Answer:
Minimum coefficient of kinetic friction between the surface and the block is .
Explanation:
Given:
Mass of the block = M
Spring constant = k
Distance pulled = x
According to the question:
<em>We have to find the minimum co-efficient of kinetic friction between the surface and the block that will prevent the block from returning to its equilibrium with non-zero speed. </em>
So,
From the FBD we can say that:
⇒ Normal force, <em>...equation(i)</em>
⇒ Elastic potential energy, =
<em> ...equation (ii)</em>
⇒ Frictional force, =
<em> ...equation (iii)</em>
⇒ Plugging (i) in (iii).
⇒
Now,
⇒ As we know that the energy lost due to friction is equivalent to PE .
⇒ <em>...considering PE as</em>
or
.
Arranging the equation.
⇒
⇒ <em>...eliminating x from both sides.</em>
⇒ <em>...dividing both sides wit Mg.</em>
Minimum coefficient of kinetic friction between the surface and the block is .
