# Work-Energy Theorem Problem

1. Mar 5, 2013

### Yosty22

1. The problem statement, all variables and given/known data

A 2.50-kg textbook is forced against a horizontal spring of negligible mass and force constant, k, of 250N/m, compressing the spring a distance of 0.250 m. When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction μk=0.30. Use the work-energy theorem to find how far the text-book moves from its initial position before coming to rest.

2. Relevant equations

Wtot=K2-K1=ΔK (work-energy theorem)
K=0.5mv2

3. The attempt at a solution

I have no idea how to even start. It says that I have to use the work energy theorem, so all I can think of doing is substitution. However, Work-energy theorem has no reference to kinetic friction, just kinetic energy. Any ideas to get me started?

2. Mar 5, 2013

### Staff: Mentor

Friction is a force, so consider the work done by it.

3. Mar 5, 2013

### Yosty22

Ok, so I used the equation friction=μ*n.

Since the table it is on is horizontal, that means that there is no acceleration or any motion up or down, so W=N. In this case, I use the weight of the box which came out to be 9.8*2.5=24.5N.

I found the force of force of friction to be 7.35N acting in the opposite direction of motion. This is where I am stuck. If I put Work due to friction in the work energy theorem, I have to multiply the force of friction by the distance over which it acts. How do I find the distance that the friction acts over? I thought that the force of friction acted over the same distance as it moved, just in the opposite direction. In this case, I still have two unknowns: the total distance that the block traveled and its velocity, but the problem only asks for the distance. How would I go about finding the velocity if it is not given and I don't know the kenetic energy or how far it traveled or any time interval?

4. Mar 5, 2013

### Staff: Mentor

Hint: What's final speed of the book?

5. Mar 5, 2013

### Yosty22

Ahh, ok, it would be zero becuase it comes to a rest. However, wouldn't it start from rest as well, since it is pushed up against the compressed spring? Or would I designate v1to be the moment it leaves the spring?

6. Mar 5, 2013

### Staff: Mentor

Yes, it starts from rest and ends up at rest.
All you need to worry about is the change in KE. What would that be? (No need to worry about intermediate points.)

7. Mar 5, 2013

### Yosty22

So wouldn't that mean the change is 0? In which case, there is no kinetic energy. Does that make sense?

8. Mar 5, 2013

### Staff: Mentor

The change in kinetic energy is zero, which makes perfect sense. After all, you're trying to find how how far the thing goes before friction brings it to rest. (That doesn't mean that there wasn't kinetic energy while it was moving, but who cares?)

9. May 21, 2016

### Sydney Austin

So since friction and the spring are both doing work, would the total work be the (work of the spring) - (the work of friction) since work by friction is against motion?

10. May 22, 2016

Sure.