- #1

sanctifyd83

- 6

- 0

## Homework Statement

A compressed spring has 138 J of energy stored in it. When it is decompressed by 125 cm, it now stores 82.6 J of energy. What is the spring constant

## Homework Equations

General:

ΔU = 1/2kx

_{f}

^{2}- 1/2kx

_{i}

^{2}

U(x) = 1/2kx

^{2}

U

_{1}= 1/2kx

_{1}

^{2}

U

_{2}= 1/2k(x

_{1}+ 1.25 m)

^{2}

## The Attempt at a Solution

U

_{1}= 1/2kx

_{1}

^{2}

k = 2U

_{1}/x

_{1}

^{2}

U

_{2}= 1/2 (2U

_{1}/x

_{1}

^{2})(x

_{1}+ 1.25 m)

^{2}

U

_{2}= U

_{1}/x

_{1}

^{2}(x

_{1}

^{2}+ 2.5m x

_{1}+ 1.5625 m

^{2}

U

_{2}= U

_{1}+ (2.5 m x

_{1}/x

_{1}) + (1.5625 m

^{2}U

_{1}/x

_{1}

^{2})

x

_{1}

^{2}ΔU = (2.5m U

_{1}/x

_{1}+ 1.5625m

^{2}U

_{1}/x

_{1}

^{2}) x

_{1}

^{2}

ΔU x

_{1}

^{2}= 2.5m U

_{1}x

_{1}+ 1.5625m

^{2}U

_{1}

Substitute values and get them all to one side:

55.4J x

_{1}

^{2}- 345Jm x

_{1}- 215.625Jm

^{2}= 0

Quadratic formula gives:

x

_{1}= 6.8 cm and -.57 cm

138J = 1/2k (.068 m )

^{2}

276J/.00462 m

^{2}= 59740 N/m = k? Obviously that can't be right.

Any help on this would be great!