Category: Physics Notes PPT

The word “Magnitude” in astronomy is the amount of brightness a celestial object upholds. 

Talking about stars like Betelgeuse or a galaxy like Andromeda galaxy, they all have some brightness, which we can calculate by using the concept of magnitude astronomy.

However, magnitude is a unitless measurement of the brightness of astronomical objects in a pre-defined passband. The defined passband is either the visible or infrared spectrum. Moreover, we can observe the brightness across wavelengths as well.

On this page, we will understand magnitude astronomy and absolute magnitude astronomy in detail.

Magnitude of Astronomical Objects

Hipparchus of Nicaea was a Greek mathematician, astronomer, and geographer. He introduced an imprecise even so systematic measurement for the determination of the magnitude of objects.

He is a well-known ancient astronomical observer. Also, he is one of the greatest astronomers of antiquity. 

Moreover, he introduced quantitative and accurate models for the movement of the Sun and Moon survival.

Magnitude Astronomy Definition

Here, we will understand the magnitude scale astronomy with a few examples on apparent visual magnitude:

Magnitude is the measure of the brightness of various celestial bodies, like stars and galaxies . 

Therefore, the brighter is the object, the lower is its magnitude in integers. 

In ancient times, astronomers ranked the star to six magnitude classes. The first magnitude class comprises the brightest stars. 

One magnitude is the ratio of brightness of 2.512 times. For instance, a star having a magnitude of 5.0 is 2.512 times brighter than a star of magnitude 6.0. 

Thus, a difference of five magnitudes relates to a brightness ratio of 100 to 1. 

After standardizing and assigning zero points, the brightest class was found to contain a huge range of luminosities. Furthermore, the negative magnitudes were introduced to spread the range.

Magnitude Scale Astronomy

Astronomers use two different measurements of magnitude:

1. Apparent magnitude

2. Absolute magnitude. 

Firstly, let’s talk about the apparent magnitude:

The apparent magnitude (m) is the object’s brightness, as it appears in the night sky from Earth. 

Apparent magnitude depends on an object’s following attributes:

1. i = Intrinsic luminosity

2. Its distance

3. Extinction reduces its brightness. 

Secondly, we have an absolute magnitude:

The absolute magnitude (M) describes the intrinsic luminosity an object emits. 

Likewise, the absolute magnitude (M) be equal to the apparent magnitude if the object is placed at some distance from the Earth. The distance should be around 10 parsecs for stars. 

Apparent Magnitude of a Star

The Apparent Magnitude (m)of a star is the brightness of an object as it seems to an observer on Earth.

For instance, the visual magnitude of stars are as follows:

• Sun’s apparent magnitude is – 26.7. 

• Furthermore, the Apparent Magnitude of the full Moon is around −11. 

• Additionally, the apparent magnitude of the bright star Sirius, – 1.5. 

• However, the faintest objects visible via the Hubble Space Telescope are of apparent magnitude 30. 

Apparent Brightness of Stars

Apparent brightness is how a star appears when we view it from Earth; however, it depends on the absolute brightness and the distance of the star from the Earth.

For instance, the apparent visual magnitude scale of a star is + 3, and the absolute visual magnitude is 0.8.

Here, absolute brightness is the luminosity that is a measure of the total power radiated by the sun.

Therefore, two stars that appear to be equally bright or glistening even so they are closer, dinner star, and the farther one, brighter.

                           

Absolute Magnitude Definition Astronomy

Absolute magnitude is the brightness an object exhibits when viewed from a distance of 10 parsecs (32.6 light-years). The Sun’s absolute magnitude is 4.8.

We must know that the absolute magnitude varies inversely with the brightness of celestial objects. 

So, if the magnitude of a star/galaxy is lower, it means that they are bright, and vice – versa.

The absolute magnitude of stars ranges from – 10 to +17. However, the magnitude of galaxies is lesser. Talking about the giant elliptical galaxy, M87, its absolute magnitude is – 22.

Here,  – 22 means the M87 galaxy is as bright as 60,000 stars of – 10 magnitude.

Absolute Magnitude Astronomy

The brightness of the star is true or absolute only if all the stars are at a uniform distance from the earth.

The absolute magnitude of stars is measured in comparison to our Sun.

For instance, 

If m of Sun = 1

m < 1,  brighter than the sun

Further, m > 1, less bright than Sun

Distance Modulus Astronomy

Do you know what distance modulus astronomy is? If not, to put it more simply, we have its definition:

A distance modulus is a way of expressing distances in astronomy. 

It describes distances on a logarithmic scale all things considered in the astronomical magnitude system.

Do You Know?

• In 1850, Norman Robert Pogson, an English governmental astronomer proposed a mathematical scale of stellar magnitudes with the ratio of two successive magnitudes being the fifth root of one hundred (~2.512). 

• Also, he referred to this relation as Pogson’s ratio. Assuredly, this system is in current use.

• Astronomers use a more complex definition of absolute magnitude for planets and small Solar System bodies. 

• They measure the absolute magnitude on the basis of its brightness at one astronomical unit from the observer and the Sun.

Mass is a fundamental characteristic property of matter. It exists independently and is autonomous of every other boundary, such as the temperature, pressure, and the area of the object in space. The matter has mass and consumes space. These two things are trained to us when we can get a handle on these ideas. A matter is anything you can contact truly, so all you see and communicate with around you have a mass. 

Mass commonly is mistaken for another boundary. This disarray happens because of the way that this boundary is erroneously utilized globally rather than mass because of its comfort and because of the way that we gauge things to discover their mass. This parameter is called weight, and weight is measured in Newton.

Definition of Mass

To define ‘how to measure mass’ alludes to the measure of matter in a specific object. This estimation of the measure of matter, for example, the mass of an object, is an inherent estimation of that body. Mass decides the quality of its common gravitational attraction for different bodies, its resistance from speeding up because of a force, inertia, and mass can likewise be utilized to determine the vitality substance of an example through the hypothesis of Relativity utilizing  Albert Einstein’s E = mc².

Mass of an object is measured by the SI Unit of mass that is the kilogram (kg). A kilogram can be separated into 1000 grams, and it was first characterized as one cubic decimetre of water at the point of melting of ice, for example, 0 ^oC. Such changes in the fundamental units of science can cause a catastrophe, which is why the Kilogram was re-imagined as the mass of the International Prototype Kilogram. 

Unit of Atomic Mass

Mass of an object is measured by the kilogram. But for excessively little and larger items we utilize different units:

• Ton (metric ton) is equivalent to 1000 kg

• The Atomic Mass Unit to kg is utilized while managing atoms and molecules whose masses are little to such an extent that the kilogram is not appropriate. One atomic mass unit is characterized as 1/12^th the mass of a Carbon-12 atom. The estimation of 1 atomic mass unit is acquired as 1.66 x 10^-27.

How do you Measure Mass?

()

To explain ‘how to measure mass,’ the mass of an object is measured by a balance. The obscure mass of a body is contrasted and a known estimation of mass. We acquire the estimation of an obscure mass as far as a known value of mass. A parity works in space and spots of no gravity since changes in gravity influence both the majority on balance similarly.

Definition of Weight

()

Mass isn’t equivalent to weight (weight is measured in newton). While the mass is the characteristic property of the body, weight is the proportion of the power applied to the mass of the body because of gravity. Mass alludes to a general estimation of the item though weight is a limited translation of the object’s mass. Weight is the impact of gravity, and consequently, we portray weight with the formula;

W = mg

Where m is the mass, and g is the acceleration because of gravity at that specific area. The weight is measured in Newton. For instance, an item with a mass of 50 kg encounters a gravitational power, for example, weight, which is equivalent to 50 x 9.8 = 490 Newton. A similar item but with a similar mass of 50 kg will gauge 1/6^th on the moon what it did on Earth. This way, we can explain ‘how to measure mass.’

Mass-Gravity-Weight

We generally use these terms interchangeably without knowing the difference but little do we realize that they are not the same. Mass of any given object is the total matter in it at that point in time whereas the weight of an object is the total force acting upon the object. On the other hand, weight is the force exerted on an object due to gravity and it changes from place to place if the gravitational force changes. For example, when we throw a plastic bottle in the water, it floats and we can consider the weight of the ball is “0”. But, this does not mean that the mass of the ball is also “0” as we can clearly see the ball is made up of some matter. The gravitational force exerted on an object is directly proportional to the mass of the object which means, when the mass of the object is heavy, it exerts more gravitational force and when the mass of the object is less, it exerts comparatively lesser gravitational force. 

Solved Questions

1. Explain the Formula of the Mass.

Ans: Mass can be calculated with three potential ways:

1. Mass=density*volume (m=ρV)

2. Mass= force/acceleration (m=F/a)

3. Mass= weight/gravitational acceleration (m=W/g)

Mass is a fundamental property that cannot be defined as per the other units like newton (in which weight is measured in) or joule. Other ways are also there to explain ‘how to measure mass.’

Fun Facts 

• The weight of the object will increase when you are close to the earth. If two cups full of dirt are taken to the high mountains, the weight of the cup will be less if we compare the weight of the cup from the sea level.

• Photons are the smallest mass known to be. 5.3 times 10^–63kg.

• The mass of the universe is believed to be 10⁵¹ kg, number 10, followed by 50 zeroes.

The word ‘Microscope’ comes from the Latin word ‘Microscopium,’ which is derived from the Ancient Greek word: μικρός, mikrós, meaning”small” and σκοπεῖν, skopeîn, means “to look” or “see”.

So, do you know what microscopes are?

The microscope is an instrument used to detect small objects that are invisible to the naked eye and the science behind this investigation is microscopy. 

The use of a microscope is, in interacting with the sample (a crystal/blood sample) and producing images by sending a beam of light/electrons through the sample’s optical path. Also, it helps in detecting photon emissions from a sample, and much more.

On this page, we will understand the use of microscopes with the application of microscopes.

What is Microscope?

The use of microscope helps us in getting a closer view of exceedingly minute objects that are in the range of  10^-n metres.

The enlarged image can be formed by waveforms including X-ray, acoustic, or electron beam, and be received by direct or digital imaging or by a combination of both methods. 

The microscope can also provide both a dynamic image just like conventional optical instruments and a static, like conventional scanning electron microscopes.

A range of power in which the microscope enlarges the image of the object is the magnifying power, and now we will discuss the same on the page.

Magnifying Power of Microscope Formula

The magnifying power of a microscope formula is a mathematical expression for the number of times the object when examined appears to be enlarged.

We express the magnifying power of the microscope formula in the following manner:

[M=frac{tanbeta }{tanalpha }=frac{text {It is the angle subtended by the final image to the eye}}{text{the angle subtended by the object seen directly}}] (dimensionless ratio)

So, the magnifying power of microscope formula is the ratio of the angle subtended by the final image to the eye to the angle subtended by the object seen directly, provided that both of these are kept at least distance of distinct vision (- 25 cm). 

We call the magnifying power of microscopes the angular magnification.

Here,

tan β ≈ β

tan 𝛼 ≈ 𝛼 

The above two cases are possible when the angles and are very small. So, we rewrite the above equation as;

[M=frac{beta }{alpha }]

Also, M Total = M Objective X M Eyepiece

So, total magnification = magnification of objective * magnification of the eyepiece. 

Now, let’s understand the types of microscopes and the uses of microscopes.

Types of Microscopes

Various types of microscopes that we find in a laboratory are as follows:

1. Simple microscopes

2. Compound microscopes

3. Scanning electron microscopes

4. Transmission electron microscopes

5. Phase-contrast microscopes

6. Interference microscopes

7. Confocal microscopes

8. Stereoscopic microscopes

9. Light microscopes: Dark field microscopes and bright field microscopes

10.  Fluorescence microscopes

11.  X-ray microscope

So, what is the use of a microscope? Let us understand it:

Application of Microscope 

Below, you can see the uses of microscope:

• Microscopes are used in examining the ailments by getting a larger view of the blood sample in detecting the parasites, bacterias attacking the red blood.

• Scientists use a microscope for studying microorganisms, cells, crystalline structures, and molecular structures.

• Microscopes help doctors diagnose the tissue sample.

1. Blood cells

2. Cheek cells

3. Parasites

4. Bacteria

5. Algae

6. Tissue

7. Thin sections of organs

8.  Detecting the UTI (urinary tract infection) in the urine sample

9. Detecting germs

10. Detect crime cases

11. Used in performing research and medical advancements

12. Determine the cause of diseases

13. An aid for prevention of diseases

14. Create electronic devices and circuits

15. Discovery of microorganisms

16. For open branches of sciences

17. In Forensics

In forensics, a microscope is used to study general criminal science, forensic epidemiology, forensic anthropology, and forensic pathology.

In every crime scene, criminals erase all the proofs of their miscreant, so a microscope in Forensic helps doctors examine organs, bones, and other parts of the body to know the cause of the death.

Do You Know?

• A German Physicist named Ernst August Friedrich Ruska designed the first electron microscope. He was conferred with a Nobel Prize in Physics in 1986 for his work in electron optics, including the invention of the electron microscope.

• The first detailed study of the microscopic anatomy of organic tissue, based on the use of the microscope was not discovered until 1644 in Giambattista Odierna’s Locchio Della musca.

• The use of microscopes was widely considered a novelty between the 1660s and 1670s when it was used to study biology by naturalists in England, Italy, and the
  Netherlands.

The months are a measure of time used with calendars corresponding to the length of time required by the Moon to revolve once around the Earth. A year is further subdivided into 12 months in the modern-day Gregorian calendar. 

The month has either 28, 30, or 31 days during a common year, which has 365 days. During leap years, which occur every 4 years, we add an extra (intercalary) day called Leap Day, on 29 February, making leap years 366 days long. 

Solar Month

The solar month originated as a way to mark time and break up the year into shorter periods based on the Moon’s orbit around Earth. The word month is derived from the word ‘Moon’.  The current Gregorian calendar and the Julian calendar, both have 12 months. However, the month names we are using today are derived from the Roman calendar, which initially had only 10 months with the calendar year starting in March (Martius). 

The Romans name some of the months after their position in the calendar year: September means the 7th month, October the 8th, November the 9th, and December the 10th month. However, when January and February were added and the beginning of the calendar year was moved to January, the position of these months no longer corresponded with the original meaning of their names. Even today also, we call the 9th month of the year September ( intended as the 7th month).

The Islamic calendar, the Hebrew calendar, and the Hindu calendar also use months to divide up the year. Even though the Gregorian calendar is a commonly used calendar today, other calendars are still used in many parts of the world to calculate certain holidays and annual feasts.

What are the Months?

The Gregorian calendar consists of the following 12 months given below along with month length:

January – 31 days

February – 28 days in a common year while 29 days in leap years

March – 31 days

April – 30 days

May – 31 days

June – 30 days

July – 31 days

August – 31 days

September – 30 days

October – 31 days

November – 30 days

December – 31 days

Origin of the Months’ Name

January

January derived its name from the Roman god Janus, protector of gates and doorways. This figure from mythology has two faces one looking into the past and the other into the future. The duality shown by this God meshes perfectly with the end of one year and the beginning of the next. In ancient Roman times, the gates of the temple of Janus were opened at times of war and closed at times of peace.

February

It derived its word from the Latin word ‘februa’ meaning “to cleanse.” As per Roman perspective, Moving into February, a month dedicated to purification. The Roman festival of February which is also called Lupercalia, began as a means of ensuring health and fertility, banishing and protecting the region, and cleansing the city. From a Roman perspective, February was termed as the last month of the year and they wanted to take out all the bad and bring in the good. 

March

Its name was derived from the Roman god of war, Mars. It was the time of year to resume military campaigns which were interrupted in winter. March was a time for many festivals, presumably in preparation for the campaigning season. Among all the regional Gods, Mars was considered second after Jupiter. Mars’ power wasn’t considered as destructive. Keeping this in mind, March is a good month for tackling a battle in our life by spiritual means.

April

It was derived from the Latin word ‘aperio’ meaning “to open (bud),” because most of the plants begin to grow in this month. This month was viewed as spring’s renewal. April is Aphrodite’s month. She was considered as the goddess of all things beautiful in Greece as well as a governess of love and romance. Her Roman counterpart is Venus.

May

It derived its name from the Roman goddess Maia, who oversaw the growth of plants. Maia was considered a nurturer and an earth goddess, which can explain the connection with this springtime month. Maia was the wife of Vulcan.  Both Greeks and Romans considered Maia as a nurturing force filled with warmth. Her name has the meaning of “Great one” so it can be considered a good month to focus on self-care or warming up a cool relationship.

June

It derived its name from the Roman goddess Juno, patroness of marriage and the well-being of women. Also from the Latin word ‘juvenis’, “young people.”  The Goddess Juno, the wife (and sister) of Jupiter for whom June was named was considered the most important Goddess in Rome. Juno is an energetic goddess with eternal youth. Her Greek name is Hera. She is considered to protect the sovereignty of Rome and aid with fertility. Juno was considered a very complex character throughout Roman myths. She had various names and each of them gives us greater insight into her powers. 

July

It derived its name from Roman dictator Julius Caesar (100 B.C.– 44 B.C.) after his death. Julius Caesar has made one of his greatest contributions in history: With the help of Sosigenes, he developed the Julian calendar, the precursor to the Gregorian calendar we use today. The 3rd quarter of the Wheel of the Year begins in July. Julius Caesar brought Rome from a republic to being an Empire. His leadership played a vital role in Rome’s expansion, and his writings continue to give an insight into the life and times of Roman citizens. His famous quote: “I came, I saw, I conquered.” With this in mind, the month was named after him so that it could support energy for victory and expanding personal horizons.

August

It was named to honour the first Roman emperor (and grandnephew of Julius Caesar), Augustus Caesar (63 B.C.– A.D. 14). Augustus (the first Roman emperor) was derived from the Latin word “augustus,” which means venerable, noble, and majestic. Similar to July, August also had another Roman leader for whom it’s named, Augustus Caesar. 

September

September was derived from the Latin word ‘septem’ which means “seven,” because it was the seventh month of the early Roman calendar. September comes from a word meaning seven because it was originally the 7th month on the calendar. 

October

According to the ancient Roman calendar, October was the name of the eighth month of the year. It got its name from the word ‘octo’, the Latin word for “eight.” When the Romans converted to a 12-month calendar, they tried to rename this month after various Roman emperors, but the name October was stuck.

In Old England, the month was named Winmonath, meaning “wine month,” because this was the time of year when wine was made. The English people used to call it Winterfylleth, or “Winter Full Moon.” They considered this full Moon to be the start of the winter season.

November

The word November was derived from the Latin word ‘novem’, which means “nine,” because this had been the ninth month of the early Roman calendar. November was named the ninth month of the Julian calendar. The Anglo Saxons also called November the wind month, while in the US it is called National Good Nutrition Month.

December

It was derived from the Latin word ‘decem’, “ten,” because this was the tenth month of the early Roman calendar.

Leap Year

After every four years, February has 29 days instead of 28. This year is called a “leap year” and the 29th day of February is called  “leap day”. A leap year has 366 days and not 365. All those years which can be divided by 4 are leap years. Eg: 2016, 2020, and 2024.

Months and Days

12 months together make One Year:

1 Year = 12 Months = 365 (or 366) Days

1 Month = about 30 Days = about 4 Weeks

Seven Days Together Make a Week. a Week Can be Any Period of Seven Days, Each Day is Special and There are Seven Different Days:

• Monday

• Tuesday

• Wednesday

• Thursday

• Friday

• Saturday

• Sunday

Did You Know?

Ancient Romans Had 10 Months Which Were:

1. Martius for the god Mars

2. Aprilis (‘aperio’ means to “open”, and flowers blossom in this month)

3. Maius for the goddess Maia

4. Iunius for the goddess Juno

5. Quintilis from Latin ‘quinque’ meaning five

6. Sextilis for six

7. Septembris for seven

8. Octobris for eight

9. Novembris for nine

10. Decembris for ten (remember “Decimal” means based on 10)

Also known as the zero-dimensional nanomaterials, nanoparticles are particles whose dimensions are below 100nm. These microscopic particles have unique properties that make them suitable for immense chemical reactivity, bio mobility, and energy absorption. Nanoparticles naturally occur in the environment but also are artificially synthesized. They are applied extensively in the development of modern medicine. It includes sophisticated processes like contrast agents in medical imaging and gene transfer into a cell. Engineering, catalysis, and environmental remediation are also areas where nanotechnology gets used widely. One of the biggest challenges is the toxicity which the nanoparticles pose to society and the environment. Nevertheless, nanoparticles are a boon to the modern world. 

Size of the Nanoparticles

Nanoparticles are invisible to the human eye. They exhibit significant chemical and physical changes in the larger materials. As their size approaches that of the atomic particles, their properties get modified even more. Each nanoparticle has a few thousand atoms. As the particles reduce in size more and more, their surface area to volume ratio increases, resulting in the surface atoms dominating the material. Moreover, these nanoparticles are enormously small and are able to confine the electrons present in them and produce quantum effects. The surface area of the nanoparticles is even larger than that of powders, plates, or sheets. 

Physicochemical Properties of Nanoparticles

Mechanical strength, large surface area, optical and chemical reactivity are properties that make the nanoparticles unique. However, there are several other physicochemical properties:

1. Noble metal nanoparticles are size-dependent in their optical properties. They have a UV-visible spectrum band that is not present in bulk metals. It appears when excited by the Localized Surface Plasmon Resonance (LSPR) and results in wavelength selection absorption and molar excitation. Ray light scatters along with enhancing electromagnetic fields. Hence the optical and electronic properties are interdependent.

2. The nanoparticles work best when their diameter is less than the critical value. The magnetic properties of the particles are very effective below 10-20 nm. It makes them useful for several applications.

3. When compared to microparticles, nanoparticles show dissimilar mechanical properties. The mechanical parameters such as hardness, elastic modulus, stress and strain, adhesion, and friction are determined. They are used to analyze if the nanoparticles have a usage in nanomanufacturing and nanofabrication. 

4. The nanofluids are used in specialized heat transfer phenomenon’s. The thermal conductivity of these fluids is more enhanced than that of conventional fluids. The metal nanoparticles have conductivities 1000 times greater than the fluids. 

Uses and Applications of Nanoparticles

Nanoparticles are produced by engineering methods or through combustion techniques. Healthcare, cosmetics, environmental preservation, and air purification are processes that involve nanoparticle technology. These particles transport chemotherapeutic drugs across the human body for the treatment of cancer. They can transfer even to the regions where the arteries are damaged. Aerospace engineers use carbon nanotubes for the morphing of aircraft wings. Zinc oxide nanowires applied in the solar cells help in environmental preservation. The nanoparticles hence have several other applications. 

Questions and Answers

1. Compare the Size of the Nanoparticles with Other Particle Types.

Answer – The following table shows the comparison:

2. Give Some Nanoparticles Examples.

Answer- There are several kinds of nanoparticles based on their morphology. For example, some nanoparticles get prepared from the precursors of metals. These metal nanoparticles get synthesized by chemical, electrochemical, or photochemical methods. They have high surface energy and hence can absorb small molecules. In scanning electron microscopes, gold nanoparticles are used for analyzing a sample. Carbon nanoparticles are other types that have fullerenes and graphene sheets rolled into carbon nanotubes. These nanoparticles are famous for their high strength and electrical conductivity. Semiconductor nanoparticles have properties between metals and nonmetals. Polymeric nanoparticles are organic-based. These structures are either Nano capsules or Nano spheres.  Their release can be controlled and hence used in the protection of drug molecules. The ceramic nanoparticles arise from the oxides, carbonates, carbides, and phosphates which are inorganic in nature. They are mainly used as drug delivery agents.

Newton’s second law of motion is related with the first law of motion. It gives the quantitative definition of force. Mathematically, it describes the causes and effects of force and changes in the motion of an object. Before understanding the equation of Newton’s second law of motion which deals with the force, mass, and acceleration of an object, let’s have a look at the three laws of motion.

Well, it’s a common fact that the students are most familiar with Newton’s law of motion, how an apple fell from the tree and resulted in a massive discovery in the history of mankind. Thanks to Sir Issac Newton for that as it has been of use for years now and has helped in the development of many new innovations. Moving forward the students are taught these concepts to make them familiar with the concepts and make their way easier for further studies.

The students are provided with all the related study material and resources on ’s website for free. The study material is available for classes 1 to 12 in the form of notes, revision notes, worksheets, sample papers, NCERT Solutions, NCERT Exemplar solutions, and other material for the students to make use of them while preparing for the exam and to clear their concepts and doubts well with ease.

The Three Laws of Motion

Newton’s 1^st law: It is also called the law of inertia. The statement depicts, “if a body is in the state of absolute rest, or in uniform motion, it will continue to remain likewise, provided it is acted upon by a foreign force.”

Newton’s 2^nd law: The statement depicts, “the rate of change of momentum of a body is directly proportional to the external force applied to the body. Further, the momentum of the body happens to be in the direction where the force is exerted.”

Newton’s 3^rd law: The statement depicts, “no matter what is the action, according to this phenomenon, always an equal & opposite reaction abides for it”.

Newton’s Second Law Statement

Newton’s first law statement, “unless a body is acted by a foreign force, it abides in its state of rest, or of uniform motion.” So, the question arises, what happens to your body when an external force is applied to it? This answer is provided by Newton’s second law of motion.

According to Newton’s second law of motion, force acting on a body is equal to the rate of change of momentum. For a body with a constant mass ‘m’, force is given by,

F = ma

Where,

a = acceleration produced in the body.

The above equation describes that, if the force is doubled, the acceleration also gets doubled, and if mass is doubled, acceleration becomes half.

Sir Issac Newton published his works about the laws of motion in 1687, in his book “Philosophiæ Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy), in which he described how objects with different masses move under the influence of applied force.

The first study regarding the laws of motion was done by Galileo Galilei. Based on Galileo’s experiments, all objects accelerate at the same rate regardless of their size and mass. Rene Descartes also published some laws regarding the motion of objects in 1644. Later Sir Issac Newton expanded the works of both these scientists and formulated his laws of motion.

Acceleration and Velocity

Newton’s second law of motion describes that, when a force is applied to an object, it produces acceleration in the object (i.e rate of change of velocity). For an object at rest, the applied force produces acceleration in the object and makes the object move in the direction of applied force.

For an object which is already in motion, the direction of the applied force matters to determine its state. If external force is applied in the direction in which the object is moving, the acceleration of the object increases. If external force is applied in the direction opposite to the motion of the object, the acceleration of the object decreases and finally comes to stop.

Force and acceleration are vector quantities, i.e they have both magnitude and direction. Multiple forces can also act in a body at a time.

Hence,

[Sigma]F = ma

Where;

[Sigma]= vector sum of all the forces acting on a body (net force).

For Changing the Mass

For this let’s assume that we have a car at a point (0) which is defined by the location X₀ and time t₀. The car has a mass of m0 and travels with a velocity of v₀. Here, after being subjected to a force ‘F’, the car starts to move to point 1, defined by location X₁ and the time by t₁. The mass and the velocity of the car changes during the travel to values m1 and v₁ respectively. Thus, Newton’s second law helps to determine the new values of m₁ and v₁ if we already know the value of the acting force.

From the difference of point 1 and point 0, an equation for the force acting on the car is formed as follows:

F=m₁v₁−m₀v₀t₁−t₀

F=m₁v₁−m₀v₀t₁−t₀

Now, let’s assume the mass to be constant here. This assumption is helpful for a car as the only change in the mass would be the fuel burned while moving between point “1” and point “0”. Here, the weight of the fuel is probably very small as compared to the rest of the car, especially looking at the small changes in time. Meanwhile, if we discuss the flight of a bottle rocket, then the mass does not remain constant here, and only the changes in momentum can be looked at.

For Constant Mass

For a constant mass, Newton’s second law can be equated as follows:

F=mv₁−v₀t₁−t₀

F=mv₁−v₀t₁−t₀

We know, acceleration is defined as the change in velocity which is divided by the change in time.

The second law then decreases to a more common form as follows:

F=ma

The above equation conveys to us that an object will accelerate if it is subjected to an external force. While the amount of force is directly proportional to the acceleration and inversely proportional to the object’s mass.

Application of Newton’s Second Law of Motion

Some applications of Newton’s second law of motion are mentioned below:

1. Kicking a Ball

When we kick a ba
ll we apply some force in it, and in a specific direction. The ball moves in this direction. If the applied force is more the distance covered by the ball will be more, and if the applied force is less the distance covered by the ball will be less.

2. Pushing a Cart

Pushing an empty card is easy as compared to pushing a loaded cart; this is because if the mass of an object is more, a large amount of force will be needed to move it.

3. Two People Walking

If two people of different masses work together, the one with the heavier mass will walk slower as compared to the one with the lighter mass. This is because more acceleration is produced by the lightweight person.

Second Law of Motion Examples

Some of Newton’s second law of motion examples is mentioned below:

• Pushing or pulling an empty cart is easy as compared to a loaded cart because the loaded cart has more mass.

• If the same amount of force is applied to move a car and a bike, the acceleration of the bike will be more because it has less mass than the car.

• When a ball drops on the ground, it exerts a downward force on the ground, and in reaction to it the ground exerts an equal upward force on the ball, thus making it bounce.

• Stopping a moving ball requires force.