Solving Max Displacement of Spring with 5kg Block and Friction

[thecaksgood]

Homework Statement

block of mass m = 5 kg is connected to a spring having stiffness constant
k = 49 N/m, as shown in the figure below.
The surface between the block
and the table has μk = 0.1
In this figure, the block is presently held in place with the spring stretched
by x1 = 0.8 m. The block is then released. Determine the maximum amount
that the spring will compressed given that the coefficient of kinetic friction
between the block and the surface is μk = 0.1.

m= 5kg
k= 49 N/m
uk= .1 (friction)
spring= x1= .8m
Dis(spring)=?

Homework Equations

Potential Energy
Kinetic Energy

The Attempt at a Solution

I don't know where to begin

 

[grzz]

figure below?

 

[physicsvalk]

This is a conservation of energy problem, but note that the frictional force will always retard the motion of the block (the compression of the block after it is released from rest must be lower than the maximum compression). This should be a good way to check your answer.

Try to start by writing down an equation for the total energy of the system, and determine how much of it is lost by friction.