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Important Question

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 ]

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 )

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**Q.What do you mean by Energy?**

Energy defines as the capacity to do work. 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.

**Q.What are the formulas to determine the energy of a matter?**

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.

**Q. What do mean by the 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.

**Q.What is the Law of Energy Conservation ?**

According to the **Law of Energy Conservation, **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.

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