Conservation of Mechanical energy

Mechanical energy is defined as the product of potential and kinetic energy in physical sciences. If an isolated system is only subjected to conservative forces, the mechanical energy is constant, according to the concept of conservation of mechanical energy. 

The potential energy of an object increases as it moves in the opposite direction of a conservative net force, and the kinetic energy of the object varies when the object’s speed (not velocity) changes. Non-conservative forces, such as frictional forces, will be present in all real applications, but if they are small, the mechanical energy does not vary much, and conservation is a useful approximation.

Kinetic Energy

It is an object’s ability to perform work as a result of its motion. Wind, for example, has the kinetic energy to rotate the blades of a windmill and so produce electricity. The kinetic energy of an item is stated as, where K is the object’s kinetic energy in joules (J), m is the object’s mass in kilograms, and v is the object’s velocity:

                                             K = 1/2mv²

Potential Energy

It is an object’s ability to perform work as a result of its configuration or position. When a compressed spring is released, for example, it can perform work. For the purposes of this essay, we’ll concentrate on an object’s potential energy as a result of its position in relation to the earth’s gravity. The following is a formula for expressing potential energy:

v=mgh

Potential energy is commonly linked with restoring forces like springs and gravity. An external force that acts against the force field of the potential performs the action of stretching the spring or raising the mass of an object. 

This work is stored as potential energy in the force field. If the external force is withdrawn, the force field operates on the body to perform the work by returning the body to its original position, reducing the spring’s stretch or causing the body to fall.

Potential energy is the energy difference between an object’s energy in a particular position and its energy at a reference position, according to a more formal definition.

Conservation of Mechanical Energy

The mechanical energy of an isolated system, according to the principle of conservation of mechanical energy, remains constant throughout time as long as the system is independent of friction and other non-conservative forces.

Frictional forces and other non-conservative forces are present in any real situation, but their effects on the system are often so minor that the principle of mechanical energy conservation can be utilised as a reasonable approximation. In an isolated system, energy cannot be created or destroyed, but it can be converted to another kind of energy.

The kinetic energy is conserved in elastic collisions, but some mechanical energy may be transferred to thermal energy in inelastic collisions. James Prescott Joule found the equivalency between lost mechanical energy (dissipation) and an increase in temperature.

An electric motor transfer’s electrical energy to mechanical energy, an electric generator translates mechanical energy into electrical energy, and a heat engine converts heat to mechanical energy, among other devices.

Equation for Conservation of Mechanical energy

Let us consider there are two different points in a track. They are point 1 and point 2 as the coaster is at two different heights and speeds at those points. As the mechanical energy is sum of potential energy and kinetic Energy

Hence 

Potential Energy = (mass×gravity×height)

Kinetic energy = (1/2 mass×velocity²)

Therefore the total Mechanical energy at Point 1 is

ME1=mgh1+1/2mv1²

Similarly, at point 2 Total Mechanical Energy is 

ME2=mgh2+1/2mv2²

If there’s no friction then at that case:

ME1=ME2

Therefore,

mgh1+1/2mv1²=mgh2+1/2mv2²

The principle of mechanical energy conservation is represented by these equations. According to the concept, if the net work done by non-conservative forces is zero, an object’s total mechanical energy is conserved; that is, it does not change.

The Above equation can be re-written as:

PE1+KE1=PE2+KE2

Conclusion

In this article we have studied mechanical energy, conservation of mechanical energy and some other important topics. The sum of a system’s kinetic and potential energy is known as mechanical energy. The concept of mechanical energy conservation says that as long as the only forces acting are conservative forces, the total mechanical energy in a system (i.e., the sum of the potential and kinetic energies) remains constant.

We might use a circular definition and define a conservative force as one that does not modify the total mechanical energy, which is correct, but it does not provide any understanding into what it implies.