Block on Spring with Friction

[Naeem]

Q. A relaxed spring with spring constant k = 50 N/m is stretched a distance di = 56 cm and held there. A block of mass M = 5 kg is attached to the spring. The spring is then released from rest and contracts, dragging the block across a rough horizontal floor until it stops without passing through the relaxed position, at which point the spring is stretched by an amount df = di/9.


What is the coefficient of kinetic friction µk between the block and the floor?

Here is what I did:

At the point the block stops the spring force is equal to the force of friction.

Fspring = Ffriction

k*x = Uk * m * g

Uk = (K * x )/ m* g

Uk = 0.0603, which the computer says is wrong.

[Doc Al]

What is the coefficient of kinetic friction µk between the block and the floor?
Note that they want the coefficient of kinetic friction.

Here is what I did:

At the point the block stops the spring force is equal to the force of friction.
Yes, when it stops the static friction will equal the spring force. But that's not what they want.

Instead, realize that some spring potential energy is transformed into work against friction.