Conservation of Mechanical Energy - Definition, Example, Formula, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 05:08 PM IST

In this article, we are going to learn about mechanical energy and types of mechanical energy. We will learn what is mechanical energy or the mechanical energy definition, what are the two forms of mechanical energy and also state the law of conservation of mechanical energy. The mechanical energy meaning is , the energy of a body due to which the body gets ability to do work for its motion or speed. By discussing some mechanical energy example we will learn how it exist in this physical world.

Conservation of Mechanical Energy - Definition, Example, Formula, FAQs

Mechanical Energy:

The sum of kinetic energy and potential energy of a body, is known as mechanical energy of a body .

Example of mechanical energy –

A ball kept on the top of a building at rest ,that is potential energy .After some time the ball is freely falling downward, this is kinetic energy .

Example of mechanical energy:

Q. Kinetic energy of an object is 12 J and potential energy 8 J, what is the mechanical energy of the object ?

Ans: kinetic energy = 12 J

Potential energy = 8 J

Total mechanical energy of the object = 12 + 8 = 20 J

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Mechanical Power:

The rate of doing mechanical work with respect to time is known as mechanical power.

Law of conservation of mechanical energy or principle of conservation of mechanical energy:

The law of conservation of mechanical energy states that, in an isolated system or if there is no energy dissipation, then the total mechanical energy of the system remains constant.

Conservation of mechanical energy formula:

Mechanical energy = Kinetic energy + potential energy

Example for conservation of mechanical energy:

If a ball of mass m is dropped from height h , initially is was at rest at that height. When it is falling freely the potential energy gets converted into the kinetic energy in the motion.

Types of mechanical energy:

There are two types of mechanical energy.

Kinetic energy
Potential energy

Kinetic energy:

The mechanical energy of a body due to its motion is known as kinetic energy. The working power of a body due to its motion can also be called kinetic energy .

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Example of kinetic energy:

A ball is moving with a velocity
A freely falling body
A bullet is fired from a gun towards the target

Mathematical formula of kinetic energy:

Kinetic Energy= $\frac{1}{2}mv^2$

Where, m is the mass and v is the velocity of the object .

Example problem :

Q. A ball of mass 50 kg is moving with a velocity 5 m/s , what is its kinetic energy ?

Ans: mass of the ball , m = 50 Kg

velocity , v = 5 m/s

kinetic energy of the ball = $\frac{1}{2}mv^2$

= $\frac{1}{2}(50kg)(5\frac{m}{s})^2$

=125 J

Potential energy:

The mechanical energy of a body due to its position is known as potential energy. The working power of a body due to its position or configuration can also be called potential energy.

Example of potential energy:

A ball is kept in rest at a height
A box is kept in rest at an incline plane (friction less)

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Mathematical formula of potential energy:

potential energy=mgh

Where, m is the mass of a body, h is the height from the ground where the object is kept, g is the gravitational acceleration.

Example problem:

Q. A ball of mass 50 kg is kept at height 15 m above the ground, what is its potential energy?

Ans: mass of the ball , m = 50 Kg

height, h = 15 m

gravitational acceleration, g = 9.8 m/s²

Potential energy of the ball = mgh

= (50 Kg)×(9.8 m/s²)×(15 m)

= 7350 J

NCERT Physics Notes :

There are few more types of potential energy:

Elastic potential energy
Gravitational potential energy

Elastic Potential energy in a spring:

The energy which is generated due to application of force .When the external force is applied to the elastic object then the elastic potential energy stays stored until the objects comes to its equilibrium position.

Example: when a spring of spring constant k is displaced from x (equilibrium position) to y position , then the potential energy of the spring will be, 1 / 2 k(y-x)²

Gravitational potential energy:

The potential energy of a body when it is kept at height from the earth’s surface, it is known as gravitational potential energy of that body.

Example: If the mass of an object is m , height from the earth’s surface is h and gravitational acceleration is g ,therefore the gravitational potential energy of the object will be mgh .

The sign of gravitational potential energy is negative (‘-‘).

When a body is lifted upwards from the earth’s surface the displacement of the body is in the opposite direction of the earth’s surface. As the displacement's direction is negative , the total gravitational potential energy becomes negative.

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Frequently Asked Questions (FAQs)

1. What is mechanical energy?

The sum of kinetic energy and potential energy of a body is called mechanical energy of a body.

2. What is the S.I unit of mechanical energy?

The S.I unit of mechanical energy is Joule.

3. What is conservative system?

When the total mechanical energy of a system is conserved , then that system is called conservative system. The force acting on such systems is known as conservative force.

4. Give some examples of conservative forces.

Gravitational force , electrostatic force, magnetic force between two poles etc.

5. What is non-conservative force?

In a system where resistive forces are present and mechanical energy of that system is not conserved, such a system is called non-conservative system. The resistive force is known as non-conservative force.

Example of a non-conservative force is frictional force .

6. What is the conservation of mechanical energy?

The conservation of mechanical energy is a fundamental principle in physics stating that the total mechanical energy of an isolated system remains constant over time. It means that energy cannot be created or destroyed, but can only be converted between different forms, such as kinetic and potential energy.

7. How does the conservation of mechanical energy relate to work?

The conservation of mechanical energy is closely related to work. When work is done on or by a system, it changes the system's mechanical energy. In a closed system with no external forces, the work done by conservative forces (like gravity) doesn't change the total mechanical energy, as it merely converts between potential and kinetic energy.

8. Can you explain the difference between conservative and non-conservative forces in the context of energy conservation?

Conservative forces, like gravity, allow for the conservation of mechanical energy because the work they do is path-independent and reversible. Non-conservative forces, like friction, do not conserve mechanical energy as they convert mechanical energy into other forms, such as heat. In systems with non-conservative forces, total mechanical energy is not conserved.

9. Why doesn't air resistance violate the conservation of energy principle?

Air resistance doesn't violate the conservation of energy principle because it converts mechanical energy into heat energy. While mechanical energy decreases due to air resistance, the total energy of the system (including heat) remains constant. This illustrates that energy is conserved in a broader sense, even when mechanical energy alone is not.

10. How does a pendulum demonstrate the conservation of mechanical energy?

A pendulum demonstrates the conservation of mechanical energy through the continuous conversion between potential and kinetic energy. At its highest points, the pendulum has maximum gravitational potential energy and minimum kinetic energy. At its lowest point, it has maximum kinetic energy and minimum potential energy. In an ideal system without friction, the total mechanical energy remains constant throughout the swing.

11. What is the formula for total mechanical energy?

The formula for total mechanical energy (E) is:

12. How does the conservation of mechanical energy apply to a roller coaster?

In a roller coaster, the conservation of mechanical energy explains the ride's motion. At the top of a hill, the car has maximum gravitational potential energy. As it descends, this potential energy converts to kinetic energy, increasing the car's speed. The total mechanical energy remains constant (ignoring friction), allowing the car to climb the next hill using its kinetic energy, which converts back to potential energy.

13. Can mechanical energy ever truly be lost?

In real-world scenarios, mechanical energy can appear to be "lost," but it's actually being converted into other forms of energy, most commonly heat due to friction. While the total energy of the system is always conserved according to the law of conservation of energy, the usable mechanical energy can decrease over time.

14. How does the concept of mechanical energy conservation apply to a bouncing ball?

When a ball bounces, it demonstrates the conservation of mechanical energy, albeit imperfectly. As the ball falls, its gravitational potential energy converts to kinetic energy. Upon impact, some of this energy deforms the ball, then converts back to kinetic energy as it rebounds. However, each bounce is lower than the last because some energy is lost to heat and sound, reducing the total mechanical energy over time.

15. What role does mass play in the conservation of mechanical energy?

Mass is a crucial factor in mechanical energy calculations, but it doesn't affect the principle of energy conservation itself. A larger mass will have more kinetic energy at the same velocity and more gravitational potential energy at the same height. However, regardless of mass, the total mechanical energy of an isolated system will remain constant if no external work is done on it.

16. How does the conservation of mechanical energy relate to perpetual motion machines?

The conservation of mechanical energy principle explains why perpetual motion machines are impossible. These hypothetical devices would produce work indefinitely without an energy input, violating the conservation of energy. In reality, friction and other energy losses always occur, converting mechanical energy to heat and eventually bringing any motion to a stop without additional energy input.

17. Can you explain how energy is "stored" in a stretched spring?

Energy is stored in a stretched spring as elastic potential energy. When you stretch or compress a spring, you do work against its internal forces. This work is stored as potential energy in the deformed atomic bonds of the spring material. When released, this stored energy converts back into kinetic energy, demonstrating the conservation of mechanical energy.

18. How does the concept of mechanical energy conservation apply to planetary orbits?

In planetary orbits, the conservation of mechanical energy explains the planet's motion. The total mechanical energy (kinetic + gravitational potential) remains constant. As a planet moves closer to the sun, its gravitational potential energy decreases while its kinetic energy increases, causing it to speed up. The opposite occurs as it moves away, maintaining a stable orbit due to this energy conservation.

19. What happens to the mechanical energy in a system when work is done by external forces?

When work is done by external forces on a system, the total mechanical energy of the system changes. If positive work is done (energy is added to the system), the total mechanical energy increases. If negative work is done (energy is removed from the system), the total mechanical energy decreases. This doesn't violate energy conservation because the energy is being transferred between the system and its surroundings.

20. How does air resistance affect the conservation of mechanical energy in a falling object?

Air resistance acts as a non-conservative force on a falling object, converting some of its mechanical energy into heat. As the object falls, its total mechanical energy (kinetic + potential) decreases due to this energy conversion. While total energy is still conserved (including the heat generated), the mechanical energy of the object-Earth system is not conserved in this case.

21. Can you explain the concept of escape velocity using the principle of conservation of mechanical energy?

Escape velocity is the minimum speed an object needs to break free from a planet's gravitational field without further propulsion. Using the conservation of mechanical energy principle, we can calculate this velocity. At the planet's surface, the object needs enough kinetic energy to overcome all the gravitational potential energy between the surface and infinity. If the initial kinetic energy is greater than or equal to the gravitational potential energy, the object will escape.

22. How does the conservation of mechanical energy apply to simple harmonic motion, like in a mass-spring system?

In a mass-spring system undergoing simple harmonic motion, the conservation of mechanical energy is evident in the continuous exchange between kinetic and elastic potential energy. At the equilibrium position, kinetic energy is maximum and elastic potential energy is zero. At the extremes of motion, elastic potential energy is maximum and kinetic energy is zero. The sum of these energies remains constant throughout the motion, demonstrating energy conservation.

23. What is the relationship between work-energy theorem and the conservation of mechanical energy?

The work-energy theorem states that the net work done on an object equals its change in kinetic energy. This theorem is closely related to the conservation of mechanical energy. In a system where only conservative forces act, the work done by these forces equals the negative change in potential energy. Combined with the work-energy theorem, this leads to the principle of conservation of mechanical energy, where the change in kinetic energy is balanced by the change in potential energy.

24. How does the concept of mechanical energy conservation help in solving problems involving inclined planes?

The conservation of mechanical energy principle is particularly useful in solving inclined plane problems. Instead of analyzing forces and accelerations, we can equate the initial and final energies of the system. For an object sliding down a frictionless incline, the initial gravitational potential energy at the top converts to kinetic energy at the bottom. This approach simplifies calculations and provides insights into the object's velocity and position at any point on the incline.

25. Can you explain how energy is conserved in a compound pendulum?

In a compound pendulum (like a swinging rod), the conservation of mechanical energy involves both translational and rotational kinetic energies, as well as gravitational potential energy. At the highest points of the swing, gravitational potential energy is maximum, while both forms of kinetic energy are minimum. At the lowest point, the opposite is true. The sum of all these energy forms remains constant throughout the motion, demonstrating the conservation of mechanical energy in a more complex system.

26. How does the principle of conservation of mechanical energy apply to collisions?

The application of mechanical energy conservation in collisions depends on the type of collision. In perfectly elastic collisions, mechanical energy is conserved, with kinetic energy before and after the collision remaining the same. In inelastic collisions, some mechanical energy is converted to other forms (like heat or deformation), so total mechanical energy is not conserved. However, the total energy of the system, including all forms, is always conserved in accordance with the broader law of conservation of energy.

27. What is the significance of the zero point in potential energy calculations?

The choice of zero point for potential energy is arbitrary but significant in calculations. It doesn't affect the conservation of energy, as only changes in potential energy matter. However, it can simplify problem-solving. For gravitational potential energy, the ground is often chosen as the zero point. For elastic potential energy in springs, the relaxed position is typically chosen. The key is to be consistent within a problem and recognize that absolute potential energy values are less important than changes in potential energy.

28. How does the conservation of mechanical energy principle help in understanding the motion of a satellite?

The conservation of mechanical energy principle is crucial in understanding satellite motion. For a satellite in orbit, the sum of its kinetic and gravitational potential energy remains constant. As the satellite moves closer to Earth, its potential energy decreases and kinetic energy increases, causing it to speed up. The opposite occurs as it moves farther away. This conservation explains why satellites in elliptical orbits move faster at perigee (closest point to Earth) and slower at apogee (farthest point).

29. Can you explain how mechanical energy is conserved in a vertical circular motion, like in a loop-the-loop roller coaster?

In a vertical circular motion like a loop-the-loop, mechanical energy conservation explains why the motion is possible. At the bottom of the loop, the energy is mostly kinetic. As the object rises, kinetic energy converts to gravitational potential energy. At the top of the loop, there must be enough total energy to maintain both the necessary speed (kinetic energy) and the height (potential energy). If the initial energy is sufficient, the object completes the loop with energy conserved throughout the motion.

30. How does the concept of mechanical energy conservation relate to the operation of hydroelectric power plants?

Hydroelectric power plants demonstrate the practical application of mechanical energy conservation. Water at a higher elevation has gravitational potential energy. As it flows down through turbines, this potential energy converts to kinetic energy of the moving water and then to rotational kinetic energy of the turbines. The turbines then convert this mechanical energy into electrical energy. The total energy is conserved throughout this process, with the original gravitational potential energy of the water being the source of the generated electricity.

31. What is the relationship between the conservation of mechanical energy and the concept of energy wells?

Energy wells are a visual representation of the conservation of mechanical energy principle. They show how an object's total energy determines its possible positions and motions within a system. The "well" represents potential energy, while the object's total energy is shown as a horizontal line. The difference between this line and the well's curve at any point represents the kinetic energy. This visualization helps in understanding how energy converts between forms while remaining constant overall, illustrating the conservation of mechanical energy.

32. How does the principle of least action relate to the conservation of mechanical energy?

The principle of least action is a fundamental concept in physics that states that the path taken by a system between two points is the one that minimizes the action (a quantity related to the system's energy over time). This principle is closely related to the conservation of mechanical energy. In systems where mechanical energy is conserved, the path of least action often corresponds to the path where kinetic and potential energy are exchanged in a way that keeps their sum constant, aligning with the conservation of mechanical energy principle.

33. Can you explain how the conservation of mechanical energy applies to the motion of a simple pendulum in the presence of air resistance?

In a real simple pendulum with air resistance, the conservation of mechanical energy is not strictly maintained. Initially, the pendulum's motion closely follows energy conservation, with gravitational potential energy converting to kinetic energy and back. However, air resistance gradually reduces the total mechanical energy by converting some of it to heat. This causes the pendulum's amplitude to decrease over time. While total energy (including heat) is conserved, the mechanical energy of the pendulum-Earth system decreases, illustrating the effects of non-conservative forces on energy conservation.

34. How does the concept of mechanical energy conservation help in understanding the motion of projectiles?

The conservation of mechanical energy is crucial in analyzing projectile motion, especially when air resistance is negligible. As a projectile moves through its trajectory, there's a continuous exchange between kinetic and gravitational potential energy. At the highest point, potential energy is maximum and kinetic energy is at its minimum (only horizontal component remains). This principle allows us to calculate the projectile's velocity at any point in its path by equating the initial and final total mechanical energies, simplifying complex trajectory analyses.

35. What is the significance of the work-energy principle in the context of conservation of mechanical energy?

The work-energy principle states that the work done on an object is equal to its change in kinetic energy. This principle is fundamental to understanding the conservation of mechanical energy. In a system where only conservative forces act, the work done by these forces is equal to the negative change in potential energy. Combining this with the work-energy principle leads to the conservation of mechanical energy: the change in kinetic energy is balanced by the change in potential energy, keeping the total mechanical energy constant.

36. How does the conservation of mechanical energy principle apply to the concept of escape velocity from different planets?

The concept of escape velocity for different planets is a direct application of mechanical energy conservation. Escape velocity is the minimum speed an object needs at a planet's surface to escape its gravitational field. It's calculated by equating the initial kinetic energy at the surface to the gravitational potential energy needed to reach infinity. Since larger, more massive planets have stronger gravitational fields, they require higher escape velocities. This principle explains why it's easier to launch spacecraft from smaller bodies like the Moon compared to Earth.

37. Can you explain how the conservation of mechanical energy relates to the concept of gravitational assist in space missions?

Gravitational assist, or gravity assist, uses the conservation of mechanical energy principle to increase a spacecraft's speed. When a spacecraft approaches a planet, it gains kinetic energy as it falls into the planet's gravitational well. As it swings around the planet and leaves its gravitational field, it retains this extra energy. From the planet's frame of reference, the spacecraft's speed before and after the encounter is the same (energy is conserved). However, from the Sun's frame, the spacecraft gains speed due to the planet's orbital motion, effectively "stealing" a small amount of the planet's orbital energy.

38. How does the principle of conservation of mechanical energy apply to the motion of a yo-yo?

The motion of a yo-yo beautifully demonstrates the conservation of mechanical energy. As the yo-yo falls, its gravitational potential energy converts to both translational and rotational kinetic energy. When it reaches the end of its string, this kinetic energy begins to convert back into potential energy as the yo-yo climbs back up. In an ideal system without friction, this process would continue indefinitely. In reality, some energy is lost to friction and air resistance, causing the yo-yo's oscillations to gradually decrease in amplitude.

39. What role does the conservation of mechanical energy play in understanding the concept of terminal velocity?

The concept of terminal velocity is closely related to the conservation of mechanical energy. As an object falls through a fluid (like air), it gains kinetic energy as it loses gravitational potential energy. However, air resistance increases with velocity, converting some mechanical energy to heat. Terminal velocity is reached when the rate of this energy conversion equals the rate of gravitational potential energy loss. At this point, the object's mechanical energy is no longer conserved, but its velocity remains constant as the forces balance.

40. How does the conservation of mechanical energy principle help in analyzing the energy transformations in a roller coaster loop?

In a roller coaster loop, the conservation of mechanical energy principle is crucial for understanding the energy transformations. At the top of the first hill, the car has maximum gravitational potential energy. As it descends, this potential energy converts to kinetic energy. Entering the loop, the car must have enough kinetic energy to overcome gravity and complete the circle. Inside the loop, there's a continuous exchange between kinetic and potential energy. The principle of energy conservation allows designers to calculate the minimum height needed for the initial hill to ensure the car completes the loop safely.

41. Can you explain how the conservation of mechanical energy applies to the concept of equilibrium in physical systems?

The conservation of mechanical energy is fundamental to understanding equilibrium in physical systems. In a stable equilibrium, the system is at a local minimum of potential energy. Any small displacement increases the potential energy, resulting in a restoring force that brings the system back to equilibrium. This process involves the conversion between potential and kinetic energy, with the total mechanical energy remaining constant. In unstable equilibrium, the system is at a local maximum of potential energy, and any displacement leads to a further increase in kinetic energy at the expense of potential energy.