Question

Select the correct alternative(s):
a) Elastic forces are always conservative
b) Elastic forces are not always conservative
c) Elastic forces are always conservative only when Hooke’s law is obeyed
d) Elastic forces may be always conservative even when Hooke’s law is not obeyed
A) a,d
B) b,c
C) b,d
D) a,c

Answer 1

Hint: Conservative forces are the force which does not depend upon the path but on the work done. As work done is a point function path is not considered in these types of forces.

Complete step by step solution:
We know that elastic force is the force formed on a deformed object itself to return to its initial shape. When an elastic material is subjected to an external force, it may undergo deformation till the force is released from the object. Whenever the external force is released, the elastic force within the body of that particular material tends its body to come back to the initial position.

As we discussed earlier, a force which is based only on the work done, it is referred to as a conservative force. When considering the case of elastic force, when the external force is released from the body of the elastic material, it will return to its initial position and shape, thus no work is done. So we can clearly say that the elastic force is a conservative force.

Let’s discuss Hooke's law; Hooke’s law states that the force needed to compress a spring by some distance is proportional to the distance compressed.
$ \Rightarrow $$F \propto \Delta x$
$ \Rightarrow F = k\Delta x$
Where, $F$- Force needed
$k$- Constant of elasticity of the material
$\Delta x$- Distance compressed
But, when a spring is in a compressed state and no further compression is not given, the force applied will not be zero. That means, the Elastic force is not obeying the Hooke’s law at that time. We can say that elastic force conservative and it is not obeying Hooke’s law always.

So the final answer is option (A), a, d.

Note: A non-conservative force is the one for which work depends on the path. This type of force will change the total mechanical energy of that system. Friction is a good example of a nonconservative force.