Problem With Work Done by a Spring Force

[Senrai]

Homework Statement

One end of a spring is attached to a block and the other is attached to a wall. The spring has no mass and the block lies atop a frictionless surface. The equilibrium point of the system is at x = 0 cm. A force of 80N must be applied to the block to hold it stationary at x = -2 cm. From this position, the block is slowly moved until the applied force has done 4J of work on the spring-block system; the block is then again stationary. What is the block's position? (There are two answers.)

Homework Equations

-F_spring = F_applied
F_spring = -kx
-W_spring = F_applied
W_spring = 0.5k(x₁² - x₂²)

The Attempt at a Solution

I first solved to get the spring's spring constant, k.
-F_spring = F_applied
-F_spring = 80N
F_spring = -80N

F_spring = -kx
-80N = -k(-0.02m)
-80N/-(-0.02m) = k
-4000N/m = k
I don't think there can be negative spring constants, so I changed this to 4000N/m.

I then solved to get the block's final position.
-W_spring = F_applied
-W_spring = 4J
W_spring = -4J

W_spring = 0.5k(x₁² - x₂²)
-4J = 0.5(4000N/m)((-0.02m)² - x₂²)

When I worked that equation out, I came up with a final position of +- 0.04899m, which was incorrect.
I've been at this for hours and can't solve it. Any help would be greatly appreciated.

 

[alphysicist]

Senrai,

I don't see anything wrong with your work. Maybe someone else can see something that I don't.

 

[heth]

I got this answer as well.

 

[heth]

I got this answer as well.

Though there may be an issue with the number of significant digits in your answer. 4 SD for your answer is a lot for a problem where all the values and given to 1 or 2 SD.

I don't know if you have some kind of automated answer system or how they're programmed, but it could be rejecting the answer because of this.

 

[Senrai]

Thanks all. It must have been a problem with the program I was inputting the answer into. I did round off to the proper amount of significant digits when inputting the final answer into the program. After several more tries of doing the problem exactly like that, it's finally accepted the answer as correct. Thanks for your help.