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Ellipse: Definition, Properties, Applications, Equation, Formulas
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Ellipse: Definition, Properties, Applications, Equation, Formulas
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April 8, 2025Conservation of Mechanical Energy: Mechanical energy is known as “movement energy,” since it is found in objects that move or have the ability to move. Except for the gravitational force, it states that the mechanical energy of an object in a closed system remains constant if it is not subjected to any friction, i.e. air resistance. When we use a hammer to, say, strike a nail and drive it into the wall, we are merely exerting force on the nail with the aid of the hammer.
A hammer has no kinetic energy but does have some potential energy when it is at rest. When we swing a hammer up to a certain distance from a nail before hitting it, kinetic energy is released, and the hammer’s combination of kinetic and potential energy, known as mechanical energy, causes the nail to drive into the wall. In this article, we will study and learn about the concept of conservation of mechanical energy in detail.
Conservation of Mechanical Energy will be more clearly understood if we first get acquainted with the concept of mechanical energy. The mechanical energy of an object is the sum of its potential energy and kinetic energy.
In this, the potential energy of an object is the energy possessed by it by virtue of its position (or configuration), whereas kinetic energy is the energy possessed by the object by virtue of its motion.
Thus, the mechanical energy of an object is the energy possessed by it due to the virtue of its position or motion or both.
In the case of a system, mechanical energy is the sum of its potential energy and the kinetic energy of the objects within it.
The principle of mechanical energy conservation asserts that if a body or system is only subjected to conservative forces, its mechanical energy remains constant.
Conservation of Mechanical Energy means that the total mechanical energy of the object or the system remains constant at any instant. Here, the kinetic energy or the potential energy at any instant can be changed, but their sum is always constant. But such a situation is possible only if the force causing the transformation of energy is conservative in nature.
A force is considered to be conservative if the work done by it or against it only depends on the initial and the final position of the body and not on the path taken between the initial and the final position. Gravitational force is a conservative force, whereas air resistance is a non-conservative force.
For example, take the case of a body undergoing a fall. During the start of its motion, it will just have potential energy, and just at the end of the fall before it hits the ground, it will just have kinetic energy. Here, the potential energy at the beginning of the fall will be entirely converted into the kinetic energy gained by the object at the end of the fall.
In the intermediate stage, we can find that the decrease in its potential energy will always be equal to the gain in its kinetic energy, and at any instant, their sum will always be the same. Thus, the total mechanical energy of the body always remains constant. Here, we are neglecting the air resistance.
Conservation of Mechanical Energy in Class 11 Physics is well formulated as a law that governs the energy transformations caused by internal conservative forces. The law of conservation of mechanical energy states that “The total mechanical energy of a system remains constant if the internal forces are conservative and the external forces do no work.”
The conservation of Mechanical Energy can be verified using the case of a simple pendulum. The simple pendulum consists of a string and a bob attached to it. The string of a simple pendulum is fixed at one end about which it is to move. The other end of the string is connected to a bob.
Now, this string with the bob (simple pendulum) is to move about the fixed end in the horizontal direction. Thus, the simple pendulum is to move towards the right and the left side of the mean position.
Let the mass of the bob be
To verify the law of conservation of mechanical energy, let us now pull the simple pendulum on the right side such that it is at a height
So, at the rightmost side, the potential energy of the simple pendulum is
Thus, the total mechanical energy
Now, when the simple pendulum is released, it starts to move leftwards due to the potential energy possessed by it and reach the mean position.
At the mean position, the potential energy is zero as the height is zero. Thus,
Due to the motion of the simple pendulum, it has gained kinetic energy, which is the maximum at this position. The velocity of the simple pendulum at this position is
Using the third equation of motion
Putting this value of
So, at the mean position, the total mechanical energy of the simple pendulum is
Now, this simple pendulum has velocity, due to which it will move leftwards and eventually reach the leftmost side and will stop for a moment. At this location, its kinetic energy will be zero as its velocity will be zero. Thus,
But as it reaches at the height
Thus, the total mechanical energy of the simple pendulum at the leftmost side will be
Hence, from the equations,
Conservation of Mechanical Energy
Where,
Example 1: An object of mass
Solution: Given that,
The mass of the object is
The height of the object is
The acceleration due to gravity is
The potential energy of the object at the height
Now, halfway down, the kinetic energy of the body can be calculated using the law of conservation of mechanical energy. At this position, the kinetic energy gained will be equal to the potential energy lost which will be half of
Thus, the kinetic energy of the object will be
Example 2: A body of mass
Solution: Given that,
The mass of the body is
The velocity of the body is
The kinetic energy of the body while throwing is
Now, according to the law of conservation of mechanical energy, the maximum gravitational potential energy gained by the body will be equal to its kinetic energy while throwing. So, its maximum gravitational potential energy will be
Hence, the maximum gravitational potential energy of the body will be
Conservation of Mechanical Energy can be applied where there are transformations of energy by the action of internal conservative forces. Some of the examples are as given below:
The most commonly asked queries on Mechanical Energy are answered here:
Q.1: Give one example where mechanical energy is conserved.
A: When a body undergoes fall, the total mechanical energy of the body remains constant, and thus, the mechanical energy remains conserved in this situation.
Q.2: What is a non-conservative force?
A: If the work done by a force depends on the path taken between the initial and the final position, it is called a non-conservative fore. The frictional force is a non-conservative force.
Q.3: What is Mechanical Energy?
A: Mechanical energy is the sum of kinetic energy and potential energy.
Q.4: What is the statement of conservation of mechanical energy?
A: The total mechanical energy of a system remains constant if the internal forces are conservative and the external forces do no work.
Q.5: What is a conservative force?
A: If the work done by a force depends only on the initial and the final position and not on the path taken, it is called a conservative force. Magnetic force is a conservative force.
Q.6: What is the formula for the conservation of mechanical energy?
A: The formula representing the conservation of mechanical energy is ({E_m} = {E_p} + {E_k} = mgh + \frac{1}{2}\,{\rm{m}}{{\rm{v}}^2} = {\rm{Constant}}).
Q.7: When is conservation of mechanical energy not applicable?
A: Conservation of mechanical energy is not applicable when the forces acting on the system are non-conservative in nature, like frictional force.
Practice Mechanical Energy Questions with Hints & Solutions
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