Geography, asked by bnaarzoo, 9 months ago

Prove the law of conservation of mechanical energy​

Answers

Answered by ananyaawasthi70
1

Answer:

V is the potential energy of the object in joules (J), m is the mass of the object in kilograms, g is the gravitational constant of the earth (9.8 m/s²), and h is the height of the object from earth’s surface. Now, we know that the acceleration of an object under the influence of earth’s gravitational force will vary according to its distance from the earth’s centre of gravity.

But, the surface heights are so minuscule when compared to the earth’s radius, that, for all practical purposes, g is taken to be a constant.

Explanation:

Therefore for every displacement of Δx, the difference between the sums of an object's kinetic and potential energy is zero. In other words, the sum of an object's kinetic and potential energies is constant under a conservative force. Hence, the conservation of mechanical energy is proved.

Answered by Archismanmukherjee
1

Answer:

Conservation of Mechanical Energy

The sum total of an object’s kinetic and potential energy at any given point in time is its total mechanical energy. The law of conservation of energy says “Energy can neither be created nor be destroyed.”

So, it means, that, under a conservative force, the sum total of an object’s kinetic and potential energies remains constant. Before we dwell on this subject further, let us concentrate on the nature of a conservative force.

Conservative Force

A conservative force has following characteristics:

A conservative force is derived from a scalar quantity. For example, the force causing displacement or reducing the rate of displacement in a single dimension without any friction involved in the motion.

The work done by a conservative force depends on the end points of the motion. For example, if W is the work done, K(f) is the kinetic energy of the object at final position and K(i) is the kinetic energy of the object at the initial position:

Work done by a conservative force in a closed path is zero. Here, W is the work done, F is the conservative force and d is the displacement vector. In case of a closed loop, the displacement is zero. Hence, the work done by the conservative force F is zero regardless of its magnitude.

proof:-

Here, Δx is the displacement of the object under the conservative force F. By applying the work-energy theorem, we have: ΔK = F(x) Δx. Since the force is conservative, the change in potential Energy can be defined as ΔV = – F(x) Δx. Hence,

ΔK + ΔV = 0 or Δ(K + V) = 0

Therefore for every displacement of Δx, the difference between the sums of an object’skinetic and potential energy is zero. In other words, the sum of an object’s kinetic and potential energies is constant under a conservative force. Hence, the conservation of mechanical energy is proved

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