A magnetic force is a force that acts from a distance. A magnetic field is the distribution of a magnetic force in the region of a magnet.


A magnet usually contains two magnetic poles, north and south. Similar magnetic poles, like north and north or south and south, repel each other with force. Dissimilar poles, like north and sough, attract each other with force.


Only nickel, iron and cobalt are attracted to magnets so they are known as ferromagnetic metals.
 The Domain theory states that all large magnets are made up of many smaller and rotatable magnets, known as dipoles. Dipoles can ineract with other dipoles close by. If dipoles line up, then a small magnetic domain is produced.

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

Resistance, Ohm's Law, and Kirchhoff's Laws

The amount of energy transferred to any device depends on two things:
1. The potential difference of the power supply.
2. The nature of the pathway through the loads that use the electric potential energy.

The amount of current flowing through a resistor changes depending on the amount of energy that's put in the resistor.


A thin wire will have more resistance, while a larger one will have less.
In order to calculate resistance, we use the formula R=V/I. Where R is the resistance in ohms (Ω), V is the potential difference in volts and I is the current in amperes.

The ratio between Voltage against Current is constant and is known as Ohm's Law.

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


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.
 
Kirchhoff's laws apply to the laws conservation of electric charge and the conservation of energy. To make it short, in any circuit, there is no net gain or loss of electric charge or energy.

Today, Mr. Chung gave us a prelab to do to prepare for the lab we are going to do tomorrow. We were asked to fill out this chart:


NAME                       SYMBOL                      UNIT                    DEFINITION

Voltage                            V                           Volts         An electromotive force or
                                                                                    potential difference expressed
                                                                                    in volts.

Current                             I                         Amperes    A flow of electric charge
                                                                                  through a conductor. The rate
                                                                                  of flow of a charge. Current is
                                                                                  measured in amperes.

Resistance                       R                          Ohms        A measure of the degree to
                                                                                  which a substance impedes the
                                                                                  flow of electric current induced
                                                                                  by a voltage. Resistance is
                                                                                  measured in ohms.

Power                               P                         Watts       The rate at which work is done,
                                                                                  expressed as the amount of
                                                                                  work per unit time and
                                                                                  measured watts.