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## Homework Statement

A spring, having a force constant of 6.0x10

^{2}N/m, is held in a vertical position and compressed 0.30m. A 5.0 kg mass is then placed on top of the spring. THe mass is then releases. Neglecting air resistance and the mass of the spring, calculate:

a) the velocity of the mass when it has moved up 0.40m from the compressed position of the spring.

b) the velocity of the mass when it has moved up 0.20m from the compressed position of the spring.

## Homework Equations

(E

_{pe}+ E

_{k})i +/- W = (E

_{pe}+E

_{k})

_{f}

## The Attempt at a Solution

a) h= 0.4m, v

_{f}=?

(E

_{pe}+ E

_{k})i +/- W = (E

_{pe}+E

_{k})

_{f}

0.5kx

^{2}=0.5mv

_{f}

^{2}+mgh

kx

^{2}=mv

_{f}

_{2}+2mgh

v

_{f}= √((kx

^{2}-2mgh)/m)

= √( ((600)(0.3)

^{2}-2(5)(9.81)(0.4))/ 5)

v

_{f}= 1.7 m/s [up]

b) h=0.20m

0.5kx

^{2}=0.5mvf

^{2}+mgh

kx

^{2}= mv

^{2}+2mgh

v

_{f}= √((kx

^{2}-2mgh)/m)

= √( ((600)(0.3)

^{2}-2(5)(9.81)(0.2))/5 )

v

_{f}= 2.6 m/s [up]

the answer for b) is 2.4 m/s [up], so I'm off by 0.2m/s. Can anybody explain to me what was wrong? I appreciate it