Kinetic Energy

The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is ½ mv². In relativistic mechanics, this is only a good approximation when v is much less than the speed of light.

Kinetic energy of rigid bodies

In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body, is given by the equation

where m is the mass and v is the speed (or the velocity) of the body. In SI units (used for most modern scientific work), mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.

For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as

E_k = (1/2) · 80 · 18² J = 12.96 kJ

Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force.

The kinetic energy of an object is related to its momentum by the equation:

where:

 is momentum

 is mass of the body

For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion, of a rigid body with constant mass , whose center of mass is moving in a straight line with speed , as seen above is equal to

where:

 is the mass of the body

 is the speed of the center of mass of the body.

The kinetic energy of any entity depends on the reference frame in which it is measured. However the total energy of an isolated system, i.e. one which energy can neither enter nor leave, does not change in whatever reference frame it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the Oberth effect. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames disagree on the value of this conserved energy.

The kinetic energy of such systems depends on the choice of reference frame: the reference frame that gives the minimum value of that energy is the center of momentum frame, i.e. the reference frame in which the total momentum of the system is zero. This minimum kinetic energy contributes to the invariant mass of the system as a whole.

From the work-energy theorem, we find that the total energy of a system remain constant neglecting work done against friction. Therefore we can say the change in K.E  = change in P.E(U)

Read More

Mechanical Energy

Mechanical Energy is the sum total of both Potential Energy and Kinetic Energy present in a mechanical system. In a mechanical system the amount of mechanical energy is a constant. This equilibrium is only possible only in the presence of conservative forces like gravity and absence of non conservative forces like friction. Friction forces a body to use more energy to over come it and thus the energy is lost in the form of heat. More precisely in elastic collisions, the mechanical energy is conserved but in inelastic collisions, some mechanical energy is converted into heat. The equivalence between lost mechanical energy and an increase in temperature was discovered by James Prescott Joule.

Conservation and inter conversion of Energy:

Of the three great conservation laws of classical mechanics, the conservation of energy is regarded as the most important. According to this law, the mechanical energy of an isolated system remains constant in time, as long as the system is free of all frictional forces, including eventual internal friction from collisions of the objects of the system. In any real situation, frictional forces and other non-conservative forces are always present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. Though energy cannot be created nor destroyed in an isolated system, it can be internally converted to any other form of energy.

Thus, in a mechanical system like a swinging pendulum subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible, energy passes back and forth between kinetic and potential energy but never leaves the system. The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points. However, when taking the frictional forces into account, the system loses mechanical energy with each swing because of the work done by the pendulum to oppose these non-conservative forces.

That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that matter is composed of. This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision, mechanical energy is conserved; i.e. the sum of the kinetic energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the total mechanical energy of the system will have changed. Usually, the total mechanical energy after the collision is smaller than the initial total mechanical energy and the lost mechanical energy is converted into heat. However, the total mechanical energy can be greater after an inelastic collision if for example the collision causes an explosion which converts chemical energy into mechanical energy. In inelastic collisions, the smaller particles of which the colliding objects consist are shaken up and rattle around. These small-scale motions are perceived as an increase in heat and need kinetic energy which must be taken from the large-scale motion of the objects that are observed directly. Thus, the total energy of the system remains unchanged though the mechanical energy has been changed.

Read More

Special article: Di-proton

A diproton (or helium-2, symbol 2He) is a hypothetical isotope of helium nucleus consisting of two protons and no neutrons, and is predicted to be less stable than ⁵He. Diprotons are not stable; this is due to spin-spin interactions in the nuclear force, and the Pauli exclusion principle, which forces the two protons to have anti-aligned spins and gives the diproton a negative binding energy.

In 2000, physicists first observed a new type of radioactive decay in which a nucleus emits two protons at once - perhaps a 2He nucleus.The team led by Alfredo Galindo-Uribarri of the Oak Ridge National Laboratory announced that the discovery will help scientists understand the strong nuclear force and provide fresh insights into the creation of elements inside stars. Galindo-Uribarri and co-workers chose an isotope of neon with an energy structure that prevents it from emitting protons one at a time. This means that the two protons are ejected simultaneously. The team fired a beam of fluorine ions at a proton-rich target to produce 18Ne, which then decays into oxygen and two protons. Any protons ejected from the target itself were identified by their characteristic energies. There are two ways in which the two-proton emission may proceed. The neon nucleus might eject a 'diproton' - a pair of protons bound together as a 2He nucleus - which then decays into separate protons. Alternatively, the protons may be emitted separately but at the same time - so-called 'democratic decay'. The experiment was not sensitive enough to establish which of these two processes was taking place.

The best evidence of 2He was found in 2008 at the Istituto Nazionale di Fisica Nucleare, in Italy. A beam of 20Ne ions was collided into a foil of beryllium. In this collision some of the neon ended up as 18Ne nuclei. These same nuclei then collided with a foil of lead. The second collision had the effect of exciting the 18Ne nucleus into a highly unstable condition. As in the earlier experiment at Oak Ridge, the 18Nenucleus decayed into an 16O nucleus, plus two protons detected exiting from the same direction. The new experiment showed that the two protons were initially ejected together before decaying into separate protons much less than a billionth of a second later.

Also, at RIKEN in Japan and JINR in Dubna, Russia, during productions of 5He with collisions between a beam of 6He nuclei and a cryogenic hydrogen target, it was discovered that the 6He nucleus can donate all four of its neutrons to the hydrogen. This leaves two spare protons that may be simultaneously ejected from the target as a 2He nucleus, which quickly decays into two protons. A similar reaction has also been observed from 8He nuclei colliding with hydrogen.

Read More

Resonance of waves

A Wave has characteristic features like amplitude, frequency etc.. Now the amplitude of a wave can be increased without increasing the frequency or the frequency can be increased without increasing the amplitude. The increase in amplitude with the increase in frequency is resonance(not the actual definition).

Resonance occurs when the frequencies of two bodies match.

Examples:

1.  When a vibrating tuning fork is kept on a surface of  wood, we hear a loud sound. This is because of resonance. The amplitude of the fork increases suddenly and thus we hear a louder sound.
2. When loud bass(pronounced as 'base') music is played, the glasses around you start vibrating.
3. If you take two guitars both tuned the same and place them side by side, when you pluck the A string on one guitar you will see the A string on the other guitar start to vibrate as well. 
4. When two pendulums of the same length are kept next to each other and one of the pendulum is made to vibrate, then the other pendulum also vibrates.

These are simple examples of resonance.

Read More

Sound

Sound is a form of energy. It is a mechanical wave. It is caused by the vibrations of the particles. Each time a particle vibrates, its vibration excites our ear and the nerve send impulses to our brain and the brain senses it.
Sound propagates in two ways. 1) as a longitudinal wave and 2) as a transverse wave.

Waves: Waves are periodic disturbances in a medium. Energy is carried from one place to another as waves. Thats ones reason waves are used to obtain energy.

Longitudinal Waves: Waves in which particles move along the direction of the wave. Its a simple mechanism.
Lets assume particles of air to be straight lines like these ' |  |  |  |  |  |  |  | '. When particles have to move, they move back and forth like oscillations. There are two stages in movement of particles as longitudinal waves. Compressions and Rarefactions.

Compressions: when the particles move front, the particles in front of them are not in motion. So the particles in motion move very close to them and their vibrations are transferred. Now the particles that are rest start moving. Before the particles move, the particles behind them are very close to them, and are compressed.
                                                           |  |  |  |  |  |  |  |  | | | | | |||||||||| | | | | |  |  |  |  |  |

                                                                                            movement of particles 

                                                                                             ------------>>>>>>

Rarefactions: Now the particles which were in motion from the beginning return back to their original positions. This creates a gap between the particles coming back to their original positions and the particles moving front.
                                                           |  |  |  |  |  |  ||||         |           |         |  |  |  ||||
                                                                     movement of particles
                                                                                             <<<<<<------------
The combination of these two phenomenon is what leads to a longitudinal wave.

Longitudinal Wave

Transverse Waves: Waves in which particles move perpendicular to the direction of propagation of the wave. The simplest example is light wave or any other electromagnetic wave.

Transverse Wave

The ripples on the water are also examples of transverse wave.

Properties of Transverse Waves:

1. Amplitude(A): It is the maximum displacement of a particle from its mean position.
2. Oscillation: One complete cycle or vibration or one set of crest and trough.
3. Frequency: Number of oscillations in one minute. It is measured in hertz(Hz) where 1 Hz = 1 cycle/s 
4. Time Period(T): Time taken for one oscillation. Time Period and frequency are reciprocals of each other
                                                  
5. Wavelength( λ): It is the distance between two crests or troughs.

A sounds can be differentiated by its charaterstics. 

Three main characteristics of a Sound wave is: 

•  Loudness or Intensity:
  Loudness is because of greater amplitude. As amplitude increases, the energy of a wave also increases. We can surely differentiate between a loud and a soft sound.It is the magnitude of sound intensity.
  Intensity is the average amount of energy transported per unit area of a surface normal to the direction of propagation.
• Frequency or Pitch:
  If a waves has a higher frequency, then it is said to be shriller. If its frequency is less, then its said to be feeble. Two sounds of the same loudness or intensity can be differentiated by the difference in their frequency.
  We can differentiate between the sound of 512Hz and 256Hz tuning fork. The 512Hz tuning force is shriller.
• Timbre or Quality: 
  Two waves of the same loudness and frequency might differ in their wave forms. Timbre is also called tone quality and tone color.
  We can surely distinguish between the sound produced by a violin and a trumpet. It is because of the fact that their wave forms are different.
                        

The Speed of sound is 343.2 m/s in air. In water it is 1497 m/s. In steel, its velocity is 5930 m/s.

Read More

Radioactivity

Radioactivity is the emission of radiations from the nucleus of a radioactive atom. It occurs due to the unstable nucleus of the atom. The nucleus of an atom becomes unstable when the ratio of neutrons to protons is greater than 1.5.

Types of radioactivity: 

Alpha Decay

1. Alpha Decay:
   In an Alpha Decay, the radioactive element emits an alpha particle 'α' or simply a  4
   2He2+. This results in the decrease of
   atomic number(Z) as well as mass number(A) of the atom.
   The atomic number decrease by 2 and the mass by 2.
2. Beta Decay:
   β−: In a β− Decay, the nucleus emits an electron and an anti
   neutrino.This results in increase of atomic
   number by 1. This happens because the neutron
   in the nucleus converts itself into a proton.
   β+: In a β+ Decay, energy is used to convert a proton into a neutron, while emitting a positron*  and a neutrino.
3. Neutron Emission: It is a type of radioactive decay of atoms containing excess neutrons, in which a neutron is simply ejected from the nucleus.

The most common radiations from a radioactive element are Alpha particles, Beta particles and Gamma rays(γ). The radioactivity usually starts with an alpha decay then followed by a beta decay and and finally and emission of gamma rays. The excess energy stored in a nucleus when the release of an alpha particle or beta particle is released as gamma radiations.  

Properties of Alpha particles: 

1. They are positively charged helium 2+ ions.
2. The are affected by electric fields.
3. They are heavy.
4. They penetrate through a body the least.
5. They ionize the surroundings the most.
6. Their velocity is 10^4 m/s.

Properties of Beta Particles: 

1. They are negatively charged particles and are electrons.
2. They are also affected by electric fields.
3. They are very light.
4. They penetrate through a body more than alpha particles but less than Gamma rays
5. They ionize the surrounding very less when compared with alpha particles.
6. Their velocity is 10^6 m/s.

Properties of Gamma Rays: 

1. They are electromagnetic radiations.
2. They are not affected by electric fields.
3. They do not have any mass.
4. They penetrate through the body the most. They can pass through 30cm thick graphite.
5. They do not ionize the surroundings.
6. Since they are electromagnetic radiations, their velocity is equal to that of light.

Read More

Utilizing the fission energy: Nuclear Reactor

The main use of Nuclear Fission process is in the nuclear reactors. In the nuclear reactors, the heat energy released is utilized and converted into electrical energy. Nuclear Reactors produce energy through controlled fission chain reaction. The process is explained below.

The diagram given here shows the internal part of the nuclear reactor. Its main constituents are 

1. Containment cell: A cell where the nuclear fuel is kept and is tightly packed with concrete so that no radiations leak out.
2. Fuel rods: Rods which are made up of radioactive metal and act as fuel.
3. Control rods: Rods usually made up of cadmium or hafnium which absorb the excess neutrons thus controlling the chain reaction.
4. Coolant: Usually water. It absorbs the heat liberated and transfers it outside the cell.
5. Condenser: To condense the coolant.
6. Inlet and Outlet pipe: Pipes which runs through the condenser to cool the coolant.
7. Steam Turbine: Turbine used to produce
   electricity from steam.
8. Steam Generator: A big structure inside the containment cell which contains water.

Working: The reaction is started in the reactor. The reaction releases huge amounts of heat and neutrons. The excess neutrons, which are not required for the reaction, is absorbed by the hafnium of cadmium rods.

The heat released now turns the coolant(water) into its vapour state. Now the coolant is polluted because it was in direct contact with the radioactive element. Thus, this coolant is taken into another chamber. The vapour passes through a tube and reaches the steam generator(the chamber) which also contains water. Now the heat is transferred form the coolant to the water which turns into steam. The coolant now condenses and is pumped back near the fuel. The steam passes through another pipe and reaches the Turbine. The turbine thus spins generating electricity. It produces an AC Voltage, either 11kV to 22kV. The steam now leaves the turbine and enters the condenser. The condenser has inlet and outlet pipes which has continuous supply of cold water. This water cools the steam. The condensed water now falls to the bottom of the condenser which has an inlet to the steam chamber and is pumped into it. 

Read More

Nuclear Reactions: Fusion

 When two nuclei are forced into one another, they repel due to electrostatic repulsion between two protons. But when some energy is provided to the nuclei, then the nuclei are able to fuse with each other. The process is called as the nuclear fusion(fusion of nuclei). Thus new elements are formed.In the process, a heavy nucleus, energy and a neutron(usually) is released.

Main uses of nuclear fusion are electric generation and in hydrogen bomb.

Interstellar reactions mainly consist of fusion reactions. The fusion of four hydrogen atoms give rise to an helium atom along with the release of energy and a neutrino. Further fusion leads to formation of heavier elements. Nuclear fusion is the main reaction that runs a star. When the fusion between atoms stops, then the star stops emitting energy and consumes itself.

Read More

Nuclear Reactions: Fission

The nucleus of any atom is very unstable. It is due to the presence of neutrons in the nucleus that it becomes very unstable. There are other particles other than neutron and proton in the nucleus. One of those are the neutrinos. These are particles which are responsible for the stable form of the nucleus. Neutrinos are affected only by the weak nuclear forces. 

Thus due to the unstable form of the nucleus, there are two types of reactions which can take place in the nucleus: Nuclear Fission and Nuclear Fusion.

Nuclear Fission: When a heavy nucleus breaks up into two or more nuclei, the reaction is known as nuclear fission. For example: When a neutron is bombarded with a nucleus of a heavy atom like Uranium 235, the product so formed is Krypton(92) and Barium(141) with the release of three neutrons.

Nuclear Fission

Explanation: For atoms with low atomic numbers, a nucleus that has a different number of protons than neutrons can potentially drop to a lower energy state through a radioactive decay that causes the number of protons and neutrons to more closely match. As a result, atoms with roughly matching numbers of protons and neutrons are more stable against decay. However, with increasing atomic number, the mutual repulsion of the protons requires an increasing proportion of neutrons to maintain the stability of the nucleus, which modifies this trend. Thus, there are no stable nuclei with equal proton and neutron numbers above atomic number Z = 20 (calcium); and as Z increases toward the heaviest nuclei, the ratio of neutrons per proton required for stability increases to about 1.5 (1.5 ratio shows instability of the nucleus).

Chain Reaction: Spontaneous fission reactions taking place one after the other is a chain reaction.

Explanation:  When a neutron is made to bombard with a heavy nucleus, the two or more(two is often) products are formed with release of three neutrons. These neutrons can further be used to bombard with three more nucleus and there is release of nine neutrons. This process is continuous and can be controlled as well as uncontrolled. Controlled processes are known as controlled fission reactions and Uncontrolled processes are known as uncontrolled fission reactions.

Fission chain reaction.

The Controlled fission reactions are used in nuclear reactors where cadmium rods are used to absorb the excess neutrons. Thus out of three neutrons, only one is made to bombard with a nucleus and hence the reaction is controlled.

Read More

Nucleus

Nucleus is the center of an atom. It is the most dense part of an atom. Nucleus is made of nucleus mainly consisting of neutrons and protons. Almost all of the mass of the nucleus is due to the mass of the nucleus and the electrons contribute only to a part of the atomic mass. Only the nucleus of the Hydrogen atom does not contain neutrons. Rutherford's experiment led to the discovery of nucleus.
The nucleus of an atom is highly unstable. Thus special forces are needed to hold the neutrons and protons together. These forces are very strong in nature and are called strong nuclear forces. Properties of strong nuclear forces are:

1. They are very strong in nature.
2. They are of very short range(1-10 fm (femtometer))
3. They are charge independent
4. They are attractive in nature.

Composition of the Nucleus: The nucleus of an atom consists of protons and neutrons (two types of baryons) bound by the nuclear force . These baryons are further composed of subatomic fundamental particles known as quarks bound by the strong interaction. Which chemical element an atom represents is determined by the number of protons in the nucleus and its chemical properties are determined by the electrons. Each proton carries a single positive charge, and the total electrical charge of the nucleus is spread fairly uniformly throughout its body, with a fall-off at the edge.

Protons: A Proton carries a net +1 charge on it. A Proton is made up of three quarks. Two up quarks and one  down quark. The 'up' quark carries a net charge of +2/3 and the bottom quark carries a charge of -1/3. Thus the charges add up to give a sum of +1 charge on the proton.

Neutron: A neutron carries no charge on it. A Neutron is also made up of three quarks. One 'up' quark and two 'down' quarks. Thus the net charge is 0.

Read More