Question

What are conservative forces?

Answer 1

HintConservative force has a property that work done in moving a particle between two points is independent of the path taken.

Complete step-by-step solution:The work done by such forces
Does not depend upon path.
Depends only and only initial and final position.
For example:- If A and B are the two points and a conservative force acts on point A and B. Then we assume the three ways to go at point B . 1,2 and 3 are the three ways.
  

If the force is conservative, then work done by this force by first path, by second path and third path are equal.
Let $$W_1$$ be the work done along path 1, $W_2$ be the work done along path 2 and $W_3$ be the work done along path 3
Then,
$W_1=W_2=W_3$
Examples of conservative forces are gravitational force , spring force, and electrostatic force.
First we talk about gravitational force, let us assume $\left(m\right)$ .Which is placed on an inclined plane.
For path 1:-
Angle between force $\left(mg\right)$ and displacement $\left(l\right)$ is$({90}^{\circ }+\theta )$

Than $\begin{array}{rl}& W_1=FS\cos \varphi \\ & W_1=mgl(\cos ({90}^{\circ }+\theta ))\\ & \end{array}$ $[\cos ({90}^{\circ }+\theta )=-\sin \theta ]$
$W_1=-mgl\sin \theta$ …………………..(i)
For path 2
First we go from point A to point B and then from point B to point C.
$W=W_{AB}+W_{BC}$
When we go from A to B then the angle between force and displacement is ${90}^{\circ }$ $(\cos {90}^{\circ }=0)$ .
Than $\begin{array}{rl}& W_{AB}=FS\cos {90}^{\circ }\\ & W_{AB}=0\end{array}$
When we go from point B to C then the angle between force and displacement is ${180}^{{}^{\circ }}$.
$W_{BC}=-mgl\sin \theta$
$W_2=W_{AB}+W_{BC}$
$W_2=-mgl\sin \theta$ ……………….. (ii)
$W_1=W_2$
So the work done in the first path is equal to work done in the second path. So it is independent of path.

Note:
Students think that whose path has long distance then work done is maximum for that path, but for conservative force work done does not depend on path distance.