Kinematics

Kinematics

 It deals with the motion of objects without taking into account the cause of motion.

Distance and Displacement

Uniform Motion:

Uniformly Accelerated Motion

Uniformly Retarded Motion
"Angle made by resultant velocity"

Types of Motion: Motion of the body can be three types

 [a]Translatory

 [b] rotational

 [c] Vibrational

It can also be classified as 1 dimensional, 2 dimensional or 3 dimensional

Distance is the actual path covered by the particle, while directional distance between initial and final position is called displacement. Distance is a scalar quantity and displacement is a vector quantity.

[a] the magnitude of the displacement is equal to the minimum possible distance between the two points.

Distance less then equal to |displacement|

[b] For moving particle distance never decreases with time while the displacement can decrease with time implying that the body is moving towards the initial point,

[c] For moving particle distance is always greater than zero whereas displacement can be positive negative or zero. Thus, a body may cover distance without having displacement but a body does not have displacement without covering distance.

Motion In One dimension: In motion of the particle we come across the terms distance, displacement, speed, velocity, acceleration and time. Of these quantities velocity, acceleration and displacement are treated as vectors. Motion in one dimension can be classified into following categories

[a] uniform motion

[b] uniformly accelerated motion

[c]Uniformly retarded motion

[d] Uniformly retarded and then accelerated in opposite direction

[e] Non uniformly accelerated or retarded motion

In uniform motion the velocity of the particle I constant, therefore acceleration is zero. Thus

S=v t

Uniform motion is possible in one dimensional motion only, as if the direction is changing the velocity will also change Moreover in uniform motion average and instantaneous values of speed and velocity are equal.

In uniform acceleration, the acceleration of the body is assumed to be equal in magnitude and direction. In one dimensional motion we also assume the acceleration to be parallel to the initial velocity. The equation of motion for uniformly accelerated motion are

[a] v = u + at

[b]v² = u² + 2aS

[c] S = ut + at²/2

[d] S_nth = u + a(2n-1)/2

In kinematics there are 5 variables u, v, a, t and s. if we know the value of 3 variables we can find the other 2 using these two equations.

In this case the initial velocity can’t be zero. The acceleration is constant in magnitude and direction and opposite to the direction of the velocity. The following equations are used in this case.

[a] v= u – at

[b] v² = u² – 2 aS

[c] s = ut – at²/2

[d] s_nth= u - a(2n-1)/2

Non Uniformly Accelerated Motion or Retarded Motion:

When acceleration of the particle is not constant, we go for basic equations of velocity and acceleration i.e.

[a] v = ds/dt       or   ds = vdt

[b] a = dv/dt     or    dv = a dt

[c] a = v dv/ds  or    vdv= ads

Using differentiation

s – t equationàv-t equation àa-t equation

Using integration with boundary conditions

a-t equation àv-t equation às-t equation

Average Speed: The average speed is defined as the ratio of the total distance traveled by the body to the total time taken.

[1] if a particle travels distances s₁,s₂,s₃………….. with velocities v₁,v₂,v₃………… then

v_av= ∆S/∆t=∑si/∑(si/vi)

If s₁=s₂=…….s_n=s, then

Own radio receiver

We’ll be able to listen to AM radio broadcasts with something we made our self.  A nice feature of this project is that you can make it as easy or as advanced as we want.

A radio is an electrical device that receives an invisible signal, or radio wave, from a radio station and converts the signal into sound that we hear and understand. A radio wave is a type of electromagnetic radiation that can be used to convey audio information. Radio waves have energy associated with them. Radio stations, using a transmitter and an antenna, transmit waves like the ones in Figure below, which shows both a 1-cycle wave and a 3-cycle wave, each occurring in the span of 1 second. The number of cycles per second is called frequency. The unit for frequency is the hertz (Hz). A 1-cycle-wave per second is a 1 Hz wave and a 3-cycle-wave per second is a 3 Hz wave. Every AM radio station transmits its signal at a given frequency, and the frequency band for AM radio stations in the United States is from 530,000 Hz to 1,710,000 Hz. So a radio station transmitting at 1,590,000 Hz (expressed in kilohertz as 1,590 kHz) is sending out a signal that is 1,590,000 cycles per second.

Waves have both a frequency and amplitude, which is the height of the wave. If someone yells at you from across a room, the amplitude of the sound wave is high. Conversely, if someone whispers to you from across the room, the amplitude of that sound wave is very low. When radio stations transmit sound (or music) waves, they can vary or modulate the amplitude of the wave and that is one way we hear the different levels and frequencies of sound. Stations that transmit signals via amplitude modulation are called AM radio stations.

A crystal radio is a very simple radio that was popular in the early history of radios. It can pick up and play sound from AM radio stations. Rather than rely on outside electrical sources, like a batteries or plugs, crystal radios get their power directly from the radio waves. The diagram in Figure shows the parts of a crystal radio: antenna, coiled wire tuner, diode, earphone, and a connection to an electrical ground.

The antenna picks up AM radio waves which create an alternating current (AC) in the antenna wire. An alternating current is one with a voltage that oscillates between positive and negative.

A diode is an electrical component that allows current to flow in only one direction (positive OR negative). Consequently, when a diode is in a circuit with an alternating current (positive AND negative), it blocks either the positive or the negative half of the wave. The other half of the wave passes through unchanged. This process is called rectification, and it results in alternating current being changed to direct current or DC. The rectified wave only has the positive portion of the original AC wave. When crystal radios were first made the diode was composed of a thin wire that scratched against the surface of a crystal of semi conductive material thus imparting the name "crystal" radio.

The earphones convert the DC to sound. The electrical current is converted into vibration, and that vibration generates sound waves. The sound waves are not very strong though, which is why earphones that fit close to the ear drum, as opposed to a speaker, are required to hear the sound.

The tuner allows you to select the AM frequency for the crystal radio to zone in on. The tuner has many coils of wire. Each AM frequency has resonance with a different length of coil. By changing how much coil is used you can alter the radio’s preferred resonance and thus "tune" in to a specific radio station. Taps, outcroppings of wire at regular coil intervals, are used as places to connect the antenna and/or diode at different wire lengths during the tuning process.

The electrical ground allows current to flow through the circuit (the crystal radio is in fact an electrical circuit). All circuits need a ground to work properly.

To do this fair project, we will need the following materials and equipment:

• Cylindrical oatmeal box, 4-in. diameter (1)
• Masking tape
• Mounting board, wood, about 6 in. × 9 in. (1)
• Screw, any size to tether wire to mounting board (1)
• Screwdriver

Spool of 20 or 22 gauge solid plastic insulated wire, 75-foot (1);

Germanium diode(1n34, 1n34a, 1n60 etc.);

47-kohm resistor, 1/4- or 1/2-watt (1);

Alligator clip (2);

High-impedance ceramic earphone (1);

PVC pipe coupling, ¾ inch, (2);

Fahnestock clips (4);

Steps for the making project:

1. Take the oatmeal container (empty, of course) and on the open end, come down about a 1/2 in. and carefully poke two holes. Thread the wire through one hole and back out through the other, as shown in Figure, below. Pull about 1 ft. of wire out, for making the connection to the rest of the circuit. Tape the wire on the inside of the oatmeal box, to keep it from slipping out.

2. Wrap five turns of wire around the oatmeal box and make a "tap,". Remove a short span of insulation, and twist the wires together.
3. Continue wrapping, and every five turns, make a tap, until you get to 40 turns.
4. At 40 turns, poke two holes next to the last turn of wire. Cut the wire off so that you have 1–2 ft. extra to connect to the rest of the circuit. Poke the wire into the first hole and back out the second hole. Tape the wire in place inside the box. You now have your coil wound, as in Figure
5. Next we will need an antenna and a ground. The antenna can be any wire (insulated or bare), as high and as long as possible. Make sure not to place it near electrical wires for your safety and the performance of the radio. Also don't let the antenna "ground out" to trees or the earth (ground). You can make insulators from plastic water pipe or couplings. See Figure, below.

The ground can be made by connecting to a metal water pipe (plastic pipes won't work), or to a metal rod that is pounded at least 2 ft. into the ground.

simple AM radio transmitter and test its broadcast range with a radio receiver

Introduction

Electromagnetic radiation is a propagating wave in space with electric and magnetic components. In a vacuum, electromagnetic waves travel at the speed of light. Electromagnetic waves such as light, x-rays, and radio waves are classified by their frequency or wavelength. Electromagnetic radiation at frequencies between about 430 tetra hertz (THz) and 750 THz can be detected by the human eye and are perceived as light. Electromagnetic radiation at frequencies ranging from 3 hertz (Hz) to 300 gigahertz (GHz) are classified as radio waves.

Radio waves are divided into many sub-classifications based on frequency. AM radio signals are carried by medium frequency (MF) radio waves (530 to 1710 kilohertz (kHz) in North America, 530 to 1610 kHz elsewhere), and FM radio signals are carried by very high frequency (VHF) radio waves (88 to 108 megahertz (MHz)). 

Understand the following terms and concepts 

• electromagnetic radiation and waves,
• electromagnetic spectrum,
• wave model,
• speed of light,
• wavelength,
• frequency,
• amplitude,
• crystal oscillator,
• transformer,
• amplitude modulation.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• 2 crystal oscillators

§  Each oscillator should be at a different frequency, within the AM broadcast band (0.53 to 1.71 MHz in North America, 0.53 to 1.61 MHz elsewhere).

§  For use with the solder less breadboard in this project, you want the 'full can' package.

§  Suitable oscillators

1 MHz, part number 520-TCF100-X
1.2288 MHz, part number 520-TCF122-X.

1 MHz, part number 27861
1.2288 MHz, part number 325307.

o    Solder less breadboard (e.g., Radio Shack 276-001).

o    1000 ohm to 8 ohm audio transformer (e.g., Radio Shack # 273-1380),

o    1/8 inch mono phone plug (Radio Shack # 274-286A),

o    a 6 V AA battery holder (holds four batteries),

o    four 1.5 V AA batteries,

o    a set of alligator jumpers,

o    Jumper wires for breadboard.

Building the circuit 

The transformer isolates the music player from the rest of the circuit, couples the music player and the crystal oscillatory, and "steps up" the signal voltage from the music player in proportion to the ratio of 1 kohm to 8 ohms. The stepped up signal from the secondary coil of the transformer modulates the power to the oscillator chip (+ power at pin 14 and − power at pin 7). A wire connected to the oscillator output (pin 8) serves as the antenna for broadcasting the amplitude-modulated radio wave.  

Points for joining the circuit

Connect the terminals of the phone plug to the 8 ohm side of the transformer :

Insert the 1 MHz oscillator across the gap in the breadboard, so that pins 1 and 7 are on one side of the gap, and pins 8 and 14 are on the other. 

  Use the breadboard to connect the positive and negative terminals of the battery holder and the 1000 ohm side of the transformer as shown in the diagram and in Figure below. Note that the 1000 ohm side of the transformer has a center tap which is not used in this project.

 Connect a long jumper wire to the output of the crystal oscillator (pin 8). This will serve as the antenna.

  Double-check to make sure that all of your connections correspond to the circuit diagram.

        Figure, below, shows a photograph of the completed setup including an iPod for generating the music and an AM radio receiving the signal.

Experimenting with the Circuit

Now that we have to built the circuit, here is the fun part—experimenting with it!

1.    Connect the phone plug to the output (headphone) jack of mp3 or CD player and tune AM radio to 1 MHz. Bring the antenna within an inch of your radio antenna. Can we hear the music that we are playing on your mp3 or CD on the radio?

2.    Now tune AM radio to a different frequency say 700 kHz. Can we still hear your music?

3.    Tune the radio back to 1 MHz where we can hear your music. But this time remove the 1 MHz crystal oscillator and in its place put the 1.2288 MHz oscillator. Can we still hear the music?

4.    Without changing the oscillator back to 1 MHz, instead tune your radio now to 1.23 MHz. Can we hear your music?

5.    Use 1 MHz crystal oscillator and tune the radio to 1 MHz. Adjust the volume control of our mp3 or CD player, is there any change in the quality of the sound we hear in our radio?

6.    Until now we have to kept our antenna within an inch of our radio antenna, now move our transmitter's antenna further away slowly and hear what happens. Does the quality of our sound improves or gets worse? Why?

7.    Rotate the radio receiver antenna relative to our transmitter's antenna (or vice versa). Does this affect the quality of the sound? Why?

8.    Try using a longer wire for the antenna. Does this affect the quality of the sound? Does this affect the broadcast range for our transmitter? Why?

Try receiving the signal from your AM transmitter with a crystal radio that you build yourself. You can explore how the relative placement of the receiving and transmitting antennas affects signal strength at the receiver

Lighting bulb via wireless power

Lighting bulb via wireless power

Wireless electricity or wireless power transmission is one of the emerging technologies today. The idea of this technology is transmitting power from a source to any receiver using the free space, same as the  TV and  radio transmission or same as your wireless lan or WIFI. Some of the uses as of the moment are for  charging iPod, cellphones, digital cameras, mp3, iPhone and other electronic devices.

Materials:

A. Source---5V sine wave or square wave source @135kHz frequency

              *555 IC square wave signal generator is a candidate see more

               on  555 timer IC

B. C2----940nF cap or parallel 2 470nF Mylar or ceramic capacitor

C. L2----1.46uH air coil inductor or 15m  #24AWG magnetic wound

               @ 2 inches diameter

D. L1---100 turns #20AWG magnetic wire @ 2 inches diameter or larger

working:

1. Source coil powered by a main supply usually your power outlet

2.Yellow line is  the energy flow from the source that is receiving coil

3.Conducting material that blocks some transmitted energies (blue line)

4.The receiving coil that is connected to the device like your cellphones, iPods, mp3, and others.

Resonant Frequency:

To achieve better wireless power transmission, the Power source must be of the same frequency of receiving coil.

Power source frequency F1 = Receiving coil frequency F2

F1=F2=  1/(2π√(L2*C2))

         *for  more LC frequency balancing use LC frequency calculator