Name: Forces: Conservative and Non-conservative
Uploaded: 2019-07-19
Duration: 4 min 29 s
Description: In this video, let us define the conservative and non-conservative forces and determine which forces are conservative and which are not. Learn more.

Question

What are conservative and non-conservative forces? Explain with examples. Mention some of their properties.

Accepted Answer

Conservative forces:

A force is said to conservative if the work done by the force (or against the force) in moving a body depends only upon the initial and final positions and is independent of the path taken.

For example, the gravitational force is a conservative force. To prove this calculate work done in carrying a body of weight $m g$ through height $h$ . from initial position $A$ to final position $B$ .

In fig. $1$ a body is being lifted vertically upwards and $W = F o r c e \times d i p l a c e m e n t$ or $W = m g \times h$

Where $h =$ height $A B$

In fig. $1$ b body is taken along a smooth inclined plane CB of height $A B = h$ . and inclination $θ$

$W = F \times C B$

$= m g \sin θ \times C B$

$= m g S i n θ \times \frac{A B}{\sin θ}$

In $∆ A C B$

$\frac{A B}{C B} = \sin θ \Rightarrow C B = \frac{A B}{\sin θ}$

$W = m g h$

In fig. $1$ c the body is being taken along a staircase. There are $n$ stairs each of vertical height $h'$ .

$W . D$ in moving through each stair is $m g h'$ .

$∴ W . D$ in moving through all the stairs $= m g h' \times n$

$n \times h' = h$

Therefore $W . D = m g h$ .

In fig. $1$ d body is being taken along a zig-zag path through some height $A B = h$ . Let it be divided into a large number of small paths each of heigh $∆ h$ . Then

$W . D = \sum_{}^{} m g (∆ h) = m g h$

Nonconservative forces:

A force is said to be nonconservative if work done in moving the body by the force or against the force between two points depends on the path followed.

Example of nonconservative force is force of friction. Friction always opposes motion. $W . D$ on a rough surface will be more if path length is more. And on a round trip also work done against friction will not be zero.

Properties of conservative forces:

(i) Work done is independent of the path taken between any two points.

(ii) Work done on any closed path is zero $\oint \vec{F} . d \vec{r} = 0$

Properties of non-conservative forces:

(i) Work done depends on the path taken by the body between any two point.

(ii) Work done on any closed path is not zero $\oint \vec{F} . d \vec{r} \neq 0$ .

What are conservative and non-conservative forces? Explain with examples. Mention some of their properties.

Important Questions on Work, Power and Energy

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