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A fundamental idea in the cosmos, energy is what drives all physical processes and makes life possible as we know it. It can be transformed from one form to another and exists in multiple forms, such as the potential energy held in an object’s location or the kinetic energy in moving things. In this article, we will learn about the different aspects of the energy and energy formula’s.

## Energy Formula

The idea of energy is essential to physics. Energy is nothing more than the ability to perform labor. Simplest Under the influence of energy, an item can perform work. In other words, an object can only work when there is energy present in it. We can obtain energy from a variety of sources, including light, atoms, heat, and other things that give rise to different types of energy. Here, we shall study the fundamentals of the energy and Energy formula with solved mathematical problems.

## Energy Definition

Energy is the capacity to carry out any type of physical action ability of an object to act is called its energy. The total amount of work an object can do is its energy. Hence energy and work are the same amounts. So, the unit of energy and the unit of action is the same.

We know the Law of conservation of energy that Energy is never created or destroyed, only we can convert it from one form to another. In. the whole universe the total amount of energy is constant. When we switch on a fan, the electronic energy is converted into mechanical energy. Energy exists in many forms. Mechanical energy, Heat energy, Light energy, Sound energy, Magnetic energy, Electrical energy, Chemical energy Atomic energy. In this topic, we learn about mechanical energy formulas in detail.

## Energy Equations

There are several energy equations used in physics to describe different forms of energy and their relationships. Here are some commonly used energy equations:

- Kinetic Energy (KE) equation: The kinetic energy of an object is given by the equation: KE = (1/2)mv² Where: KE is the kinetic energy (measured in joules, J) m is the mass of the object (measured in kilograms, kg) v is the velocity of the object (measured in meters per second, m/s)
- Potential Energy (PE) equation: The potential energy of an object depends on its position or state. Here are a few examples:a. Gravitational Potential Energy: The gravitational potential energy of an object near the Earth’s surface is given by the equation: PE = mgh Where: PE is the gravitational potential energy (measured in joules, J) m is the mass of the object (measured in kilograms, kg) g is the acceleration due to gravity (approximately 9.8 m/s²) h is the height or vertical distance of the object from a reference point (measured in meters, m)b. Elastic Potential Energy: The elastic potential energy stored in a stretched or compressed spring is given by the equation: PE = (1/2)kx² Where: PE is the elastic potential energy (measured in joules, J) k is the spring constant (measured in newtons per meter, N/m) x is the displacement from the equilibrium position (measured in meters, m)
- Conservation of Energy equation: According to the law of conservation of energy, energy cannot be created or destroyed but can only be converted from one form to another. The conservation of energy equation is: Total Initial Energy = Total Final EnergyThis equation states that the sum of all forms of energy (kinetic, potential, thermal, etc.) at the initial state of a system is equal to the sum of all forms of energy at the final state, assuming no energy is lost to external factors.

## Energy Formula Physics- Units of Energy (Joules)

As we know earlier that the ability of a substance to do work is called its energy. The unit to measure Energy is **Joules (J)**, commonly known as** Newton-meters,** which is the SI unit of energy. The energy used is measured in Joules, or Newton-meters, when an item is subjected to a specific amount of force in Newton and moves a certain distance in meters.

## What is the Formula of Energy Dimension

We can find the dimensional formula for energy by using the basic concepts of unit. The dimensional formula for energy is given by:

[M^{1} L^{2} T^{–}^{2}]

where M is the dimension for Mass

L is the dimension foe length

T is the dimension for Time

## Formula of Energy in Physics Class 9, 10, 11, and 12

Energy is mainly classified into two types. Kinetic Energy and Potential Energy.

The formula to determine the Kinetic energy of an object is – **K.E = ½ mv²**

[ where,m= Mass of the object, V = The velocity of the object]

The formula to determine the Potential energy of an object is –** P.E = mgh **

Where m denotes the object’s mass, g denotes gravitational acceleration, and h denotes height.

Let’s understand these terms and forms one by one.

## What is the Mechanical Energy formula in Physics?

The ability of an object to do work due to its motion, position, or shape, or all three is called it’s mechanical energy. Mechanical energy is divided into two parts – (i) kinetic energy and (ii) potential energy.

## Kinetic Energy

Without the aid of Newton’s equations of motion, it is feasible to analyze the dynamics of a mechanical system using the ideas of work and kinetic energy. Many complicated occurrences can be simply analyzed, especially when this notion is applied. But Newton’s law of motion serves as the cornerstone of the idea of work-kinetic energy. Therefore, the outcome is the same regardless of how the dialogue is conducted.

## Definition Of Kinetics Energy

The ability of a moving object to do work due to its motion is called it’s kinetic energy. To stop an object in motion, an external force must be applied. The amount of work the object does against the applied force before it stops is a measure of the object’s kinetic energy.

## Examples of kinetic energy

We see many examples in our daily life where a force is transferred to an object when it is in motion and the object is able to do work. For example,

(i) Bullets fired from guns can penetrate glass windows. But if the bullet is stopped on the glass, the bullet cannot penetrate the glass. So it is understood that bullets are capable of doing something for speed.

(II) When hammering a nail into a wall, the hammer is not only pressed against the head of the nail. Bringing the hammer from some distance and striking the head of the nail with great speed, it penetrates the wall. A dynamic hammer is capable of acting for its motion.

The kinetic energy of water and wind is used for various purposes of human welfare. Electricity is generated by running dynamos using the kinetic energy of rapid water flows in waterfalls and torrential mountain rivers. By harnessing the current of air, the machine drives the grain and draws water from the well.

## Derivation of Kinetic Energy Formula in Physics

Let us assume an object of mass m. moving along a straight line with velocity. What is the amount of kinetic energy of the object? Suppose, a certain force F is applied against the object to stop its motion. As a result, the object decelerates and object travels a distance, and stops. As we know, S is the measure of the kinetic energy of the object against F before it stops. therefore,

The kinetic energy of an object = work done against the force

F = F. s = mas [F = ma] …….(1)

The inertial velocity of the object can be written as v = 0,

V² = u² – 2as. [By using formula v² = u²+ 2as]

or, 2as = u²

or, as = u²/2 ……. (2)

Substituting the value of as in (1) from (2) gives,

The kinetic energy of the object =½ mu²

Linear kinetic energy of object is.= 2 x mass x (linear velocity) ²

We can conclude when an object is accelerated by a force, its speed increases but when it is decelerated, its momentum decreases.

## Potential Energy- Definition of Potential Energy

The ability of an object to act due to its particular position or shape is called its potential energy.

Here, the condition (i.e. position or shape) of an object is considered as proof or standard condition except all other conditions are called special conditions. The amount of work done by an object in returning it from a particular position or shape to its proof position or shape is a measure of the static energy of the object. Note that the proof or normal state of an object is also called zero states.

## Example of Potential Energy

Hydroelectricity is generated mainly by using the static energy of water. The water of the river is retained by a dam at a high place. This water is equipped with stability. This static energy is converted into kinetic energy when falling down. Then the turbine is rotated using the kinetic energy of the water. As a result, electricity is generated.

## Derivation of Potential Energy Formula in Physics

Let’s say, An object of mass (m) is lifted to a height of h above the surface.

Force acting on object = Gravitational force = mg

Work against gravitational force = force × displacement = mg h

This work is stored in the object as static energy.

Static energy of matter = mgh = Mass of the object x Gravitational acceleration × Height of the object from the reference surface

[ the value of g can be taken as constant in cases where the value of height / is negligible compared to the radius of the earth ]

## Energy Formula Physics in Terms of Force: Problems

Q**.Find the kinetic energy of an object of mass 10 kg just before it falls from a height of 10 m to the ground. g = 980 cm/s² .**

→ Let’s say the velocity of the matter just before he touches the ground

V² = 2gh = 2 x 9.8 x 10 ( Here, h = 10m )

= 196 m²/s²(Answer)

**Q. An object of mass 1 kg is thrown vertically upwards with a velocity of 250 cm per second from a height of 8 m above the ground. What will be the kinetic energy of the object at the moment before it touches the ground?**

→ Let’s say the velocity of the object is v just before it hits the ground

The upper side is found on the positive side, v²=u²+2gh

= (2.5)²+2 x 9.8 x 8

[” u” = 250 cm / s = 2.5m / s, g = 9.8m/s]

and h = -8m]

= 163.05 m²/ s²

Hence the kinetic energy of the object just before it touches the ground= is ½ mv²

= ½x 1 x 163.05 = 81.525 J . ( Answer )

## Power Formula Physics

In physics, the power formula relates the amount of work done or energy transferred to the rate at which it is done. The power (P) is defined as the amount of work (W) done or energy transferred per unit time (t). The power formula is given by:

P = W / t

Where: P is the power (measured in watts, W) W is the work done or energy transferred (measured in joules, J) t is the time taken (measured in seconds, s)

This formula indicates that power is directly proportional to the amount of work done or energy transferred, and inversely proportional to the time taken. In other words, if the same amount of work is done in less time, the power output will be higher.

It’s important to note that power can also be calculated using other formulas depending on the context. For example, in electrical circuits, power can be determined using the formula P = VI, where V represents voltage and I represents current. In rotational systems, power can be calculated as P = τω, where τ is the torque and ω is the angular velocity.

## Power Equation Physics

The power equation in physics relates the rate at which work is done or energy is transferred to the amount of work or energy and the time taken. The power (P) is given by the equation:

P = W / t

Where: P is the power (measured in watts, W) W is the work done or energy transferred (measured in joules, J) t is the time taken (measured in seconds, s)

This equation indicates that power is the amount of work done or energy transferred per unit time. It shows that power is directly proportional to the amount of work or energy and inversely proportional to the time taken.

Another related equation for power can be derived using the concept of force (F) and velocity (v). If an object is moving with a constant velocity, the power can be expressed as:

P = Fv

Where: P is the power (measured in watts, W) F is the force applied (measured in newtons, N) v is the velocity of the object (measured in meters per second, m/s)

This equation states that power is equal to the product of force and velocity. It is commonly used in situations involving a constant force acting on an object in motion.

It’s important to note that there are other power equations specific to different areas of physics, such as electrical power equations involving voltage and current or rotational power equations involving torque and angular velocity. The choice of the appropriate power equation depends on the specific context and physical system being analyzed.

## Energy Formula in terms of Power

We can express the relation between energy and power. This formula is valid even in the case of electricity. The formula of energy in terms of power is given by:

Energy = Power x Time

## Energy Formula Force

There is a very strong relation between the force and energy. As we know, work done and energy are equivalent physical quantity. We can show the formula for energy in terms of power. The same is explained below.

As work done = Force x displacement

work done = energy

so, energy = force x displacement

## What is energy in Physics?

In physics, energy is a fundamental concept that describes the ability of a system to do work or cause changes. It is a scalar quantity that can exist in different forms and can be transferred or transformed from one form to another.

Energy comes in various forms, including:

- Kinetic Energy: This is the energy possessed by an object due to its motion. The kinetic energy of an object depends on its mass and velocity. The equation for kinetic energy is KE = (1/2)mv², where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
- Potential Energy: Potential energy is associated with the position or state of an object. There are different types of potential energy, including:
- Gravitational Potential Energy: This is the energy possessed by an object due to its position in a gravitational field. The equation for gravitational potential energy is PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical distance.
- Elastic Potential Energy: This is the energy stored in an elastic material when it is stretched or compressed. The equation for elastic potential energy is PE = (1/2)kx², where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

- Thermal Energy: This is the energy associated with the temperature of an object or a system. It is related to the random motion of particles at the microscopic level.
- Chemical Energy: Chemical energy is stored in chemical compounds and is released or absorbed during chemical reactions.
- Electrical Energy: Electrical energy is associated with the movement of charged particles, such as electrons, in an electrical circuit.

These are just a few examples of the various forms of energy. The law of conservation of energy states that energy cannot be created or destroyed but can only be transferred or transformed from one form to another. This principle underlies many fundamental concepts and equations in physics.

## Energy Formula in Physics: Most Important

The formula for energy depends on the context and the type of energy being referred to. Here are some common formulas for different types of energy:

**Kinetic Energy**: The energy of motion. The formula for kinetic energy (KE) is: ${\mathrm{}}^{}$**Potential Energy**: The energy stored due to an object’s position or arrangement. The formula for gravitational potential energy (PE) near the Earth’s surface is: $\u210e$**Elastic Potential Energy**: The energy stored in elastic materials as the result of their stretching or compressing. The formula for elastic potential energy is: $\frac{\mathrm{}}{}$**Thermal Energy**: The internal energy of an object due to the kinetic energy of its atoms and molecules. There isn’t a simple formula for thermal energy, as it depends on various factors like temperature, material, and state of the substance.**Einstein’s Mass-Energy Equivalence**: This famous equation relates mass and energy, showing that they are interchangeable: ${\mathrm{}}^{}$

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