Question

a spring of spring constant k placed horizontally on a rough horizontal surface is compressed against a block of mass m placed on the surface so as to store maximum energy in the spring.If the coefficient of friction between the block and the surface is μ the potential energy stored in the spring is

Answer 1

Given details:

Spring constant is k

Mass of the block is m

Coefficient of friction between the block and the surface is μ

Solution:

Maximum enrgy is stored in the spring

Kinetic frictional force on the block is given by μmg

Spring's restroring force will be -kx, where x is the maximum compression

At equilibrium, spring will be at rest postion where the two forces will be equal.

-kx= μmg

x= -μmg/k

We know that, Potential energy is 1/2kx^2

Therefore, P.E = 1/2k * (μmg)^2

Answer 2

The stored potential energy in the spring will be denoted as ½ kx^2.

In this, x stands for the elongation from the mean position.

For the maximum potential energy, it is essential that the x is maximum and the force applied is equally balanced.

When equal and opposite forces are applied, energy is maximum in the spring.