AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess.

9 Perfectly Elastic Collision Examples:Explanations,Facts

January 20, 2024December 24, 2021 by AKSHITA MAPARI

In a perfectly elastic collision, two objects collide and rebound without loss of kinetic energy. Example: two identical billiard balls striking at equal speeds; they exchange velocities while conserving total kinetic energy and momentum. Pre-collision velocity of ball A (1 m/s) equals post-collision velocity of ball B, and vice versa, assuming no external forces or rotational effects.

Ping-pong ball

A ping pong ball bounces conserving its kinetic energy and momentum on every bounce. The more the potential energy is given to the ping pong ball, the more it will attain the height on the bounce by converting all the potential energy into kinetic energy while approaching the ground surface due to the gravitational force pulling it downward. This will create an impact on the ground and the ball will bounce up vertically in the air stream.

The gravitational force acting downward is equal to the force due to the air stream upward. The kinetic energy of the ball, the momentum, and the height up to which the ball is bouncing is governed by the potential energy of the ball and the decrease in the static pressure.

Moreover, a ping pong ball is light in weight and springy, it loses only a small amount of kinetic energy due to the less frictional force experienced. Hence, the kinetic energy and momentum, both are conserved by the bouncing ping pong ball.

Hitting the Marbles

Marble is associated with the potential energy on lifting it to a certain height. This potential energy is converted into kinetic energy which is the energy of motion.

Blue, Glass, Marbles, Kids, Games, Play, Round — **Marbles;**
**Image Credit: pixabay**

The kinetic energy is released on hitting the marble kept stable at the center. Upon striking, the kinetic energy of the marble released is transferred to the marble on the ground and it displaces with the amount of kinetic energy it receives.

Newton’s Cradle

Newton’s cradle is a perfect example of elastic collision as it conserves both momentum and energy. The bobs hanging on the cradle with a string of equal length consist of equal masses. Usually, Newton’s cradle comes with five bobs.

When one bob from the corner is given momentum, it transfers the energy in the form of potential energy and released back the energy by swinging the bob at the end of the row in the air and again passing the potential energy to the bobs at the middle. Thus conserving the energy once given to the cradle and momentum of the bobs is also conserved.

perfectly elastic collision examples — **Newton’s Cradle**

For a collision of the bobs to be perfectly elastic, the momentum and the energy associated with the bobs must be the same even after the collision and this can be formulated for the Newton’s cradle in the equation below:

Since, m₁=m₂=m₃=m₄=m₅=m and there is kinetic energy associated with the bobs 2,3 and 4 the velocity of bob 2-4 is equal to zero. And the initial velocity of bob 5 is zero and after the collision, the velocity of bob 1 becomes zero.

Therefore,

mu₁=mv₅

The momentum and the kinetic energy of bob 1 & bob 5 are the same, as it is conserved by the bob in the middle of them both.

Collision of Billiard Balls

On targeting a billiard ball with a billiard stick, the kinetic energy is given to the ball due to which it starts accelerating and collides with the target ball. On colliding, the kinetic energy is transferred to the target ball and is directed towards the pocket.

Carrom

When the striker strikes the carrommen, the kinetic energy and momentum of the striker are transferred to the carrommen. On gaining the kinetic energy, the carrommen travels further towards the net hole of the carom board.

Compton Scattering

This is an example of a collision of photons with a stable charged particle. A photon approaching from infinity strikes the charged particle possessing energy:-

E_photon=hc/λ

On colliding with the charged particle the kinetic energy of the photon is transferred to the charged particle which is then recoiled by the particle and the remaining energy is scattered by the particle releasing out the photon.

The change in the wavelength of the photon before and after colliding is given by the equation:-

The momentum and energy of the photon is conserved in this collision, hence it is an elastic collision.

Trampoline

A person jumping on a trampoline gains potential energy due to the elasticity of the trampoline which throws the body into the air converting this potential energy into the kinetic energy that sets the body in motion.

This kinetic energy is converted back into the potential energy when the body attains the height where all the kinetic energy is converted into the potential energy and hence there is a pause for some milliseconds in the air before the body starts returning down due to the effect of gravity.

The energy of the body and the momentum is conserved while jumping on the trampoline, hence is an example of perfectly elastic collision.

Air Bags

Molecules in air move in random motions due to the wide separation between them. As the temperature of the system increases the agility of the molecules in the air increases and there are more chances of collision due to the randomness in motion of the molecules.

These molecules bombard with each other in the air, releasing and gaining an equal amount of energy depending upon the molecular masses, and get scattered maintaining an equivalent measure of kinetic energy and momentum that was before the collision of the molecules.

Frequently Asked Questions

What is a perfectly elastic collision?

If a particle on colliding retains its kinetic energy and momentum then it is called an elastic collision.

In a perfectly elastic collision, the kinetic energy and the momentum of the particle do not change after a collision.

Does the kinetic energy change after collision in a perfectly elastic collision?

No, it does not change after the collision in a perfectly elastic collision.

The kinetic energy does not transform into any other form of energy and no kinetic energy is lost in the collision.

How elastic collision is different from perfectly elastic collision?

Both types of collision are elastic collisions hence we know that the kinetic energy, as well as the momentum, is conserved in the process.

But in the case of perfectly elastic collision, there is no loss in the kinetic energy at all; so is not the case in an elastic collision.

How can you minimize the force acting on the object during the collision?

The less the kinetic energy the object, the smaller will be the impact of the object during the collision.

A force can be minimized by lowering the time required for the collision of the object that is by reducing the velocity of the object.

Also Read:

23 Perfectly Inelastic Collision Examples: Detailed Facts And FAQs

January 21, 2024December 23, 2021 by AKSHITA MAPARI

In this article, we are going to discuss various perfectly inelastic collision examples and detailed facts on each.

The following is a list of perfectly inelastic collision examples:-

Car accident

A car approaching with a speed thwacks the car standing at rest, then the kinetic energy of the car is transferred to the car at rest converting into some other form of energy that could be potential energy or heat energy and sound energy. This is an example of inelastic collision because the kinetic energy between the collisions of cars is not conserved.

Boxing

Boxing is an example of an inelastic collision. The two players hit each other using their muscular force. Each punch hitting the opponent player is an example of a collision, the energy is not conserved here, and it turns into either the frictional energy due to rubbing of body or potential of the muscular force.

Shooting

When a bullet is fired from the gun, it moves with its kinetic energy towards the target. After hitting the target, its kinetic energy is reduced to zero after traversing inside the target, and even if it travels through the target plate then the momentum and the kinetic energy of the bullet changes thus does not follows the law of conservation of energy and momentum and hence is an example of inelastic collision.

Mud ball thrown on a rigid wall

If you threw a mud ball on the wall, it will collide and stuck with the wall changing its shape. No kinetic energy will be conserved and hence is an inelastic collision.

Kayak boat crossing the steeper slope

While riding a kayak, if you cross a steeper slope and come to the gentle level of the water, the water will splash over you equal to the force exerted by the kayak on the volume of water. We have to maintain the momentum of the kayak, well the kinetic energy of the kayak varies.

Stone thrown in water bodies

On throwing a stone in water, the kinetic energy of the stone is converted into vibrational energy on immersing through the layers of the water, which is reflected as a wavy concentric pattern by the molecules on the surface of the water.

Striking a matchstick on the matchbox surface

On striking a matchstick on the surface of the matchbox, the frictional force is produced. This frictional energy is converted into heat energy. Since red phosphorous on a matchstick is highly volatile, it catches fire on rubbing on a surface. Here, the frictional energy is not conserved but converted into heat energy.

An Object falling on the ground

The object falling on the ground converts its gained potential energy into kinetic energy for its flight. After making a fall on the ground it doesn’t bounce back or elapse the distance but stands at rest making its velocity zero and thus the kinetic energy becomes zero. Hence is an example of inelastic collision.

Breaking a glass

Glass, Broken, Shattered, Broken Glass, Shattered Glass — Shattering glass,
Image credit: pixabay

On hitting a glass with any object, it breaks into pieces. The kinetic energy imparted on the glass by the object converts into the vibration pattern in the molecules constituting the glass that results in the glass breaking.

Drawing water from the well

While drawing water from the well using a pot, a pot is released into the well tied to the rope on a pulley. The pot will initially collide with the surface of the water.

On the collision of a pot with the water surface, the kinetic energy of the pot is converted into vibrational energy creating ripples on the surface of the water. The water is filled up in the pot due to the ripples formed on collision.

Ball bouncing back on the ground

The ball bouncing on the ball gives away its kinetic energy on every bounce. This implies that the kinetic energy of the ball drops frequently and is not conserved.

Two molecules of different masses colliding with each other

Consider a molecule 1 of mass ‘m’ approaching molecule 2 at rest having a mass ‘2m’ which is double than that of molecule 1. The velocity of molecule 1 is ‘v₁’.

perfectly inelastic collision examples — **Before collision**

On colliding, molecule 1 with molecule 2, they move with the velocity ‘v’.

As per the law of conservation of momentum

Since m₁=m, m₂=2m and v₂=0

This implies that for momentum to be conserved, final velocity after collision should be equal to the 1/3^rd times the velocity of the colliding molecule.

Henceforth, the kinetic energy of the molecules is not conserved and therefore it is an inelastic collision.

Waves hitting the rock cliff

The ocean water has more potential energy stored with it in the central volume of the oceanic water columns. The water surface lying at the coastline constitutes the kinetic energy with it.

This wave approaches the coastline, hitting the rock cliffs smacking across the cliff, and returning back to the ocean. This consequence in the erosion of a rock cliff is due to abrasion and hydraulic actions. The kinetic energy of the wave is transferred into some other form of energy, hence it is a type of inelastic collision.

Waterfall

The flowing water bodies always carry debris along with it, which gets deposited into the sedimentary basin when the water makes its fall along with the debris. The flowing water is associated with kinetic energy with it.

The velocity of the water increases while making its fall from the cliff. After making the fall, the kinetic energy of the water decreases converting a part of it into frictional energy pushing debris of rocks along with it.

Clouds colliding with each other

The water vapours condense to form clouds and store enough potential energy with them. When they have enough potential energy, two mobile clouds collide and this energy is converted into kinetic energy and the water droplets flow down to the earth’s surface due to gravity.

On rainfall, the kinetic energy of the raindrops decreases to nil on meeting the ground surface.

Shot bombs

On throwing a shot bomb on the ground, the kinetic energy given to the shot bomb is converted into frictional energy when it touches the ground surface and creates heat and sound energy.

Car hitting a tree

A car accelerating at a certain speed if hits the tree by accident then the kinetic energy of the car is converted to heat energy, sound energy and results in the deformation of a car. The kinetic energy is converted to some other form of energy hence it is an example of inelastic collision.

Weight falling on the object

If a heavy mass falls on the object causing the damage, is an example of an inelastic collision, as there is no movement of the object causing the deformation.

Slider

When you take a drift on a slider, the body freely moves from the upper point to the lower point of the slider because of the steeper slope converting the potential energy of the body into kinetic energy. The body accelerates down the slope.

The body comes to rest on colliding with the ground converting the kinetic energy into the frictional force. Since the upper part of our body is still in the kinetic motion in the slanting direction downward, the body continues to move in that direction causing the body to move a little ahead even after the feet touch the ground surface.

Mixer grinder

The spinning of the blades due to the rotation of a shaft sets the mixture into circular motion. The energized mixture particles collide with the blade that resulting in a grinding of the mixture into fine particles and generating heat which is released out by the mixture.

Since the energy is not conserved in the process, subsequently converting the kinetic energy into heat energy, this is a type of inelastic collision of blades and mixture particles.

Fruit falling from the tree

The kinetic energy of the fruit falling on the ground due to gravity is not conserved after it makes the fall on the ground.

In case the momentum of the fruit is conserved then it will bounce back utilizing its potential energy into kinetic energy and finally dropping on the ground with nil energy. Hence the kinetic energy is not conserved by the fruit fallen on the ground. This is a type of inelastic collision of fruit with the ground.

Crash of tin bottle

On crashing the tin bottle it does not regain the original shape rather deforms its shape due to the force applied and is not an elastic material. Crashing a tin bottle is an example of an inelastic collision.

Ringing a bell

In old days, before the electric bell was invented, the bell was rung by hammering the metallic plate that produced the sound waves. On hitting the bell, the potential energy is converted into sound energy. No energy is conserved in this collision, hence is also an example of inelastic collision.

Comet

Most of the time due to the strong attraction of the planet, small comets tend to fall into the atmosphere of the planet. The kinetic energy of the comet is converted into heat energy by colliding with the atmosphere of the planet due to friction.

What is Inelastic Collision

The particle after colliding does not retain the kinetic energy and momentum then the collision is called an inelastic collision. The kinetic energy is not conserved due to the internal friction, and conversion of energy in some other form.

Consider a body of mass m₁ moving with the velocity v₁, collides with the body of mass m₂ approaching with velocity v₂. After colliding, the final velocity ‘v’ of the body is given by the relation

It shows that the momentum, as well as the kinetic energy of the object, after the collision is not conserved, hence it is an inelastic collision.

Frequently Asked Questions

What is Collision?

Two particles bombarding with each other exchanging their energy and momentum with one another is called a collision.

The collision of the particles and thereafter the transfer of the energies and momentum depend upon the mass, initial velocity of the particle, and the force applied on the particles.

Why does the kinetic energy of the particles not conserved in an inelastic collision?

For a collision to be an elastic collision, the kinetic energy has to be conserved even after the collision.

In an inelastic collision, the kinetic energy of the particle is converted into some other form of energy depending upon the mass and configuration of the particle it is colliding with and the energy it is associated.

Why coconut falling on the ground is not an elastic collision?

The coconut falling on the ground is not an elastic collision as the momentum and the kinetic energy of the coconut are not conserved.

The kinetic energy of the coconut falling on the ground due to gravity is not conserved rather than it comes to a rest with zero velocity once it strikes the ground surface.

What type of collision is between the marbles?

The collision of the marbles is a type of elastic collision.

On striking the marble on another marble at rest, the kinetic energy of the striking marble is transferred to the marble at rest hence conserving the kinetic energy and momentum after the collision.

Also Read:

15 Elastic Collision Examples: Detailed Facts And FAQs

January 21, 2024December 21, 2021 by AKSHITA MAPARI

In this article, we are going to discuss various elastic collision examples and detailed facts on each.

The following is a list of elastic collision examples:-

Newton’s cradle

It consists of bobs of equal masses hanging on the cradle with the support of a string of equal length. When the momentum is applied to the bob at one end, bob 1 moves with velocity V₁ having the momentum of mu₁ and gaining kinetic energy (1/2)m₁u₁²

elastic collision examples — **Newton’s Cradle**

On colliding the bob 1 to bob 2 this kinetic energy is supplied to the bob 2 in the form of potential energy, as bob 2 to 4 are in close vicinity to each other, hence the momentum is conserved and the potential energy is transferred to the subsequent bobs and eventually releasing to the last bob in a line, which then swings in the air by converting the potential energy received into the kinetic energy equal to the given kinetic energy to the bob 1.

Let us formulate how momentum and energy are conserved in the case of Newton’s cradle.

As per the conservational law of momentum, the equation is written as

Since, m₁=m₂=m₃=m₄=m₅=m and the velocities of the bobs 2,3 and 4 remains unchanged in the collisions, that is equal to zero. And initial velocity of the bob 5 is zero and after collision the velocity of the bob 1 becomes zero.

Therefore,

mu₁=mv₅

The velocity of the bob 1 and 5 remains the same, and hence,

u₁=v₅=v

therefore mv=mv

The momentum before and after the collision is equal.

The same way the kinetic energy of bob 1 and 5 remains the same as the velocities of both the bob is constant. We need not consider the kinetic energies of bob 2-4 as there is no velocity of the bobs seen.

Ball bouncing back on the ground

The ball bouncing on the ground is an example of the elastic collision too. The ball retains its momentum while returning down to the ground and hence bounce back until its energy is reduced.

Collision of billiard balls

See the source image — **On striking billiard ball; Image credit: jrnl.ie**

When you hit a billiard ball to target another ball, you apply a force on the ball, it moves with the kinetic energy and transfers this energy to the next ball on colliding. Since there is a transfer of the kinetic energy from one ball to the next and the momentum is conserved, we can say that this is an elastic collision.

Carrom

For hitting a carrommen by a striker, you are actually giving momentum to the striker supplying the kinetic energy to the striker to hit the carrommen. On striking the energy is transferred to the carrommen making its way to the net hole of the carom board.

Tennis

The kinetic energy is supplied to the ball by hitting it with a tennis racket. The ball collides with the net of the racket which in addition provides elastic potential energy to the ball which is converted into kinetic energy. The opponent hits the ball maintaining the energy of the ball and the process continues until the ball drops its momentum. This is also an example of collision as the momentum and the kinetic energy of the ball are conserved after every collision.

Cricket

A batman hitting the ball is also an example of an elastic collision. The ball approaching the batman from the bowler has kinetic energy and momentum, which is maintained after hitting a ball with a bat and carries away the ball with momentum and the kinetic energy until drops down.

Compton Scattering

Compton scattering is also an example of elastic collision in which both momentum and energy of the particles are conserved.

It is a collision between a photon and a charged particle. A photon with high kinetic energy strikes the electron at rest making an angle of 180 degrees. The energy of the photon can be calculated by

E_photon=hc/λ

The kinetic energy of the photon is transferred to the stable charged particle, this energy is recoiled by the electron and then scattered making an angle φ with the plane. The photon is scattered away making an angle θ releasing or gaining the energy by the electron. If the energy of the photon decreases it implies that its wavelength is increased.

The difference in the wavelength of the photon before and after colliding is given by the equation:-

Trampoline

A person jumping on a trampoline exerts elastic potential energy that helps him to jump higher converting the elastic potential energy into kinetic energy. After every jump attaining a certain height, a person makes a pause in the air when the total kinetic energy of the body is converted into potential energy, and a person comes vertically down due to the gravitational force.

When a person jumps on the trampoline, the energy of the person on the trampoline and the elastic potential energy of the trampoline is conserved even after the frequent jumps. Hence it is a type of elastic collision.

A car hitting a bike in motion

If a car at very high speed hits a bike in motion, then the bike will accelerate with an increase in velocity, and be carried away to a distance before collapsing, at the same time the car experiences a back jerk.

This is because the kinetic energy of the car accelerating at very high speed transfers its energy to the bike that resulting in a carried away of the bike increasing its velocity. Here we can see that the energy is conserved.

Molecular collision in the air

In the air, molecules move in a random motion as the molecules in the air are separated by a large distance between them and hence are free to move. There are more probabilities of molecules colliding with each other.

The momentum and energy of the molecules are conserved hence showing elastic collisions.

Plucking a mango from a tree using a slingshot

A slingshot comes with a rubber belt which when stretched produced enough potential energy and is supplied to the stone holding across it. This stone applies force on the targeted mango and changes its direction and falls back to the ground due to gravity. Here, kinetic energy is conserved.

Two boats tied to the mooring buoy

The boat floats due to buoyant force by the volume of river water. As the river water is turbid the boats tied to the mooring buoy will shake along with the small waves upwelling on the water surface. The potential energy of the huge water bodies is very high.

As a result of turbidity and unstable boats, there are more chances of two boats colliding with each other. On collision the boats of equal weight repel away from each other maintaining equal momentum and energy is transferred equally to both the boats. Hence is an example of elastic collision.

Rubber band

When the rubber band is stretched, it stores potential energy with it; which when released, gives out an immense amount of energy. The rubber band is an elastic item that regains its shape and size even after stretching. The energy is conserved in a process and hence is an example of an elastic collision.

Skipping stone in water

When a stone is targeted over the water body, a stone bounces on the upper level of water because of the conversion of its energy from kinetic to potential and from potential to kinetic energy depending on the spin and force applied onto a stone by the person. The momentum of the stone is conserved in the process making it possible to skip the long-distance and bounce on the surface of the water.

Two river tributaries joins to form a single water way

Two rivers flowing with two different velocities combine and direct the water in a single direction. As the volume of the water in the river after joining into single tributaries doubles, the speed of the flowing water slightly lowers but the momentum of the flowing water is conserved.

What is Collision

The striking of two or more particles against each other in space transferring their energies and momentum to one other is known as a collision.

When the object is in a stable state of rest, it has enough potential energy associated with it, which is converted into kinetic energy during its motion. As the object is in motion, there are probabilities of bombarding with another object in the surrounding.

On collision the object transfers its energy to the object it collides with, which depends upon whether the opposite object is at rest or into motion, the speed and direction of the object too; based on it the object may gain or transfer its energy.

What is Elastic Collision

After the collision of particles, if there is a transfer of momentum and energy to the particle colliding with each other, then it is known as an elastic collision. In an elastic collision, both momentum and energy are conserved.

Consider a particle of mass m₁, moving with velocity V₁ collides with a particle having mass m₂ at rest. After the collision, the mass m₂ displaced from its place with velocity V_2, and mass m₁ comes to rest after diverting in a different direction. The momentum of the two particles colliding with each other can be given by the formula

m₁u₁+m₂u₂=m₁v₁+m₂v₂

Where m₁, m₂ are masses of particle 1 & 2 respectively

u₁, u₂ are initial velocities of both the particle before colliding, and

v₁, v₂ are final velocities of the particles after collision.

Since the sum of the velocities of the two particles before and after collision remains the same, it is evident that the momentum of the particles is conserved before and after the collision in the case of elastic collision.

Same way the kinetic energy of the particles is formulated as

The sum of the kinetic energies of the particles before and after collision are equal, hence the kinetic energy of the particle in elastic collision is conserved.

Frequently Asked Questions

A man pushing a box of mass 20kg at velocity 1m/s hits an object at rest having mass 2kg. What will be the velocity of the object of mass after collision?

Given: m₁=20kg

m₂=2 kg

v₁=1m/s

Since this is an elastic collision, the momentum of the box and object is conserved.

m₁v₁=m₂v₂

v₂=m₁v₁/m₂

v₂=(20kg*1m/s)/2kg

v₂=10m/s

Hence the velocity of the object will be 10m/s after colliding with a box of mass 20 kg.

What is the difference between elastic and inelastic collision?

In an elastic collision, the kinetic energy, as well as the momentum, is conserved before and after a collision.

Unlike the elastic collision, inelastic collision does not obey the law of conservation of energy. The kinetic energy of the object before and after a collision is not the same; it converts into some other form of energy.

How can one minimize the impact after collision?

To reduce the consequences that will result after the collision, we can lower the force while colliding the two objects.

The force exerting on the colliding objects can be reduced by increasing the time duration of a path taken for a collision to occur.

Why kinetic energy is not conserved in the case of inelastic collision?

In an inelastic collision, the momentum and the energy are not conserved after collision.

The kinetic energy is converted into some other form of energy, maybe heat energy, potential energy, mechanical energy; hence, kinetic energy is not conserved in the case of inelastic collision.

Also Read:

What Increases Potential Energy: Detailed Facts And FAQs

January 21, 2024December 20, 2021 by AKSHITA MAPARI

In this article, we are going to discuss various facts about what increases potential energy.

The potential energy can be increased by increasing the mass of the object, by varying the distance between the two objects, decreasing the kinetic energy of the molecules, by freezing, by compressing or stretching, etc.

Which example increases potential energy

There are many examples which we can list of increasing potential energy. Lifting the weight from the ground increases the potential energy of the weight, ice cubes in the refrigerator, watermelon kept on the table, the person sitting on the chair, food has chemical potential energy, clothes hanging on the hanger in the cupboard, cushions stack one above the other, climbing up the hill, photo frame hanging on the wall, jumping on the trampoline, etc.

what increases potential energy — Compressing the object increases its potential energy

What increases the potential energy of the particles

The particle at rest has the potential energy associated with it which can be calculated using the coulombs formula for potential energy, according to which the potential of the particle depends upon the charge of the particle and how far it is located from the source and is formulated as below:-

The potential energy of the particle depends upon the charge that they carry and vary depending upon the distance between the source differs. For positive charge, the potential energy of the particle will decrease as the distance from the source increases, whereas the potential energy of a particle carrying a negative charge, will increase as the distance between the source increases.

Therefore, the charge of the particles as well as the distance separating the two charge particles, both governs the potential energy stored by the particles.

Does heat increase potential energy

On subjecting any object to heat, the heat energy is supplied to the object. This energy multiplies the energy holding the covalent bonds of the atoms. The potential energy associated with the molecules holds the covalent bonds between the atoms.

The molecules become unstable due to immense energy supply and the bonds between the molecules breaks, which is then converted into kinetic energy, and particles become more agile and drift in random motions, thus decreasing potential energy.

Does freezing increases potential energy

When the object is kept in the system at freezing temperature, the object will give out energy in the form of heat into the surroundings to attain the equilibrium state for equating the temperature in the surrounding.

Releasing the heat energy by the object will reduce the kinetic energy of the particles in the object, thus decreasing the mobility of the molecules. This will result in the rise of the potential energy of the molecules constituting the object. Therefore, freezing increases the potential energy of the object.

Does potential energy increase with pressure

If the object is above the surface then it will attain some potential energy with respect to the height of the object from above the ground. If we go below the surface, the pressure and temperature gradient will increase by every 10kms. The potential energy decreases with pressure and is zero below the surface of the earth.

Does melting increase potential energy

To melt the material, it has to be subjected to heat. Heat will supply the energy to the molecules in the material. The molecules bonding to each other due to the potential of the covalent bonds will eventually break giving away the energy in the form of kinetic energy to the molecules. That is why the molecules in the system show more agility when supplied with heat energy.

Does potential energy increase with height

The potential energy of the object is directly proportional to the height of the object above the surface of the Earth. Every object exerts a force due to gravity, as the object is moved away from the gravitational attraction, it starts building its own potential. Hence the energy associated with the object along with increasing height also increases.

Does potential energy increase during phase change

It is understood that the kinetic energy of the gas is more compared to the solid. This is because molecules in the air are not tightly bonded and hence are free to move, whereas, in solid, the molecules are tightly bonded thus making it a compact mass and molecules are not free to move.

When solid is lain onto the heat source, the heat supplied breaks the covalent bonds between the atoms increasing the spacing between the molecules that results in a change of phase. Every time the phase change from solid to liquid and from liquid to gas, the potential energy of the mass is utilized to break the bonds between the atoms.

Hence, the potential energy decreases during each phase change. While the same is the opposite during the reversal process when the gas is compressed to form a liquid or liquid to solid.

Does potential energy increase during evaporation

Evaporation is a process of liquid turning into the gaseous phase. This results when the liquid gives out the heat received by its layers in the form of vapours to bring itself to the equilibrium state by matching the temperature of the system to the surrounding.

As the vopours commence their journey through the air opposing the gravity of the Earth, it inhales the energy from the surrounding building enough potential to drag above the atmosphere. Hence, the potential energy of the vapours increases as they move higher and higher above the surface.

What process increase potential energy

Increasing the distance of the objects from the ground
Minimizing the distance between the like charges
Extending the distance between the two attractive particles
Condensation
Compression & Stretching
Freezing

Increasing the distance of the objects from the ground: Potential energy of the object due to gravity is formulated as P.E.= mgh according to which potential energy intentionally depends upon the height of the object from above the ground as weight is constant, hence increasing the distance between the object and the surface of the Earth, its potential energy will be increase as the gravitational pull of the Earth on the object will decreases as we increase the distance between them both.

Minimizing the distance between the like charges: As the like charges repel from each other the work has to be done to bring the charges closer to each other. Hence, as the separation between the two becomes shorter the potential energy generated by each other also increased.

Extending the distance between the two attractive particles: If the two charges of oppositely charged particles are kept closer to each other then they will easily attract converting their potential into kinetic energy. Hence, the work has to be done in the direction opposite to the force of attraction thus building the potential energy which increases by enlarging the distance between both.

Condensation: The process of concentrating and concise the volume of the gas under high pressure to form a liquid is called condensation. The gas condenses in the form of small liquid droplets. If we take an example of the formation of clouds, the water vapours evaporated in the atmosphere and condensed into clouds in the troposphere. When clouds have enough potential energy, this energy is converted into kinetic energy and flows down to the earth’s surface in the form of rain. Hence condensation causes the gaining of potential energy.

Compression & Stretching: When we apply pressure on any object, we supply the energy which is stored by the object in the form of potential energy until the force is released. The potential energy due to both is given by the relation U=1/2kx^2 and is directly proportional to the change in configuration of the object.

Freezing: lowering down the temperature lowers the kinetic energy of the molecules thus storing the potential energy.

Frequently Asked Questions

Does the kinetic energy of the particle depends upon shape and size of the objects?

The object accelerates from one place to another is because of the external force that results in the conversion of its potential energy into kinetic energy.

If the object is made up of a circular shape then it becomes easy to displace it than the objects having triangular or square shapes. The more the mass of the object greater the force required to displace and less will be it’s kinetic energy.

Does the potential energy of the object depend upon the mass of the object?

Potential energy is the energy stored by the object and is related to mass by the relation P.E.=mgh.

As per the above relation, the potential energy directly depends upon the mass; hence the potential energy will be greater for heavier objects.

Also Read:

Potential Energy Vs Potential Difference: Detailed Facts

January 20, 2024December 20, 2021 by AKSHITA MAPARI

In this article, we will see the difference between the potential energy and potential difference.

The potential energy is the energy stored in the system whereas the potential difference is the difference between the potential at two points.

Potential Energy Vs Potential Difference

Potential Energy	Potential Difference
Potential energy is the energy acquired and stored by the body.	A potential difference is a difference between the potential energy of the body at two different points.
Electric potential energy is the energy required to do the work per unit charge in bringing a charged particle from infinity to a point.	Electric potential is a difference between electric potential energy in displacing a charge of 1C from infinity to source.
The gravitational potential energy is the energy required to displace the unit mass from one point to another.	The gravitational potential difference is the work done in moving the unit mass
Potential energy increases by raising the object to height.	It is a difference between the potential energies of the object at two different heights.
It is the energy acquired by the elastic material by either compressing or stretching the material.	It is a difference between the potential energy stored by the material at two different lengths of compression or stretching.
Electric potential energy depends upon the magnitude of two charged particles.	It is a difference in the potential of a single particle at two different points.
It is measured in Joules	It is measured in Volts or Joule/Coulomb
The particles in nature always tend to occupy the least potential energy state.	The potential difference can be more or less depending upon the work done.
The potential energy is negative in case the force is attractive.	The potential difference is always positive.

Some Facts on Potential and Potential Energy

The energy acquired by the system due to the varying potential between the two positions on the system is potential energy.
The object at a certain height above the ground, having its own potential energy decreases with the distance as it approaches the ground.
The gravitational potential energy of the Earth tends to pull the objects towards the center of the gravity of Earth, decreasing the potential energy of the object converting it into kinetic energy while approaching towards the ground.
In an atom, a region with the least potential exists near the nucleus, and electrons in an atom tend to be near the nucleus attaining the low potential energy.
Once the electron built enough potential energy it becomes unstable and jumps into a higher energy level, releasing its energy falls back to the lower energy level of the atom.
Potential energy is available in 5 main different categories; gravitational, electrical, nuclear, elastic and chemical.
Electric charges move from the higher potential level to the lower potential level after transmitting their energy to a higher energy state on exciting.
In the case of capacitors, the potential difference is generated due to the separation of the opposite charge carrier plates, due to the separation of the plates the potential energy is stored inside the capacitor to do the work.
Potential energy on the close loop conductor is always zero.
In elastic materials, the potential energy can be stored by either stretching or compressing.

Let us evaluate the potential energy and potential difference relationship of some fundamental forces in nature:-

Gravitational Potential Energy and Potential Difference

The potential energy is the energy required to displace the unit mass from one point to another. The potential energy associated with the object due to gravity is given by the relation

U=mgh

Since, the weight of the object due to the gravity on the earth becomes the product of the mass of the object and its acceleration due to gravity which is constant, the only variable is the height. Hence, the potential energy of the object mainly varies depending upon the rise and fall of the object from above the ground. As the object opposes the gravitational pull of the Earth increasing the distance of separation between the ground and the object, it starts gaining its own potential.

The gravitational potential difference is the work done in moving the unit mass and is given by

ΔU=Work/m

We have seen above that the only variable quantity is the height of the object from above the ground

ΔU=mg/Δh

Where Δh is the change in height

ΔU is the potential difference

Since the gravitational force between the two objects having mass M and m separated by the distance ‘r’ is given by

F=G*(Mm)/r²

The work done on the objects due to gravity

Work=∫F.dr

Work =-GMm/r²

Since the potential difference is the work done per unit mass

Read more on gravitational potential energy.

Electric Potential Energy and Potential Difference

Electric potential energy is the energy required to bring the charged particle from infinity to the point of consideration. This is equal to the work done on the particle in bringing the unit charge.

Consider two point charges of charge q₁ and q₂ separated by a distance ‘r’ between them.

potential energy vs potential difference — Two charged particles separated by a distance r

The force acting between the two charges q₁ and q₂ is equal to

The work is done in bringing the charge q₁ at point ‘s’ to a distance r₂. Work is the force required to displace the charge q₁ to a distance r₂.

Work =Force*displacement

Therefore the work done on the particle to displace it from r₁ to r₂ is

Work done is equal to the potential energy of the charge.

The difference between the potential energy between the two points is the potential difference resulting due to the action of work.

Electric potential is a potential energy per unit charge; given by the relation

V=U/q
Where V is a potential
U is potential energy
q is a charge

Implies U=qV

Therefore, from above relation, electric potential will be equal to

Elastic Potential Energy and Potential Difference

When the elastic material is stretched or compressed, it gains potential energy. The amount of potential energy acquired depends upon the change in the length of the material. The static potential energy of the elastic component is given by

U=(1/2)kx²

Where k is an elastic constant and x is a displacement due to stretching or compression.

The potential difference is the difference between the potential energy stored in the object by the change in the position of the object or the load applied to stretch or compress the object.

Therefore, the potential difference is measured as

ΔU=(1/2)kΔx²

Where Δx=x₂-x₁

SI Units

The SI unit of potential energy is Joules. SI unit for gravitational potential energy is N.m/kg. Whereas, the SI units of potential difference is Volts also written as Joule per Coulomb J/C. One volt is equal to 1 J of energy per to displace a unit charge of 1C.

Frequently Asked Questions

Q1. Calculate the work done by the charge of 2C to displace from point A to point B having a potential difference of 10 Volts.

Given:

Charge Q=2C

Potential difference V=10V

V=W\Q

=>W=QV

=2C*10V=20 J

Q2. The potential energy of the ball at height 2m is 4J. If the ball is thrown in the air. Calculate the potential difference of the ball attaining a height of 10m above the ground.

The potential energy of the ball at a height is 1J.

Therefore, the mass of the ball is 204 grams.

On reaching the height of 10m, the potential energy of the ball becomes

U=mgh=0.204*9.8*10=20J

Hence, the potential difference is

Δ=U₂-U₁=10-4=6

What is nuclear potential energy?

The nucleus comprises protons and neutrons, thus adding a positive charge to the nucleus and hence electrons tend to remain towards the nucleus.

It is potential energy that keeps the neutrons and protons bonded in the nucleus. During nuclear fusion, the nucleus gains energy while on nuclear fission nucleus gives out energy along with the products.

What is chemical potential energy?

Chemical potential energy is the energy acquired by molecular bonds.

During the exothermic reactions, the bonds break, and energy is released, while in endothermic reactions the energy is acquired from the surroundings to make new bonds.

Also Read:

What Does Not Affect Potential Energy: Detailed Facts

January 21, 2024December 17, 2021 by AKSHITA MAPARI

In this article, we are going to discuss various factors what does not affect potential energy of objects and detailed facts.

The potential energy is converted into another form of energy but the velocity, rigidity, wavelength associated with the object, brittleness, size of the object, length, the volume does not affect the potential energy of the object.

What Object does not affect potential energy

The potential energy of the object is said to have remained unaffected only if the potential difference traced between the two different schedules is found out to be the same.

The rigid objects are unable to compress or stretch and hence, does not gain or release the energy that it possesses. The energy stored by the rigid object is therefore constant unless and until some extreme conditions affect them. These objects are non-elastic whose shape and size do not deform by the application of external forces.

For a system at rest, the potential energy of a system associated with it will remain unchanged until some external forces will act on the system. Hence, the object whose position is at a state of rest will not change the potential energy of a system.

In the case of elastic collision, the momentum and energy of the object are conserved. Newton cradle demonstrates an example of conservation of energy and momentum. It consists of five bobs of equal sizes and masses attached to the cradle with the support of strings perfectly aligned in a straight line.

what does not affect potential energy — Newton’s Credle; Image Credit: hearthsong

If a ball number 1 is given momentum and released, it will collide with the second bob transferring the energy to the last ball present in the line. The energy gained by the 5^th bob will make the bob sway in the air and return back, transferring back its kinetic energy to the 4th bob, where the energy will convert into potential energy. This energy will be transferred to all the bobs in the middle and finally supplied back to the first bob; now, the potential energy will be converted to kinetic energy and will make the bob swing into the air; and this process continues.

In this case, the potential energy of the cradle remains unchanged as both momentum and energy of the bobs are conserved.

What properties of an object does not affect its potential energy

Strength of the gravity: The center of mass of an object is where the gravity of an object persists. The strength of gravity of an object determines how fast the object will accelerate down the surface of the Earth by the effect of Earth’s gravity.

Velocity: Potential energy is energy stored by the object and utilized during the work is done. The object at its stable position has enough stored energy with it. Only when the external force is exerted on the object, the object is displaced from its position. As it is displaced, the speed or the velocity of the object does not change while the potential energy is converted to kinetic energy.

Hardness: Hardness is the ability of the objects to resist the external forces exerting on the object.

Brittleness: It is the property of the material to withstand permanent deformation; they break on the application of force rather than bending under any impact.

Rigidity: It is a property of the material that determines the strength and plasticity of the material enabling it to withstand even vigorous external pressure and impact.

Ductility: The materials which are not brittle and can be deformed and molted into any shape and size without losing its property of toughness are said to be ductile.

Size: Potential energy of the object is independent of its size; well it depends only on the mass per unit cross-section area of the object.

Volume: Potential energy depends upon the mass of the object other than its volume. More the volume of the object but lighter the weight then the object will be associated with a very small potential energy. Due to less mass, it will not experience sufficient gravitational pull by the Earth and will remain in the air for a longer duration.

Length: Potential energy is independent of the length of the object. Longer or shorter the length of the object, but the potential energy stored in the object depends upon the total mass of the object.

Albedo: Albedo is the property of the object to reflect the rays of light absorbed by the object and it is directly proportional to the rays of light incident on the surface of the object.

Wavelength associated with the object:The wavelength associated with the moving object is given as ƛ=h/p where h is a Plank’s constant h=6.626*10^-34Js. Hence, the wavelength is independent of the potential energy of the object and is not responsible for the change in the potential energy of the system.

Momentum: The momentum of the object does not affect the potential of the object if the momentum is conserved. If energy is conserved then the potential energy is also conserved.

What does not affect the amount of potential energy of an object

The potential energy of the object depends upon the mass of the object, its acceleration due to gravity, the height of the object from the surface of the Earth, types of forces acting between the two objects, external sources affecting the objects, electrostatic forces, the elasticity of the object, etc.

The density of an object does not decide the amount of potential energy the object can store. The more the density of the mass, the faster the object will fall back on the surface due to gravity. The mass per unit volume of an object will change by the influence of external heat but the mass will remain the same. Hence, the amount of energy stored does not depend upon the density of the object.

The acceleration due to the gravity of the Earth is constant and does not affect the potential energy of an object.

What does not affect gravitational potential energy

The weight of the object owing to gravity is mass times the acceleration due to gravity. The gravitational potential energy is the energy obtained by the object due to the presence of gravitational force. The potential energy due to gravity is given by V=mgh; which shows that the potential energy stored by the object is directly dependent on the mass of the object, its height from above the ground, and its accelerations due to gravity.

The potential energy of the object near the ground is negligible compared to the object raised at a certain height above the ground. The speed of the object due to gravity does not affect the gravitational potential of the object. It evidently depends upon the height of the object that will vary its potential energy.

Since the gravitational force is an attractive force, the work done to bring the two objects which show the force of attraction towards each other will be negative as the work is done is in the direction opposite to the direction of the attractive force.

Gravitational potential energy does not depend upon the size, volume, and density of the object.

Frequently Asked Questions

What is gravitational potential?

The gravitational potential is always negative because it is an attractive force.

The work done in bringing the point charge from infinity to the source by the effect of the gravitational pull is called the gravitational force and is given by the formula:-

Gravitational Potential=V=-GM/r

How can you increase the potential energy?

If the mass of the object is constant then the gravitational potential energy of the object can be increased by raising the height of the object from above the ground.

The potential energy between the two objects attractive to each other can be increased by increasing the distance separating them both and by decreasing the distance between the objects repelling away from each other.

Which state of the matter will possess the highest potential energy state?

The potential energy will be highest for a state of matter whose kinetic energy will be lower.

Hence, solid will have the highest potential level as its kinetic energy compared to all the other states of matter will be less.

Also Read:

What Affect Potential Energy: Detailed Facts

January 21, 2024December 17, 2021 by AKSHITA MAPARI

In this article, we are going to discuss various facts on what affect potential energy of the system.

The potential energy of a system may affect due to the gravity of the Earth, mass, temperature, height, displacement, work done, and there are various other factors.

What reduces potential energy

Every object in nature tends to occupy the least potential state as it can. This may be because every object governs upon the gravitational pull of attraction on every other object depending on the quantity of mass of the system. Every system in the surrounding is inbounded to attain the equilibrium state of rest.

what affect potential energy — The gravitational potential energy of the ball at height ‘h’

If the object is raised above the ground then it gains the potential energy V=mgh and the potential level increases as the distance of the object from the ground increases. But eventually, the object returns down to the lower state of the energy by converting its potential energy to kinetic energy while accelerating down to the Earth due to gravitational attraction. Hence gravity of the Earth along with the height of the object from the ground are both correlated for the reduction of the potential energy of the system.

The mass of the object does affect the potential energy of a system. Less the mass of the object, less will be its potential. A small unit of a mass at rest can produce an immense amount of energy. The potential energy is stored in the form of internal energy of a system which depends upon the heat stored by the mass and the work done by the system.

A change in the internal energy is equal to a change in the temperature of the system. If there is a fall in the temperature of the system then it is evident that there is a change in the internal energy of the system and hence the work done by the system is positive. Since there is work done, the potential energy of the system is reduced.

Moreover, the object with higher internal energy than the surrounding will have greater potential energy, thereby the object will tend to attain the lower potential energy state by transforming its energy to some other form, may be heat energy, and releasing it into the surrounding decreasing the temperature of the system. Hence, the potential energy decreases as the system endeavour to attain an equilibrium state.

If any object accelerates due to any external sources may be due to physical force, air resistance, or drag then the potential energy will be converted into kinetic energy. Hence potential energy of the object will reduce.

What affect potential energy

Mass: More the mass of the object more will be its energy. During free fall, the mass is equivalent to energy hence the body feels light and the potential energy is reduced.

Height: If the height of the object above the surface of the ground decreases the potential energy decreases and is zero on the surface of the Earth.

Temperature: With a decreasing temperature of the system, the potential energy of the system also lowers.

Gravity: Gravity always tends to pull the objects towards the center of the Earth, since potential at the surface of the Earth is zero, gravity is responsible for the reduction of the potential energy.

Internal energy of the system: The internal energy of the system is reduced only when the external work is done, hence the potential energy is decreased.

External work done: On application of the external force, the particles may displace from their original position. The displacement of the particle is due to the kinetic energy which is generated from the conversion of the potential energy of the particle. Hence, external forces result in the reduction of the potential energy of the system.

Elasticity: Greater the elastic property of the material, the more will be its capacity to store the potential energy.

Heat: When the heat is supplied to the system, its potential energy is increased. To attain the equilibrium state, the system transfers the heat into the surrounding. With decreasing heat of the system, the potential energy is also reduced.

Charge of the particle: The potential energy between the two similar charge particles will be higher whereas the potential energy of the two dissimilar charges will be less compared to the two like charges.

Distance: As the distance between the repellant increases, the potential energy will decrease; whereas, as the distance between the attractive charges will decrease, the potential energy will decrease.

What has the greatest effect on potential energy

The greatest effect on the potential energy is the gravitation force, elastic properties of the material, the distance separating the object from the source, and the mass of the object.

Since gravity is predominant on the Earth, it exerts a pull on all the objects on and around it. It majorly affects the potential of any object by attracting all the objects closer to the surface of the Earth and reducing it to zero.

Gravitational force is a weak attractive force existing in nature. Work done to keep the two systems bounded by the attractive pull from each other is negative since the work is done in a direction opposite the direction of the force of attraction. Thus, less potential energy is required as the distance between both increases. Since the gravity is inversely proportional to the distance between them.

Elasticity also shows the greatest effect on potential energy. Elasticity is the property of the material that can be stretched or compressed but the material regains its original shape and size. The potential energy is stored in this elastic object either by compressing or stretching. While doing so, the kinetic energy used is converted into potential energy and is stored in the object, which when unhand, lets out the energy in the form of kinetic energy. The energy stored due to compression and stretching is so high in the elastic material that when released gives out a tremendous amount of energy that the object is displaced suddenly at a high speed.

What determines the potential of energy

The mass of the object and its acceleration due to gravity determines the quantity of energy an object can hold. Whereas, how much energy is available with the system to do the work, and how much is the capacity of the object to do the work will determine the potential of the energy.

The greater the potential energy stored by the object more will be the work done by the object.

For example, the work done to bring together the two equally charged particles will be greater than the work done to bring closer the two oppositely charged particles. Because, two dissimilar charges will attract hence no work has to be done on those, while like-charged particles will repel away from each other hence greater work is to be done to bring the similar charges closer to one another.

The potential energy of the system corresponds to the work done by the system. If the work done by the system is large then the potential energy used to do the work is more. This in turn depends upon the mass of the object, the more the mass, more will be the energy stored with it; because every unit of mass can produce a large amount of energy. Potential energy is directly proportional to the weight of the object and the acceleration due to the gravity of the Earth.

Frequently Asked Questions

What is Potential Energy?

Potential energy is energy stored by the object either by converting any form of energy to potential energy or by its relative position to another object, by static force, electric force, or any other medium.

There are various types of potential energies, and the most common are gravitational, elastic, nuclear, electric, magnetic, chemical potential energy. Depending upon these the potential energy depends upon various quantities like mass, height, elastic constant, capacitance, voltage, magnetization, magnetic field, acceleration due to gravity, displacement, the height of the object from the surface of the Earth, a charge of the particles, etc.

How is the gravitational potential energy different from electric potential energy?

Gravitational potential energy is the energy stored by the system by the gravitational pull of the system whereas the electric potential energy is the effect of the charged particles.

Gravitational potential energy depends upon the mass, acceleration due to gravity, and height of the object from the ground whereas electric potential energy depends upon the charge and the length of the separation between the two objects.

Also Read:

Relationship Between Potential Energy And Distance:Detailed Facts

January 21, 2024December 16, 2021 by AKSHITA MAPARI

In this article, we are going to discuss the relationship between potential energy and distance.

The potential energy may increase or decrease with distance depending upon the types of forces acting on the system. For repulsive forces, the potential energy will reduce and for attractive forces, the potential energy will escalate with increasing distance.

Does Potential Energy Increase with Distance between Particles

The potential energy of any system veritably depends upon the distance depending upon the types of forces acting on the objects. The potential energy undeniably depends upon the distance and is inversely proportional to each other. If the force between the two is attractive then the potential energy will increase with increasing distance between them both, and if the force is repulsive then the potential energy will increase will decreasing the distance between them.

Let us elaborate our discussion on how does the change in distance will affect the potential energy.

Gravity:

A weak gravitational pull is felt on all the objects present near and on the surface of the Earth due to the gravity of the Earth. The potential energy of any object on the surface of the Earth is always equal to zero. The potential energy related to any object depends upon the weight of the object due to gravity and the height of the object from the ground. Thus the potential energy is denoted as:-

V=mgh

This shows that the potential energy is directly proportional to the height of the object above the ground. But, as the gravitational force of the Earth is exerted on the objects surrounding it, the object is pulled back towards the Earth’s surface and during that time the potential energy of the object is utilized to return back to the ground converting the potential energy into kinetic energy that accelerates the object to the ground. This is the universal fact that all the objects tend to occupy the least potential energy level.

Gravitation Potential Energy between two bodies in space:

The gravitation force exerted on the two bodies in space is inversely proportional to the square of the distance between them both. It is represented by the formula

F=G*(m₁m₂)/r²

Where G is a gravitational constant.

The potential energy of the masses due to the gravitational force is the integral value of the attractive force experience between the two masses and hence we can write

Potential energy –

From the above equation, we can say that the potential energy of the two bodies depends upon the distance between the two joined in a line. The negative sign indicates that the work done is negative and hence the force is an attractive force. Therefore, if the distance between the two increases then less will be the work done and the potential energy will increase.

This clearly shows that, if the distance between the heavenly bodies is large, this means that the potential energy associated with the heavenly object is also greater.

Electric potential energy:

Electric potential is the amount of potential per unit charge, whereas electric potential energy is the amount of energy required to bring the charged particle from the distance to that point.

Consider a charge particle q₁ having a positive charge of 1C kept at a distance ‘r’ from the point charge.

relationship between potential energy and distance — Charge particle at a distance ‘r’ from source

Then the potential of a charge q₁will be

When the point charge is replaced by a charge q₂ having the same charge as that of q₁ then the force experience on charge q₁ due to q₂ and on charge q₂due to q₁ is

Two equal charges separated by a distance ‘r’

Since potential energy associated with the particle is the integral result of all the forces acting on the particle. Therefore, the potential energy will be equal to

In this case, as the separation between the two charges will increase, the potential energy will decrease with respect to distance. As two equal charges will repel away from each other, large potential energy is required to bring the two charges closer to one another.

Now, if the charge kept at the source was negatively charged, then the electrostatic force exerted equally on each particle would be

Two oppositely charged particles separated by a distance ‘r’

The negative sign of the potential energy indicates that the force between the two oppositely charge particle is attractive. In this case, as the distance between the two charge particles increases the potential energy generated by the particles to attract each other will also increase.

Potential energy due to spring:

Consider a wooden block of mass ‘m’ attached to the one end of the spring having spring constant value ‘k’ and another end of the spring attached to the rigid wall. The force is applied in the direction as shown in the figure to displace the wooden block to the distance ‘x’ from the initial position. The force required to pull the wooden block attached to the string is kx. A block will gain enough potential energy which when released is converted into kinetic energy and due to the elastic property of the spring, a block will move slightly towards the rigid wall.

The potential energy of the spring is equal to the work done by the spring and is given as the integral of the force acting on the mass due to spring. Therefore,

If the mass attached to the string is pulled further, the potential energy will also increase by the square of the displacement.

How Mass and Distance of an Object Affect the Potential Energy

As per the mass-energy equivalence relation described by Albert Einstein and formulated by the equation E=mc²; the mass of the object is correlated to the energy it is associated with. The internal energy stored in the object is its potential. To do any work this potential energy is utilized by transforming this energy to some other form of energy.

In most of the cases as seen above, the potential energy decreases with distance because the potential energy is inversely proportional to the distance between the object and the source or between the two objects. But we have also noticed that when the force between the two bodies is attractive then the potential energy increases as the distance separating both increases.

Why Does Potential Energy Increase with Distance

If the distance separating the two objects increases then the potential energy will also rise if the force acting between the two objects is an attractive force. This is because; less and lesser force will be required to keep the objects apart from each other if we keep on increasing the distance between them both since the force decreases to the square of the distance between them increased.

Work done by the system resembles the potential energy required to do the work. If the two bodies attractive to each other are placed closer to one another, then very less potential energy will be required to bring the two objects closer. If the bodies are far away then more potential will be required to do the same work. More and more potential energy will be required if the distance between the two objects becomes larger.

Frequently Asked Questions

Find out the potential energy of the string having a spring constant 25Nm^-1 and displacement 20cm.

Given:

k=25Nm^-1

x=20cm=0.2m

The potential energy stored in a string stretched at a distance of 20 cm is 0.5 J.

Why does the potential energy of the attractive force is negative?

In attractive forces, the particles exert a force of attraction to pull them closer to each other. Work has to be done to keep them both at a finite distance.

Force applied to do so is in the direction opposing the force of attraction between the two particles and hence the work done in a direction to oppose the attractive force. Since the potential energy applied is in corresponds to the work done, therefore it is negative.

Also Read:

21 Examples of Potential Energy: Detailed Facts

January 21, 2024December 15, 2021 by AKSHITA MAPARI

In this article, we are going to discuss some examples of potential energy in details.

The following is a list of examples that exhibits the potential energy:-

Man Lifting a Weight

A man receives the potential energy that he receives from the food that he intakes and is stored in the form of chemical potential energy. Potential energy is required to lift the heavy load is equal to the weight of the load due to the force of gravity acting downward and the height at which the weight has to be raised and can be represented as

Work done=Potential Energy=mgh

Work done is equal to the potential energy released.

Water Stored in the Dam

As the volume of the water stored in a dam rises and the point of elevation of the water level in the dam goes high, the potential energy of the volume increases. Until the water is stored in the dam, it keeps on adding the gravitational potential energy until the volume of the water reserved in between a sturdy construction is stable, and when released, the potential energy of the water is converted into kinetic energy and water flows from the dam.

Ocean currents

The ocean current generates enough energy which is also used to run a turbine to generate electricity. The potential energy present in the ocean current is due to the gravitational potential energy as well as the tidal energy. As the density of water is less than the plates floating on the asthenosphere, hence the gravitational pull effects exerted on the Earth by the Moon is seen on the oceanic water developing tides. More the quantity of water more will be the effect observed.

A car parked on the top of the hill

Consider a car parked on the top of the hill on a steeper road as shown in the diagram above. The force due to gravity is acting slightly backward that would result a car tosweep down the hill. Plus the frictional force on being in contact with the metallic road and the air resistance drags the car backward. But still, the car does not sweep down is only because of the potential energy that keeps the car in a steady position.

The freefall of a ball

Change in the form of energies of ball thrown in the air

When you throw the ball high up in the air, it raises high due to the potential energy applied to a ball in a particular direction being changed to the kinetic energy,and hence the ball accelerates in the air. As the height of the ball above the ground increases, the kinetic energy of the ball is converted into potential energy. When enough potential energy is stored into a ball, means when all the kinetic energy of the ball is converted to the potential energy, the ball is held stable in the air for a few milliseconds and then returned towards the grounds due to the gravitational pull and is called the free fall of the ball.

But due to the free fall of the ball, it still has potential energy associated with it and hence it bounces back after bouncing the ground converting its potential energy to kinetic energy.

Slinky walking down the stairs

If you have a slinky, place it on the step of your staircase and drag another end of the slinky to one step down and leave it. You will observe that the slinky will walk down the stairs by itself without applying any external force to it.

This is because, for the coils of the slinky to collapse from one end to another, the potential energy stored is converted into kinetic energy. The kinetic energy is then converted into potential energy and supplies enough potential to the slinky to raise its topmost end and step onto the next. This is how the slinky is able to walk down the steps independently.

examples of potential energy — Slinky at equilibrium;
Image Credit: etsy

On reaching the plane ground, the slinky comes to a rest at the equilibrium position, distributing equal energies on both the ends and the balance is created. While walking down the stairs, the force due to the gravity was also acting on the slinky that made the coil collapse together one above the other and there was no chance for the mass or the energies to balance out and attain the equilibrium state.

Stretched rubber band

The rubber is an example of an elastic material that regains its original shape and size after being stretched. When a rubber band is stretched the potential energy is inbuilt in the rubber band which is equal to half times the elastic constant and the square of the change in length of the rubber band on stretching and is called the elastic potential energy due to elasticity of the rubber.

This elastic potential energy is converted into kinetic energy when the rubber band is released. This energy is so high that it will thump on your finger if you released it in your hand or swerve away with the energy.

Archer’s bow with string pulled back

The archer attaches the bow and pulls the string back. On pulling the sting back, it built enough potential energy in the string. When the string is released the potential energy is supplied to the bow which is then converted into kinetic energy to direct the bow towards the target.

A rock sitting at the edge of a cliff

A rock sitting at the edge of a cliff would have rolled down the cliff if there was no potential energy stored in the rock. Hence, a rock sitting on a cliff possesses potential energy. If the rock slides from the cliff and falls due to the external pressure or air resistance then this potential energy is converted into kinetic energy used in the acceleration of the rock.

Nuclear Fission

A nucleus splitting into two in a spontaneous nuclear reaction is called the nuclear fission. This energy released during the fission reaction is tremendous. The potential energy stored inside the nuclear is converted into kinetic energy hence the after splitting into two nuclei, both the nuclei divert from each other attaining very high speed.

Football on the ground

Football at rest has zero kinetic energy with it. On kicking the football, the potential energy is supplied to the football. The ball is displaced from its initial position by converting this potential energy into kinetic energy.

Tree branches high up on the tree

Have you wondered how the branches of trees remain amalgamated together even at high heights then attracting down the ground due to gravitational force and falling off from the trunk of the tree. This is mainly because of the potential energy stored in the tree.

Food

The food that we eat has chemical potential energy that provides energy after metabolism. This potential energy is stored in our body and is utilized while doing any activity.

Batteries used in a remote control car

The batteries that are used in remote control carspossess chemical potential energy which is supplied to the car to accelerate. The chemical energy stored in the batteries is released in the form of heat and light through a chemical reaction.

The gravitational potential energy of the Earth

The gravitational pull of the Earth is exerted on all the objects surrounding it and present on its surface, the energy acquired by the Earth to exert a force due to gravity is known as the gravitational potential energy of the Earth.

The potential energy associated with the object above the ground at height ‘h’ is given by the formula

Potential Enery=mgh

Where ‘g’ is the acceleration due to gravity,

Electric potential energy

Electric potential energy is a potential energy stored by the charged particles in corresponding to the conservation of the Coulomb forces acting between the two charged particles separated by the distance ‘r’ and is formulated as

Potential Energy

Firecrackers

Firecrackers are made from chemical powders that are highly reactive and fissionable. When the firecrackers are lit, the chemical potential energy is released and hence becomes explosive.

Mass pulled attached to the string

Consider a mass attached to the one end of the string and another end of the string is fixed on the wooden plank attached tightly to the wall.When the mass is displaced to a distance ‘x’ from its initial position, the potential energy is set into the string is equal to the half times the spring constant and the square of the displacement given by P.E = (1/2)kx²

Hooke’s law states that the force required to either extend or compress the string is directly proportional to the displacement within the limit of the elasticity of the spring and represented as F=-kx where k is a spring constant.

When the wooden block is released, the block on the table slightly moves ahead from its initial position because of the elastic potential energy in the spring, the potential energy is converted to the kinetic energy, and finally, the block of mass returns to its initial position.

Trampoline

While jumping on the trampoline, Newton’s 3^rd law acts which states that “Every action has an equal and opposite reaction.” The force exertedon the trampoline on making a jump over it will react back on the body exerting a force equal in magnitude and opposing the direction of force pushing the body in vertical direction from the trampoline. This is due to the elastic potential energy of the trampoline.

On jumping, the potential energy is supplied to the body which is then converted into kinetic energy utilized for the nextjump on the trampoline. The body is held in the air for few milliseconds because it exerts enough potential energy.Due to gravitational force, the force of the body acts downward and the body returns back to the trampoline and the process repeats each time increasing the potential associated with the body and hence experiences free fall while returning down on the trampoline.

Athletic running

For running for a long distance, the athlete needs enough potential energy. The potential energy is effective while running which is a form of a kinetic energy.

If a person doesn’t have enough potential energy then the person will fall down on the ground. The intake of food provides us with the required energy which is stored in the form of chemicals inside our body.

Ferris wheel

As the wheel rotates from the ground to the topmost point on the wheel, the potential energy is stored in the body and hence the passenger feels heavier by weight. After reaching the top of the wheel, the potential energy is converted into kinetic energy and the body freely accelerated downward due to the effect of gravity, hence the passenger feels lighter till reaching at the bottom of the wheel.

Frequently Asked Questions

What is the gravitation potential energy of a ball having a mass of 280 grams when it is raised to a height of 5 m above the ground?

Given: Mass of the ball m = 0.28 kg

Height h = 5 m

Acceleration due to gravity g = 9.8 ms^2

Therefore, potential energy

U=mgh=0.28*9.8*5=13.72J

What are the different types of potential energies you can classify?

The potential energy is internal energy stored in the system.

The five main classifications of the potential energies are the gravitational, electrical, nuclear, chemical and elasticity.

What are the various factors affecting the potential energy?

The energy is always conserved; well it can be transformed from one form of energy to another.

The factors affecting the potential energy are the mass of the object, its accelerations due to gravity, height from the source, the external sources applied, mobility of the particles, etc.

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Is Gravitational Force A Central Force: Why, How And Detailed Insights

January 20, 2024December 14, 2021 by AKSHITA MAPARI

In this article, let us discuss whether gravity is a conservative force or non-conservative, and secondly, is gravitational force a central force or non-central.

Gravitational force is said to be a conservative force because the work done on the object to travel from one position to another is independent of the time taken and the magnitude of the force is constant.

What is Gravitational Force

The gravitational force is one of the fundamental forces in nature and is the weakest force of attraction.

The two objects having mass exert a force of attraction on each other, and this force is centralized at a focus between the line joining the two objects. As the distance between the two increases, this gravitational pull among the both becomes weaker and weaker by the square of the distance separating them both.

The law of Gravitation states that “Every object attracts every other object in the universe by the force which is directly proportional to the product of the two objects and inversely proportional to the square of the distance between the two” and is denoted by the equation:

F=G*(m₁m₂)/r²

G=6.67*10^-11

Where

m₁ is mass of object 1

is mass of object 1

m₂ is mass of object 2

is mass of object 2

‘r’ is a distance between the two objects

At r=∞, the gravitational force will be equal to zero.

Why Gravitational Force is Central Force

When the two bodies are bounded by the gravitational force of attraction, the force imposed is equal in magnitude and acts in opposite directions towards each other separated by a distance.

Consider a satellite revolving around the Earth. The mass of the satellite compared to the Earth is very negligible and hence the Earth will accelerate at a very minute rate than that of the satellite. The gravitational attraction between both will tend the satellite having less mass than the Earth to revolve around the Earth in a circular orbit. This follows Kepler’s 2^nd Law, according to which “the line joining the satellite to the planet Earth will sweep equal areas in equal interval of time”.

For a body to keep in a continuous motion the force has to always act towards the center and the velocity of the object radially pointing outward. The magnitude of the force at the focus depends upon the length of the separation between the centers of gravities of both systems. The gravitational pull between the two keeps the satellite revolving around the Earth in a circular orbit, hence gravitational force is a central force.

is gravitational force a central force — Satellite revolving around planet Earth; Image Credit: Quora

The satellite around the planet will move in uniform circular motion under the action of a centripetal force given by

F_c=mv²/r

Equating this with equation of gravitational force

mv²/r =G*(Mm)/r²

‘v’ is the speed of orbiting satellite around the Earth.

The cycle maintains its momentum while riding is actually because of the central force absorbed by the spinning wheels that help to keep the momentum of the cycle constant and hence the rider is able to keep the cycle in a vertical position. If the momentum applied to the cycle is equal to zero then the cycle will fall on the ground. The direction of the angular momentum lies along the axis of rotation. The greater the speed of the wheels more will be the momentum of the cycle. We can ride a bicycle as the momentum is conserved because of the circular motion of the wheels.

In the same manner, the momentum of the satellite is conserved due to the central force acting due to the gravitational force between the Earth and the satellite.

Why Gravity is Conservative Force

Gravity is a force of attraction experienced by objects towards the center of the Earth. Every object having mass possesses a center of gravity and is bonded to one another by the gravitational pull of attraction. The gravitational force is a long-range force between the two bodies having mass and does not depend on any field and therefore is a non-contact force.

The weight of any object on the Earth will be the mass times the acceleration due to gravity. The potential energy of the object at a certain height above the surface of the Earth is P.E. = mgh. Work done in bringing the object from height ‘h’ to the surface of the earth is the same as the potential energy associated with that object at a particular height ‘h’.

The body at rest has some potential energy associated with it, if there is a slight change in potential energy then it is obvious that there is some work done by the system. The work done in a close path is always zero as the force experienced on the bodies is independent of a path taken and hence the gravitational force is conserved.

Work done to displace the object from one place to another is

Work done to displace the satellite from point 1 to point 2 is

Since work is associated with the potential energy, Potential Energy U= -G*(m₁m₂)/r²

The negative sign indicates that the gravitational force is always attractive.

ThereforeForce F=-dU/dr;

In central force, the total energy T.E. = K.E. + P.E. =(1/2)mv²+mgh

The angular momentum between the two masses L=r*mv=Constant

This implies that the momentum of the object in orbit is conserved and no work is done in this process hence the total energy is conserved. Therefore a gravitational force is conservative.

Unit of Gravitational force

The unit of gravitational force is Newton, named after the scientist Isaac Newton for his discovery.

The value of the universal gravitational constant G is 6.67*10^-11 N.m²/kg². In the CGS unit we have

Therefore, the unit of the gravitational force is Newton.

Frequently Asked Questions

What is the force of gravity acting on the object having a mass of 1.5kg on the surface of the Earth?

We know:

Mass of the Earth M_E=5.98*10²⁴ kg

Mass of the object m=1.5kg

The radius of the Earth r=6.38*10⁶m

Acceleration due to gravity g=9.8m/s²

Gravitational constant G=6.67*10^-11Nm²kg²

Solution:

What is the range of gravitational force?

The gravitational force is equal in magnitude and acts in opposite directions towards each other.

The range of the gravitational force is infinite. The gravitational force is strongest between the objects having high masses and are closest to each other; the same becomes weaker if the distance between the objects is much larger and at an infinite distance, no gravitational force is observed.

What is a central force?

Spring force, electrostatic force, gravitational force, centripetal forces are some examples of the central forces.

Force acting on the object is directed along the line joining the object and the origin is called central force.

Will you observe a change in your weight if you move from Goa to Greenland?

Yes. Greenland is located near the North Pole of the Earth.

As the acceleration due to gravity is greater at the poles there will be a slight increase in the weight than your weight measured in Goa.

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