Finding the distance a spring compresses

[dal11]

Homework Statement

An object of mass m=2.2 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.2. The object has speed v=0.57 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. What is the total distance, d, that the object moves after first touching the spring?

Homework Equations

KE+Espring = KEi+Wfriction
Espring=.5k(x^2)
Fspring=kx

The Attempt at a Solution

I am really confused I don't think I have enough knowns to solve the problem.

 

[LowlyPion]

Homework Statement

An object of mass m=2.2 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.2. The object has speed v=0.57 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. What is the total distance, d, that the object moves after first touching the spring?

Homework Equations

KE+Espring = KEi+Wfriction
Espring=.5k(x^2)
Fspring=kx

The Attempt at a Solution

I am really confused I don't think I have enough knowns to solve the problem.

I think you may have more information than you realize.

You start with an initial KE at x = 0.

There are two sources of work against the mass from that point.

There is friction and the spring.

But the spring gains potential energy ... but then gives it back until the object it at rest just as it gets to x = 0 again. So how much net work did the spring do?

 

[dal11]

0 I guess, I don't understand how that helps

 

[LowlyPion]

0 I guess, I don't understand how that helps

If the spring does no net work in stopping the object doesn't all of the kinetic energy of the object need to be accounted for by just the friction over the distance of 2*(d/2) ?

Doesn't mv²/2 = Work of Friction = Ffriction * distance