Question

Define conservative force.Prove that the total mechanical energy of a freely falling body remains constant throughout the fall

Answer 1

A conservative force is a force whose work done is independent of the path taken and depends only on the initial and final position of the particle

Explanation: A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path. if a particle travels in a closed loop, the total work done by a conservative force is zero.

 total mechanical energy = potential energy +kinetic energy

At A : PE = mgh   ; KE = 0 (u=0)                                    

           E = mgh+0=mgh

At B :  PE = mg(h-x)  ; KE = mgx

           E= mgh-mgx+mgx = mgh

At C :  PE = 0(h=0)   ; KE = mgh

           E = 0+mgh = mgh

Answer 2

Conservative forces are the ones that depend on initial and final points only for the work done.

Explanation:

Conservative force:-

There exists a conservative force whenever the work performed through an item by that force is independent of the path of the object. The jobs completed by a conservative force, instead, depend only on the momentum's endpoints.

Conservative friction is a push with the principle which the cumulative work performed in transferring an object among two or more points is irrespective of the route set. As an object moves through one position to the next, the force increases the entity's energy stored by a sum not contingent on the route set.

An example of a conservative force is gravity.

• It can be shown that the mechanical energy of a body stays unchanged in the absence of outside force applied.
• Therefore we have shown that the amount of free-falling body's potential and kinetic energy remains the same at all points. The mechanical energy of a body remains constant, under the force of gravity.

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