# Homework Help: Spring Problem, help!

1. Oct 15, 2007

### bulldog23

1. The problem statement, all variables and given/known data
A moving 1.3 kg block collides with a horizontal spring whose spring constant is 491 N/m.

A) The block compresses the spring a maximum distance of 5.0 cm from its rest postion. The coefficient of kinetic friction between the block and the horizontal surface is 0.49. What is the work done by the spring in bringing the block to rest? REMEMBER: Work has a sign.

B) How much mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring?

C) What is the speed of the block when it hits the spring?

2. Relevant equations
W=F_0*d

3. The attempt at a solution
I am unsure how to approach this problem. If someone could please walk me through it, that would help a lot! My teacher gave us this problem, but we haven't even learned this stuff yet. So please help me out!

Last edited: Oct 15, 2007
2. Oct 16, 2007

### Hootenanny

Staff Emeritus
Let's take question (A) first. So, when the block collides with the srping it has some kinetic energy, when the block stops it has no kinetic energy. Some of this kinetic energy will be used to do work against friction, what do you think the rest of this kinetic energy will be used for?

3. Oct 16, 2007

### bulldog23

Is the rest of the kinetic energy used to hold the spring in place?

4. Oct 16, 2007

### Hootenanny

Staff Emeritus
Not hold in place, but to compress the spring yes. So, do you know the expression for the potential energy stored in a compressed spring?

5. Oct 16, 2007

### bulldog23

Is it F=kx?

6. Oct 16, 2007

### Hootenanny

Staff Emeritus
Close, thats the force required to compress a spring by xm; how about the energy stored?

7. Oct 16, 2007

### bulldog23

PE=1/2kx^2?

8. Oct 16, 2007

### Hootenanny

Staff Emeritus
Sounds good to me. So, how much potential energy is stored after the block collides with the spring?

9. Oct 16, 2007

### bulldog23

So then do I plug in the 491 N/m for k and 5 m for x? If I do that I get 6137.5 J.

10. Oct 16, 2007

### Hootenanny

Staff Emeritus
The value is correct, but what about the sign?

11. Oct 16, 2007

### bulldog23

It should be negative because it is opposing the force of the block, right?

12. Oct 16, 2007

### bulldog23

So is that all you have to do for part A?

13. Oct 16, 2007

### Hootenanny

Staff Emeritus
Yes, since the force extered by the spring is in the opposite direction to the direction in which the block is moving, the work is negative.
Yup. Now for part (B) you do exactly the same, but this time for friction.

14. Oct 16, 2007

### bulldog23

It says that the answer for part A is wrong though. Doesn't the coefficient of the kinetic friction play into the problem somewhere?

15. Oct 16, 2007

### Hootenanny

Staff Emeritus
Is this a Webassign problem? Try rounding your answer to 3sf. And no, the spring is still compressed the same amount regardless of friction, therefore, the work done by the spring will be the same.

16. Oct 16, 2007

### bulldog23

I tried it again and it said that it was wrong. We must have gone wrong somewhere...

17. Oct 16, 2007

### Hootenanny

Staff Emeritus
Wait, I see what's happened, we've used x = 5m, when actually x = 5cm = 0.05m

I can't believe I missed that.

18. Oct 16, 2007

### bulldog23

So then the answer should be -.61375 J ? So then how do I do the same thing with friction for part B?

Last edited: Oct 16, 2007
19. Oct 16, 2007

### Hootenanny

Staff Emeritus
Yes, but be careful, web assign is notoriously pedantic about accuracy and rounding, I would say use 3sf or the accuracy it tells you to use in the question.

20. Oct 16, 2007

### bulldog23

Alright, it accepted the answer. I am lost when it comes to Part B