[Physics Class Notes] on Conservation of Mechanical Energy Pdf for Exam

Mechanical Energy

In the science of physical streams, mechanical energy is the sum of potential energy and kinetic energy. It is the macroscopic energy associated with a system. The conservation principle of mechanical energy states that if an isolated subject of a system is only to conservative forces then the mechanical energy is constant. 

If an object really moves in the direction which is opposite of a conservative net force, the energy which is potential will increase and if the speed of the object changes. The kinetic energy of the object also changes. 

Conservation of Mechanical Energy 

In all systems which are real, the force which is nonconservative. For example, frictional forces will be present but if they are of negligible magnitude the mechanical energy changes a little and its conservation is a useful approximation.

In the elastic collisions, the kinetic energy is conserved. but in the inelastic collisions, some mechanical energy may be converted into thermal energy. 

Many devices are used to convert mechanical energy to or from other forms of energy. An electric motor converts electrical energy to mechanical energy while an electric generator converts mechanical energy into electrical energy and a heat engine converts heat energy to mechanical energy.

 

Law of Conservation of Mechanical Energy

If we see that according to the principle of conservation of mechanical energy, in an isolated system the mechanical energy remains constant in time, provided the system is free of friction and other forces which are non-conservative. In any situation which is real and frictional forces and other non-conservative forces are present, the energy though cannot be destroyed or created in an isolated system, it can be converted to another energy form.

In a swinging pendulum which is subjected to the conservative gravitational force and frictional forces like air drag and friction, at the pivot are energies which are negligible. The passed energy is back and forth between kinetic and potential energy but never leaves the system. The pendulum reaches the greatest kinetic energy and least potential energy when in a vertical position. This is owing to the greatest speed and be the direction which is nearest to the Earth at this point. 

On the other hand, we can see that it will have its least kinetic and greatest potential energy at the extreme positions of its swing because it has zero speed and is at the farthest from the earth at these points. However, taking the frictional force into account,  there is a loss of mechanical energy with each swing because of the work which is negatively done on the pendulum by these forces which are non-conservative.

Principle 

Mechanical energy is the sum of the kinetic and potential energies in a system. The principle of the conservation of energy states that the total mechanical energy in a system is the sum of the potential and the kinetic energies which remain constant as long as the forces which are acting are conservative forces. 

We could easily use a circular definition and that says that a conservative force doesn’t change the total energy. Fiction, on the other hand, a force which is non-conservative because it acts to reduce the mechanical energy in a system. Note here that forces which are non-conservative do not always reduce the mechanical energy. 

[Physics Class Notes] on Copernican System Pdf for Exam

The Copernican system is an idea proposed by the Polish astronomer Nicolaus Copernicus (1473–1543) that the sun is at the centre of the solar system, with the planets (including the earth) orbiting it. His research eventually contributed to the extinction of the current geocentric cosmology, when he suggested a model of the solar system in which the planets orbited in complete circles around the earth. In addition, the Copernican definition is defined as the earth rotates daily on its axis and the planets revolve in orbits around the sun.

The Copernican system was the first European heliocentric theory of planetary motion, in which the sun was fixed at the centre of the Copernicus solar system and all the planets, including the earth, revolved around it. He derived his Copernican hypothesis from old astronomical sources in the early 16th century.

Also, his Copernican hypothesis provided a clear and elegant explanation for the planets retrograde movements (the annual motion of the Earth must be mapped into the motions of the planets in geocentric astronomy) and definitively resolved the planets’ order (which had been a tradition in Ptolemy’s work). Copernicus also had the advantage of circular motion, but he had to create his planetary orbits from circles on top of circles and inside circles, much like his forefathers. His tables were only slightly better than those already in use.

Besides being circulated a description of his own heliocentric Copernican hypothesis to colleagues before 1514, he did not intend to publish it until his pupil Rheticus pressed him to do so late in his life. Copernicus’ task was to provide a realistic solution to the Ptolemaic model by calculating a solar year more elegantly and precisely while maintaining the theoretical implications of a mathematically orderly universe. 

The Copernican system, which was geocentric or centred on Earth, provided a more accurate view than the older Ptolemaic system. It accurately represented the Sun as being in the centre of the solar system about Earth and other planets. Copernicus used Ptolemy’s fictional clockwork of epicycles and deferents (orbital circles upon circles) to describe the planet’s extremely irregular motions in terms of circular motion at uniform speeds, though in a somewhat altered manner.

Copernican Revolution

The Copernican Revolution was a revolution in astronomy from a geocentric, Earth-centered view of the system to a heliocentric, Sun-centered understanding, as expressed by the Polish astronomer Nicolaus Copernicus in the 16th century. This change shows the beginning of a larger Scientific Revolution that laid the groundwork for modern science and helped it to develop as a separate discipline. Copernicus concluded that the best way to accomplish his goal was to abandon Ptolemy’s geocentric model of the universe, which failed to meet Aristotle’s criterion for the universal circular motion of all celestial bodies and to remove Ptolemy’s responsibilities of a human resource, an imaginary point around which the bodies seemed to follow the requirement. Then Copernican proposed his Copernicus model of the universe. Hence this model is also called Copernicus theory of the universe. Copernicus turned the world inside out, putting the Sun at the centre and revolving the Earth around it, relying on almost the same specifics as Ptolemy. The Copernican model claims to be able to describe the physical reality of the universe, something the Ptolemaic model was no longer thought to be capable of.

Copernicus deduced the Earth was no longer at the centre of the world, that the heavenly bodies rotated around the Sun, and that the Earth rotated on its axis regularly.

Copernicus not only proposed a hypothesis on the origin of the sun about the earth, but he also worked hard to disprove some of the geocentric theory’s minor specifics.

The Copernican Revolution provides an important framework for understanding the Universe.

We should not have a unique or special place in the Universe. A collection of simple physical rules may be used to understand and forecast the Universe and everything in it.

Copernican Model

Copernicus solar system is proposed by N. Copernican, in which the Sun was at the centre, with the planets circling it, and the stars were well above the planets. The model kept the Ptolemaic system’s revolving orbits and epicycles, but added Copernicus’ findings. The axial rotation of the Earth causes the sky to move in Copernicus’ model.

Since the idea of elliptical orbits has not yet been developed, the Copernican system reproduced circular motion no better than the Ptolemaic system, and after that advance, by J. Kepler, it found little acceptance. It was, however, significant in dethroning the Earth as the centre of the Universe. The earliest theories about the Sun being the centre of the universe and the Earth being one of the planets orbiting it date from the third century BCE. 

He uses the issue of how many grains of sand there are in the universe as an example.

To make the problem more difficult, he chooses the heliocentric universe suggested by Aristarchus of Samos, which will have to be several times larger due to the lack of detectable stellar parallax.

We know that thinkers were at least toying with this idea in Hellenistic times and that Aristarchus’ speculation was well-known in Europe starting in the High Middle Ages due to its mention in Archimedes’ journal, but not seriously entertained until Copernicus.

[Physics Class Notes] on Curie Weiss Law Pdf for Exam

The Curie-Weiss law states that the magnetic susceptibility of a ferromagnet in the paramagnetic zone is greater than the Curie temperature point of the ferromagnet. A magnet’s magnetic moment is a property that determines its torque in the presence of an external magnetic field. A magnetic moment can be found in a bar magnet, an electric current loop, a molecule, or an electron, for example.

 

The magnetic polarization or magnetization of a magnetic material expresses the density of induced or permanent magnetic moments in the vector field. The magnetic moment can form as a result of the small electric current generated by the spin of electrons, electron mobility in an atom, or nuclei spin.

 

The response of the materials in the external magnetic field determines the net magnetization. They can, however, exist even in the absence of an external magnetic field, such as in cold iron as spontaneous magnetization. Other materials with similar qualities include magnetite and nickel, which are referred to as ferromagnets. Curie temperature is the temperature at which a ferromagnetic substance becomes ferromagnetic.

 

What is Curie?

The Curie is a radioactivity measurement unit. Curie has a value of 3.7 x 1010 per second. The Curie point and temperature are likewise derived from the Curie. The extreme temperature at which magnets alter their magnetic characteristics is known as the Curie temperature.

Curie-Weiss Law refers to one of the most important laws in the field of electromagnetism. It states that the magnetic susceptibility of a material above a specific temperature (also known as the Curie Temperature), becomes ferromagnetic. With this feature, the object’s magnetic moment helps in understanding the torque of a magnet in response to an external magnetic field. For substances above the Curie temperature, the moments can be oriented at random, causing the net magnetic polarization to be zero. The formula can be expressed as: 

 

χ = CT−TC    … eqn. 1

 

Here C represents the Curie Constant, T depicts absolute temperature, and TC is the Curie Temperature.

 

 

The above graph represents that at the Curie Temperature, the paramagnetic properties still exist as the magnetization is zero (because of the absence of a magnetic field). The internal field increases the susceptibility of the element, and the plot of 1 produces a straight line in a zero magnetic field; however, it can turn to zero as the temperature approaches Curie Temperature.

Temperatures of Curie

The following are some of the Curie temperatures of ferromagnetic substances:

  • Iron (Fe) has a Curie temperature of 1,043K.

  • Gadolinium (Gd) has a Curie temperature of 293K.

  • Nickel (Ni) has a Curie temperature of 631K.

 

Understanding Ferromagnetism and Weiss Law

Ferromagnetism is known to be the phenomenon of spontaneous magnetization, where magnetization appears in a substance when there’s a complete absence of applied magnetic field. Some of the most popular ferromagnets are known to be Fe, Co, Ni, few alloys that show ferromagnetism properties. It occurs when there’s an alignment of the molecular moments in a suitable direction. 

 

For ferromagnetism to appear, there’s a threshold temperature (also known as the ferromagnetic transition temperature), which can go as high as 1000K for elements like Fe, Co, Gd, etc. It occurs as there is the presence of atomic magnetic dipoles in parallel directions within the complete absence of an external field. For example, in Iron, the induced magnetic moment depends on the spinning of the electrons in the nuclei’s outer shell. According to Pauli’s exclusion principle, no two electrons present in the exact location can have similar spins directed in the same direction. It creates an absolute repulsion between the two electrons. For electrons having counter-direction spins can exhibit attractive interaction with magnetization. Therefore, such an attractive effect found in oppositely spinning electrons can make the iron atoms align with each other. This can be expressed in the following equation: 

 

In this formula, the influence of exchange forces yield and effective molecular field Hint, that depends on the size of magnetization M; 

 

Hint

= λM … eqn. 2

Where, λ is the Weiss Constant. 

 

The yielding magnetization (represented by M) can also be represented as a sum and product of the magnetic susceptibility, χp

χp

(H + λM) = M   …eqn. 3

The above equation serves as the base for the Curie-Weiss Law equation. 

 

Limitations of the Curie-Weiss Law   

[chi = (frac{1}{T-T_{c}})gamma] …eqn. 4

 

To answer the question of what happens to a ferromagnetic substance heated above Curie temperature, the Curie Weiss Law fails to provide an explanation for the susceptibility of certain elements. It is because, when the temperature (Θ) gets to a place where it is at a really higher value than the Curie Temperature and replaces T C, the entire susceptibility becomes infinite. 

 

Relationship of the Curie Law with the Curie-Weiss Law

According to the Curie Law, the magnetization of any paramagnetic element is directly proportional to the applied magnetic field. Often represented as: 

 

M = [Ctimes frac{B}{T}]

 

here M = Magnetization, B = Magnetic Field, T = absolute temperature, C = Curie Constant. 

 

The Curie Constant is represented as: 

 

[C = frac{mu_{0}mu_B^2}{3k_{b}}*ng^{2}J(J+1)]

 

here, kB represents the Boltzmann’s constant (1.380649 x 10⁻²³), n represents the magnetic atoms per unit volume, g is Landé factor,  μB is Bohr magneton, and J = angular momentum quantum number.

 

The fluctuations that occur in the Curie temperature is because of the deviations in the magnetic moments of an element as it reaches the phase transition temperature. Therefore, in a more accurate way, the Curie law can be represented in the modified Curie Weiss Law equation: 

 

[chi = frac{M}{H} = frac {Mmu_{0}}{B} = frac{C}{T}]

 

where μ0 is the permeability of free space. 

Therefore, taking from eqn. 2, the new equation would be, 

[chi = frac {Mmu_{0}}{B+lambda M} = frac{C}{T}]

 

Since

 

[chi = frac{C}{T-frac{Clambda}{mu_{0}}}]  and [chi = frac{C}{T-T_{c}}]

 

Therefore, [T_{c} = frac{Clambda}{mu_{0}}]  …. eqn. 5

 

Here are the Curie Temperatures for a Few Ferromagnetic Substances

Substance Name

Curie Temperature

Iron (Fe)

1,043K

Gadolinium (Gd)

293K

Nickel (Ni)

631K

 

The following graph shows the saturation in magnetization observed in Nickel at a high magnetic field. With an increase in temperature, the saturation magnetization decreases till it reaches zero at Curie temperature. Here, Nickel becomes paramagnetic. 

 

 

Differentiating the equation, [chi = frac{M}{H}] in terms of temperature represents the maximum susceptibility of any substance at Curie temperature. 

 

It proves that the magnetic moment can be effortlessly increased for any transition material with the application of a magnetic field in its transition. The graph above represents the susceptibility of Nickel reaching infinity, as the Curie temperature gets closer to Curie temperature. 

[Physics Class Notes] on Dark Side of the Moon Pdf for Exam

Side of the Moon

The near side of Moon, which is permanently turned towards Earth, is the only visible lunar hemisphere from Earth. The opposite side is the farther side.

The speed of rotation of Moon along its axis is the same as its orbital velocity around the Earth. For this reason, only one side of Moon is visible from Earth. It is called synchronous rotation or tidal locking.

The Moon is illuminated by the sun, and it also causes variations in the lunar phases.

There are times when the far side of the Moon is faintly visible from Earth. It occurs due to earthshine, the indirect reflection of sunlight from the surface of Earth onto the Moon.

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(Far Side of the Moon, photography taken from Apollo 16)

  • The far side of the Moon is the lunar hemisphere that always faces away from Earth. The far side has a rough and rugged terrain with a large number of impact craters. It has less area of the flat lunar surface as compared to the near side.

  • The far side has one of the largest craters of the solar system, called an Aitken basin located in the South Pole. 

  • Both the far side and the near side experience two weeks of sunlight, then two weeks of night consecutively.

  • The far side of the Moon is also called a “dark side of the moon”, where “dark” actually means the unseen side of Moon rather than that of lacking light.

Dark Side of the Moon Discovery

Approximately 18% of the far side of the Moon is occasionally visible from Earth due to libration. The remaining 82% remained unobserved until 1959, when the Soviet Lunar 3 space probe photographed it.

In 1960, the Soviet Academy of Sciences published the first atlas of the far side.

In the year 1968, the Apollo 8 astronauts became the first humans to see the far side of the Moon in person. 

All spacecraft, whether manned or unmanned, used to have soft landings on the near side of the Moon. On 3 January 2019, for the first time, 4 spacecraft landed on the far side of the Moon.

What Are the Different Phases of the Moon?

Half of the surface of Moon is always illuminated by sunlight, and the other half is dark.

However, the amount of light reflected by Moon that we can see from our point of view from Earth varies every day. This gives rise to different phases of the Moon.

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  1. The Lunar Month

  2. New Moon

  3. Waxing Crescent Moon

  4. First Quarter Moon

  5. Waxing Gibbous Moon

  6. Full Moon

  7. Waning Gibbous Moon

  8. Third Quarter Moon

What is the Temperature on the Moon?

Temperatures on the Moon are extreme; it depends on the warmth of the sun. Temperature ranges from boiling hot to freezing cold.

There is no atmosphere on the Moon, so heat cannot be trapped to insulate its surface.

The rotation of the Moon about its axis occurs in about 27 days. Daytime one side of the Moon is of about 13 and a half Earth days, while the other side experiences equal night time.

  • The temperature of the surface of the moon can reach about 127° C during the daytime, in the presence of sunlight.

  • The temperature of the surface of the Moon can reach about -173°C during night time, in the absence of sunlight.

  • Temperature changes across the Moon occur rapidly.

The near and farther portion experiences sunlight every lunar year due to the rotation of the Moon.

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Why Can’t We See the Dark Side of the Moon?

We can see only about 59% of the total surface of Moon.

We can see only one side of the Moon from the surface of Earth. Moreover, it seems to be at rest although it keeps on rotating about its axis and the earth.

John Keller, the deputy project scientist for NASA’s Lunar Reconnaissance Orbiter project, said that “the moon is tidally locked to the Earth”, and that’s why we can’t see the far side of the Moon.

The rotational speed of the Moon is the same as that of the Earth.

The Moon completes one full rotation about its axis at the same time as it takes to orbit around the Earth. This means that the same side of the Moon is always turned towards Earth.

The Moon has a tendency to spin faster. It is the Earth’s gravitational force that holds it in place.

Explanation

The mass distribution of Moon is uneven. It appears spherical, but its geometric center is different from its center of mass. This offset is responsible for creating a gravitational gradient between the Earth and the Moon.

Initially, the Moon used to rotate faster, but it has slowed down its rotation when it tidally locked with the Earth.

The slowing down of the rotation of the Moon is due to the frictional force, which arises due to the gravitational gradient.

Consequently, the rotation of the Moon about its axis releases energy in the form of heat, until the relative motion of Moon and Earth is completely reduced.

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[Physics Class Notes] on Derivation of Kinetic Energy Formula Pdf for Exam

The word Kinetic energy came from the French word travail mécanique (mechanical work) or quantité de travail (quantity of work). The kinetic energy of a body is the energy possessed by the body by virtue of its motion.

For example, there are various applications of kinetic energy:

  • A nail is driven into a wooden block on the amount of kinetic energy of the hammer striking the nail.

  • A baseball thrown by a pitcher has a small mass but a large amount of kinetic energy due to high velocity.

On this page, we will learn about the following:

  • The formula for kinetic energy

  • Derive the formula of kinetic energy

  • Kinetic energy equation derivation

  • Kinetic energy derivation calculus

  • Derivation of kinetic energy using algebra

The Formula for Kinetic Energy

A dancing man is said to be more energetic than a snoring man. In physics, a moving particle is said to have more energy than the particle at rest. Quantitatively the energy of the moving particle is defined by:

                                                          

[k(vec{v})=frac{1}{2}mvec{v}.vec{v}]

                                                

This is the kinetic energy of the particle.

Therefore, the sum of the kinetic energy of a system of particles is the sum of all its constituent particles. Which is given by:

[k=sum_{i}frac{1}{2}m_i{v_i^2}]

The kinetic energy of a particle or a system of particles can increase or decrease or remain constant as time passes.

Deriving The Kinetic Energy Formula by Algebra

The kinetic energy can be obtained by either of the following:

  • The amount of work done in stopping any moving object.

  • The amount of work done in giving the velocity to the body from the state of rest.

Let’s consider the second case:

Suppose m =  mass of the body at rest.

u = Initial velocity of the body.

                F = The force applied to the body

                a = acceleration produced in the body in the direction of force applied

               v = The velocity acquired by the body while moving a distance s.

K∆S = W = m∆a….(1)

Using the third equation of motion:

v2u2=2as

a=[frac{v^2-u^2}{2s}]….. (2)

Where,

v- The final velocity of the body

u- The initial velocity of the body

S- The total displacement of the body

We know that according to Newton’s law of motion:

F=ma……(3)

Substituting the value of ‘a’ in eq(3) we get:

[F=m(frac{v^2-u^2}{2s})]……(4)

Combining eq(1) and (4), we get that:

[Delta K=m(frac{v^2-u^2}{2s})]……..(5)

Substituting u = 0  in eq(5), we get that:


[Delta K=m(frac{v^2}{2})]….(6)

Work done on the body is given by:

W = Force x distance….(7)

This statement states that a work W is done by a body to move from one position to another by a distance s when the force F is applied to a body at rest.

Putting u = 0  in eq(2), we get that:

[a=(frac{v^2}{2s})]

F = m  a

Therefore, we get:

[F=m(frac{v^2}{2s})]

Putting the value of F in eq(7), we get that

[W=m(frac{v^2}{2s}times S=frac{1}{2}mv^2)]


K.E of body=[W=frac{1}{2}mv^2)] 

This work done on the body is because of the Kinetic energy (K.E) of the body.

Derivation of Kinetic Energy Formula by Calculus

The formula for kinetic energy can be obtained by the method of calculus:

Suppose

m = mass of a body

u =  Initial velocity of the body 

[vec{F}]  =  The force applied to the body in the direction of the motion

[vec{ds}] = A small displacement of the body in the direction of motion

The small amount of work done by the force will be:

              

dW =  [vec{F}]  . [vec{ds}] = F ds Cos 0°  = Fds  (∵  Cos 0° = 1)

                                                     

dW = F ds = m  [vec{a}] ds    (∵  [vec{F}] = m   [vec{a}]  )  ( [vec{a}]  is an acceleration produced by the force)

[dW=m(frac{dvec{v}}{dt})ds] (∵[vec{a}=frac{dvec{v}}{dt}ds]

[dW=m(frac{ds}{dt})dv]

[dW=mvdv] (∵[vec{v}=frac{ds}{dt}])

Total work done by the force is increasing the velocity of the body from  u  to v is:

[W=int_{u}^{v} mvdv=mv[frac{(1+1)}{(1+1)}]^{v}_{u}=[frac{mv^2}{2}]^{v}_{u}]

Rightarrow [frac{1}{2}m(u^2-v^2)]

Total work done by the force is increasing the velocity of the body from  u  to v is:

[int_{0}^{W}dW=int_{u}^{v}mvdv]

[Rightarrow W=m[frac{v^2}{2}]_{u}^{v}=frac{m}{2}(u^2-v^2)]

[Rightarrow W=frac{mv^2}{2}-frac{mu^2}{2}]=Final K.E – Initial K.E…..(8)

    < span>∴ Work done = Final K.E. – Initial K.E.

W = change in kinetic energy

The work done by a force is a measure of the change in kinetic energy of the body which proves the work-energy principle.

On putting u = 0  in eq (8) , we get that:

[W=frac{1}{2}mv^2]-0

K.E. of the body = W = [frac{1}{2}mv^2]

Importance Of Kinetic energy:

Kinetic energy is the energy that an object receives from its movement.

If we wish to accelerate an object then we need to apply force. In order to apply force, we need to work. Once the work is completed the energy is transmitted to the subject which means that the item will then be moving at a constant speed. The energy transfer is known as kinetic energy and is dependent on the mass and the speed that is achieved.

The energy of kinetics can transfer between different objects and later be transformed into different forms of energy. For instance, a flying squirrel could encounter chipmunks that are stationary. After the collision, a portion of the initial energy of the squirrel may be transferred to the chipmunk’s body or transformed into an alternative type of energy.

1) It’s a key component in the calculation of work.

For example, if you lift an object with a certain amount of force, that object has gained kinetic energy. The more distance the object travels as it’s being lifted, the more kinetic energy it will have. Once you’ve moved the object to its final destination, you then must use another type of energy (potential energy) to keep it there. This is why lifting something heavy can be so tiring – you’re not just using muscle power to do the work, you’re also expending energy to overcome gravity and keep the object in place.

2) It’s frequently used in the study of motion.

For example, engineers need to know how much kinetic energy a moving object will have in order to design things like cars and airplanes that are safe for people to use. The faster an object is traveling, the more kinetic energy it has – and if that object collides with something else, that energy can be converted into other forms (such as heat or sound). This is why it’s important for car designers to make sure that their vehicles can withstand crashes.

3) It can be harnessed to do work.

For example, you can use kinetic energy to power a machine by converting it into electrical energy. This is how wind turbines and hydroelectric dams work – they capture the kinetic energy of flowing water or air and turn it into electricity that can be used to power homes and businesses.

4) It’s a fundamental part of Einstein’s famous formula E = mc².

Although this equation is most often used in reference to nuclear energy, remember that all matter has both mass and kinetic energy – the faster an object moves, the greater it’s kinetic energy will be. When you add up all forms of potential and kinetic energy possessed by a body, you get its total mass (m). If something contains more potential or kinetic energy than it does mass, then that extra amount can turn into other types of energies such as heat or light. This holds true whether we’re talking about atoms or entire galaxies!

Summary

  • The force does some work on a body, the kinetic energy increases by the same amount. Thus, according to this principle, work and energy are equivalent to each other.

  • A force is necessary to change the kinetic energy of the particle. If the resultant force acting on a particle is perpendicular to its velocity, the speed does not change and hence the kinetic energy does not change.

Example:

Q1: Calculate the average frictional force needed to stop a car weighing 600 kg at a distance of 35 m, if the initial speed is 36 km/h.

Solution:  Given m = 600 kg, s =35 m

                       v =  final velocity = 0  (Since the body will stop finally)

                        u= 36 km/h       

                u = 36 kmph = 10 m/s

According to work-energy principle,

W = Change in K.E. =[frac{1}{2}m(v^2-u^2)]

F x s =[frac{1}{2}m(v^2-u^2)]

and, W = F x s 

F x 35 = [frac{1}{2}600times (0-10^2)]

On solving, we get that:

Average frictional force (F) = 857 N

[Physics Class Notes] on Diamagnetic Elements Pdf for Exam

Magnetism is the resultant product of electrons’ spin motion and their interaction with one another. Different objects respond differently to different objects. So, we can describe the various magnetic materials by describing their responsiveness to magnetism. When you study the behavior of objects, you will find that most of the objects are like magnets, and in other words, we can say that all the matter is magnetic. Their magnetism may be different. Some matters are more magnetic, and some are less magnetic. Well, you will be surprised by what makes the difference between the magnetism of different matters. We have already discussed that the motion and interaction of electrons are responsible for the magnetism property of any object. The level of electron interaction makes such variation in magnetism. Some materials have no collective interaction while other materials may have intense atomic electron moments and interaction.

 

Discovery of Diamagnetism

The special property of diamagnetism came to be known in the late 1700s, by the discoverer Anton Brugmans in the element Bismuth, which showed repelling properties to a magnetic field when brought near to it. However, it was the great physicist Michael Faraday, who first concluded the presence of diamagnetism. He also concluded that all materials exhibit this property to some extent. He showed that all materials respond to magnetic fields in one or another way (either attracting or repelling). At the suggestion of English Polymath and fellow scientist William Whewell, Faraday termed the phenomenon to be “Diamagnetic” which later changed to “diamagnetism”. 

In Chemistry, these magnetic properties are assigned to the electron based on their pairing with each other and spin at the subatomic level. At these levels we understand diamagnetism to be retrained electrons being settled in their orbitals, effectively producing zero resistance and acting like loops of current. However, paramagnetism and ferromagnetism arise once they gain energy and lose their effective position in assigned orbitals. The electrons may then start to become unpaired and show ferromagnetic or paramagnetic properties in a magnetic field.  As a thumb rule, if the electrons are paired, the material is said to be Diamagnetic; if the electrons are unpaired, the material is called to be paramagnetic.

 

Magnetic Materials: Classification

How objects respond to the external magnetic energy defines the magnetic property of objects. Here we will discuss the magnetism of solid substances, and classification can be done in three categories.

Diamagnetic: Diamagnetic Meaning

Generally, the Magnetic field of external substances attracts the materials, but some materials are prone to a magnetic attraction. Such materials or substances are called Diamagnetic. Examples of Diamagnetic fields are water, mercury, gold, copper, and bismuth.

Paramagnetic

Substances that are weakly attracted to magnetic materials are paramagnetic. Examples of paramagnetic materials are Lithium, Molybdenum, Magnesium.

Ferromagnetic

Materials that are strongly attracted to magnetic materials. Examples of ferromagnetism are Nickel, Iron, and Cobalt. 

 

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Diamagnetic (Magnetic Field)

Diamagnetic materials, for the most part, repulse from a magnet. These solids make an instigated attractive field toward a path inverse to a remotely applied attractive power and are repulsed by the applied attractive field. This wonder is the polar opposite conduct shown by paramagnetic materials. 

The orbital movement of electrons present on the molecules of Diamagnetic solids produces attractive fields as it makes little nuclear current circles. At the point when attractive outside power is applied to a material, these current circles will, in general, adjust to restrict the applied field. 

In Diamagnetic materials, there is no perpetual net attractive second per iota as all the electrons are combined. Because of the impact of an attractive outside power, Diamagnetic properties emerge from the realignment of the electron pathways. Most components in the occasional table like copper, silver, and gold, are Diamagnetic. Sebald Justinus Brugmans found diamagnets in the year 1778. Michael Faraday further showed that diamagnetism or attraction is a property of an issue, and each material or durable response needs be. 

 

Attractive Susceptibilities of Diamagnetic Materials  at 20°C 

Km is the relative penetrability which is only an amount that quantifies the proportion of the in-charge to the applied attractive field. 

Material

χm= Km-1 (x 10-5)

Carbon (graphite)

-1.6

Ammonia

-2.6

Silver

-2.6

Bismuth

-16.6

Carbon (diamond)

-2.1

Mercury

-2.9

Lead

-1.8

Water

-0.91

Copper

-1.0

Sodium chloride

-1.4

The gasses N2 and H2 are weakly Diamagnetic with susceptibilities of -0.0005 x 10-5 for N2 and -0.00021 x 10-5 for H2. The gasses N2 and H2 are weakly Diamagnetic with susceptibilities of -0.0005 x 10-5 for N2 and -0.00021 x 10-5 for H2.

 

What is Magnetic Susceptibility?

Susceptibility is a measure to extend to which material gets magnetic energy under the influence of an external magnetic object or field. In other words, we can use the term “magnetizability” for the susceptibility of magnetic material.

Polarization or magnetism is created when an object interacts with the magnetic field. Polarization may either augment or oppose the external field. Object’s active field is reduced because of the opposition of the applied magnetic field by the polarization. In this situation, the magnetic lines are dispersed because of polarization, and this effect is called Diamagnetic.

 

Magnetic Susceptibility of Diamagnetic Substance

Attractive materials might be named Diamagnetic, paramagnetic, or ferromagnetic based on their susceptibilities. Diamagnetic materials, for example, bismuth, when put in an attractive outer field, mostly remove the outside field from inside themselves and, whenever molded like a bar, line up at right edges to a nonuniform attractive field. Diamagnetic materials are portrayed by consistent, little unfavorable susceptibilities, just marginally influenced by chang
es in temperature.

 

Superconductivity

An unusual property arising out of diamagnetism, and only recently known, is the property of superconductivity. The phenomenon was first discovered by Dutch physicist Heike Kamerlingh Onnes, who demonstrated that when materials are cooled to an absolute zero, phase transition occurs accompanied by special magnetic properties, not known to exist otherwise. Unlike other materials, Diamagnetic substances, under special circumstances (specific temperature and pressure conditions) act like superconductors. They have a specific set of physicochemical properties such as zero electrical resistance, net zero magnetic flux fields, and phase transition with no latent heat. It then shows the characteristic Meissner Effect. It is the “idealization of perfect conductivity” in classical physics. An electric current that loops through such a superconducting material can continue to exist indefinitely (for an infinite time) even after the source of current is removed. These special properties conferred upon by diamagnetism make it a swiftly developing field of classical physics.