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## Homework Statement

A spring of negligible mass has force constant k = 1800N/m .

You place the spring vertically with one end on the floor. You then drop a book of mass 1.20kg onto it from a height of 0.500m above the top of the spring. Find the maximum distance the spring will be compressed.

## Homework Equations

K

_{i}+ U

_{i}= K

_{f}+ U

_{f}

## The Attempt at a Solution

First I calculated the velocity of the block when it makes contact with the spring and I got v = 3.96 m/s.

Then I used conservation of energy to find the spring compression distance by setting the point where the block makes contact with the spring to be zero (y=0).

So:

K

_{i}= U

_{f}

(1/2)mv

_{i}

^{2}= (1/2)kx

^{2}- mgx

Then I substituted the values in and had to use the quadratic formula to find x which I got x = 0.10898m or x = -0.0959.

I used the negative x value because the spring is being compressed downward, but my answer is still incorrect somehow.