Elastic Potential Energy and velocity of spring

AI Thread Summary
The discussion focuses on calculating the velocity of a mass released from a compressed spring using the conservation of energy principle. For a spring with a force constant of 600 N/m compressed by 0.30 m, the velocity at 0.40 m above the compressed position is calculated as 1.7 m/s. When calculating the velocity at 0.20 m, an error occurs due to neglecting the elastic potential energy (EPE) still present in the spring. The correct approach requires including the EPE at the new height, leading to a recalculated velocity of 2.4 m/s. The key takeaway is that the energy stored in the spring must be considered at all heights during the mass's ascent.
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Homework Statement



A spring, having a force constant of 6.0x102 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



(Epe + Ek)i +/- W = (Epe +Ek)f

The Attempt at a Solution


a) h= 0.4m, vf=?

(Epe + Ek)i +/- W = (Epe +Ek)f
0.5kx2=0.5mvf2 +mgh
kx2=mvf2 +2mgh
vf= √((kx2-2mgh)/m)
= √( ((600)(0.3)2-2(5)(9.81)(0.4))/ 5)
vf = 1.7 m/s [up]


b) h=0.20m
0.5kx2=0.5mvf2 +mgh
kx2= mv2+2mgh
vf= √((kx2-2mgh)/m)
= √( ((600)(0.3)2-2(5)(9.81)(0.2))/5 )
vf= 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
 
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In the second case only part of the compressed energy is used to push the block upward. So x should be 0.2 m, not 0.3 m.
 
But before the mass is released it's still being compressed 0.3m, and then after it moves up 0.2m.

I tried that anyway, and it wasn't the correct answer...
 
But you are neglecting the fact that the spring still has EPE at 0.2 m up from the initial compressed position . You must include that EPE of the spring on the right side of the conservation of energy equation.
 
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