Question

State and prove the principle of conservation of mechanical energy.

Answer 1

$\huge \underline \green{\sf{ Answer :- }}$

• $\small \underline {\sf{principle \ of \ conservation }}$

The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant.

• $\small \underline \blue {\sf{ Proof :- }}$

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’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.

Answer 2

Explanation:

\huge \underline \green{\sf{ Answer :- }}

Answer:−

\small \underline {\sf{principle \ of \ conservation }}

principle of conservation

The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant.

\small \underline \blue {\sf{ Proof :- }}

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’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.