How Is the Coefficient of Kinetic Friction Calculated in a Spring-Block System?

[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.

 

[wais]

Your approach to solving this problem is correct. However, there may be a small error in your calculation or rounding. I recommend double-checking your calculations and making sure to use the correct values for k, m, and g. Also, make sure to use the same units for all quantities (e.g. if k is in N/m, make sure m is in kg and g is in m/s^2). It is also possible that the computer's answer is slightly different due to rounding or significant figures. Overall, your approach is correct and you should be able to arrive at the correct answer with some careful calculations and attention to units.