# Homework Help: Find the distance the spring compresses

1. Nov 8, 2009

### joemama69

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

a block of mass m slides along ahrizontal table with speed v. At s = 0, it hits a spring with spting constat k and begins to experience a frictin oforce. the coefficient of frictio is u, find the distance the spring compresses when it momentairly comes to rest.

2. Relevant equations

3. The attempt at a solution

i belive the frictin part is umgs, is this correct

.5mv2 = .5ks2 + ugms

if this is correct, how do i get the s alone

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2. Nov 8, 2009

### Staff: Mentor

Re: springs

It's a quadratic equation. Put it in standard form and solve it.

(That attachment doesn't seem to match the problem you described.)

3. Nov 8, 2009

### joemama69

Re: springs

s = -mg + or - (((mg)2 - 4(.5k)(mgh))/k).5

4. Nov 8, 2009

### Staff: Mentor

Re: springs

How did you get this from the equation you gave in your first post?

I suspect you're solving a different problem.

5. Nov 8, 2009

### joemama69

Re: springs

haha ya i had a very similar one sorry about that

s = -umg + or minus (((umg)2 - 4(.5k)(-.5mv2))/k).5

6. Nov 9, 2009

### Staff: Mentor

Re: springs

That's almost right. (Redo it more carefully. Each term must have the same units.)

Also, only one of the + or - choices will make sense for this problem.

7. Nov 9, 2009

### joemama69

Re: springs

i redid and came up with the same

.5ks2 + umgs - .5mv2 = 0

a = .5k
b = umg
c = -.5mv2

-b - $$\sqrt{b^2-4ac}$$/2a

-umg - $$\sqrt{()^2 - 4(.5k)(-.5mv^2)}$$/2(.5k)

s = -umg - $$\sqrt{()^2 +kmv^2}$$/k

8. Nov 9, 2009

### Staff: Mentor

Re: springs

Careful with how you do the division by 2a. Everything is divided by 2a, not just the square root term. (Use parentheses to show this.)

And don't forget that it's + or -, not just -.

9. Nov 9, 2009

### joemama69

Re: springs

ok

i think it should be minus because the spring is being compressed, do you concure

10. Nov 9, 2009

### Staff: Mentor

Re: springs

No...

11. Nov 9, 2009

### joemama69

Re: springs

s = -umg + (((umg)2 - 4(.5k)(-.5mv2)).5/k

s = -umg + (((umg)2 + kmv2).5/k

12. Nov 9, 2009

### Staff: Mentor

Re: springs

You still haven't corrected the "division by 2a" problem from post #8.

13. Nov 9, 2009

### joemama69

Re: springs

= (-umg + ((umg)2 + kmv2).5)/k

the answer how ever is Wnc = -m(v0)^2/2 (1 + k/bmg)^-1 after simplifying

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