plzzzz.... explain meaning of conservative force feilds with an example

plzzzz.... explain meaning of conservative force feilds with an example


2 Answers

deeksha sharma
40 Points
11 years ago

conservative force is the force, work done by which is independent of the path followed but depends just on the initial and the final points.

 Example is gravitational force.

Explanation: suppose a body reaches a height H by first stairs, then by lift, and finally via an inclined plane. In all the cases net displacement is the same, <mind it not the distance>

So the magnitude of work done will also be the same which is weight of the body*displacement.

So the work done against gravitational force will be same.






AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago


Dear Kedar

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

Suppose that a non-uniform force-field ${\bf f}({\bf r})$ acts upon an object which moves along a curved trajectory, labeled path 1, from point $A$ to point $B$. See Fig.. the work $W_1$ performed by the force-field on the object can be written as a line-integral along this trajectory:

\begin{displaymath} W_1 = \int_{A\rightarrow B: {\rm path} 1} {\bf f}\!\cdot\!d{\bf r}. \end{displaymath} (1)

Suppose that the same object moves along a different trajectory, labeled path 2, between the same two points. In this case, the work $W_2$ performed by the force-field is

\begin{displaymath} W_2 = \int_{A\rightarrow B:{\rm path} 2} {\bf f}\!\cdot\!d{\bf r}. \end{displaymath} (2)

Basically, there are two possibilities. Firstly, the line-integrals (1) and (2) might depend on the end points, $A$ and $B$, but not on the path taken between them, in which case $W_1=W_2$. Secondly, the line-integrals (1) and (2) might depend both on the end points, $A$ and $B$, and the path taken between them, in which case $W_1\neq W_2$ (in general). The first possibility corresponds to what physicists term a conservative force-field, whereas the second possibility corresponds to a non-conservative force-field.


Figure : Two alternative paths between points $A$ and $B$

\begin{figure} \epsfysize =2.5in \centerline{\epsffile{line.eps}} \end{figure}



Informally, a conservative force can be thought of as a force that conserves mechanical energy

The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces (in both cases, the energy is converted to heat and cannot be retrieved)


All the best.




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