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**1. Homework Statement**

http://edugen.wiley.com/edugen/courses/crs4957/art/qb/qu/c07/pict_7_11.gif

In the above figure, we must apply a force of magnitude

**82.0 N**to hold the block stationary at

**x=-3.0 cm**. From that position, we then slowly move the block so that our force does

**+8.0 J**of work on the spring–block system; the block is then again stationary. What are the block's positions, in cm? ((a) positive and (b) negative)

**2. Homework Equations**

F

_{s}=-kΔx

-kx

_{o}

^{2}-0.5kx

^{2}= W

**3. The Attempt at a Solution**

I'm sort of lost when it comes to springs, but this is my best shot:

F

_{s}=-kΔx

82N=-k(-3-0cm)

k=2733

W=-kx

_{o}

^{2}-0.5kx

^{2}

8J=-2733(-3)

^{2}- 0.5(2733)(x)

^{2}

8J=-24597-0.5(2733)(x)

^{2}

24605=-0.5(2733)(x)

^{2}

-18.01=x

^{2}

And that's where I'm stuck, so I definitely know it must be wrong. The only thing I can think is maybe I got the wrong sign on k, the spring constant. If so,

k=-2733

8J=2733(9)-0.5(-2733)(x)

^{2}

-17.99=x

^{2}

Either way, it's not a real number, so where did I go wrong...?