Finding the Block's Position After Work is Done on a Spring System

[Supernejihh]

Homework Statement

We must apply a force of magnitude 80N to hold the block stationary at x = -2.0cm. From that position, we then slowly move the block so that our force does +4.0J of work on the spring-block system; the block is then again stationary. What is the block's position? (Two answers.)

Homework Equations

F = -kx

W = (1/2)*k*xi^2 - (1/2)*k*xf^2

The Attempt at a Solution

80 = -k(-.02m)
k = 4000 N/m

With the spring constant, i plug it into the Work equation to find xf

4 = .5*4000*(-.02^2) - .5*4000*xf^2

3.2 = -2000xf^2
-.0016 = xf^2

And this is where I am stuck. The answer cannot be an imaginary number, but a real one. I know the equations are correct, so what am I doing wrong? Please explain.

 

[Doc Al]

W = (1/2)*k*xi^2 - (1/2)*k*xf^2

You want final minus initial, not the other way around.

 

[Supernejihh]

You want final minus initial, not the other way around.

The problem is that, that is how the book presented us with the equation. It was initial minus final. I understand where you are coming from, but that's how it is.

 

[Doc Al]

The problem is that, that is how the book presented us with the equation. It was initial minus final. I understand where you are coming from, but that's how it is.

Then what does W stand for in your book? The work done by the spring? The work done by you will be opposite to that.

 

[Supernejihh]

Then what does W stand for in your book? The work done by the spring? The work done by you will be opposite to that.

Doc Al. So what you are telling me is that the Work of +4.0J is caused by me. And its positive because the direction and force are directed towards one way. But the force of a spring is always opposite the displacement. So the work of the spring is -4.0J because its moving one way, while the force is directed towards the opposite?

 

[Doc Al]

Doc Al. So what you are telling me is that the Work of +4.0J is caused by me. And its positive because the direction and force are directed towards one way. But the force of a spring is always opposite the displacement. So the work of the spring is -4.0J because its moving one way, while the force is directed towards the opposite?

Right.

 

[Supernejihh]

Right.

Thanks for your help Doc. I really appreciate it.