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## Homework Statement

[PLAIN]https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-08-GPE-ME/mass_vertical_spring/7.gif [Broken]

A spring with spring constant k = 35 N/m and unstretched length of L0 is attached to the ceiling. A block of mass m = 1 kg is hung gently on the end of the spring.

a) How far does the spring stretch?

Now the block is pulled down until the total amount the spring is stretched is twice the amount found in part (a). The block is then pushed upward with an initial speed vi = 3 m/s.

b) What is the maximum speed of the block?

## Homework Equations

[tex]W_{Total} = \Delta K[/tex]

[tex]W_{NC} = \Delta ME[/tex]

## The Attempt at a Solution

Part a was easy, got the answer to be ~.28m

Part b is where I'm having problems. So far this is what I've done:

I decided to use U

_{0}+ K

_{0}= U

_{f}+ K

_{f}and set U = 0 at the spot where the spring is at equilibrium with the mass on it. So I got this equation:

[tex]\frac{1}{2}kx^{2} - mgx + \frac{1}{2}mv_{0}^{2}= \frac{1}{2}mv_{f}^{2}[/tex]

Where x is .28 (the additional stretch). I'm not getting the correct answer which is around 3.4m/s

Any ideas whats wrong?

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