Spring constant, vertical ball launch speed.

AI Thread Summary
The discussion revolves around calculating the speed of a ball launched by a compressed spring with a spring constant of 128 N/m. The potential energy of the spring when compressed is determined to be 256 J, and the maximum height reached by the ball is calculated to be 6.53 m. The challenge lies in finding the speed of the ball at the moment it leaves the spring's equilibrium position, which is not simply derived from the potential energy. By applying conservation of mechanical energy and accounting for the gravitational potential energy gained as the ball rises, the correct speed is found to be approximately 9.4 m/s. The discussion highlights the importance of considering energy transformations in such problems.
SteelDirigibl
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Ok I have most of this solved but can't get the third part right.

Homework Statement


A spring of spring constant 128N/m is compressed a distance of 2.0m from its equilibrium position, and used to project a ball of mass 4.0 kg directly upwards. Neglect air resistance.

1. What is the potential energy of the spring in its compressed position? 256 J
2. To what maximum height above its initial (compressed) position does the ball reach? 6.53m

3. Earlier, just when the spring is returned to its equilibrium position, as the ball was moving upwards, how fast was the ball moving? undetermined?


Homework Equations



KE=1/2*mv2
PE=mgh
Us=1/2kx2



The Attempt at a Solution



The first thing I tried was simply using the previously calculated energy, 256J, and solving for velocity in the KE equation. This gets 11.3 m/s using mass of the ball, but I'm sure I'm supposed to account for some other motion of the spring, because it doesn't transfer all of that energy to the ball. The correct answer is 9.4 m/s. Where do I go from here?
 
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Don't assume that all of the spring PE goes into KE--the ball also rises. Use conservation of total mechanical energy.
 
Ah I get it.

The ball rises 2.0m at that point. PE of the ball is 2*4*9.8=78.4

256-78.4=177.6

1/2*m*v^2=177.6

177.6*2/4=88.8
88.8^.5=9.42 m/s

Thanks a lot! it looks like I just need to think a little more about what I'm doing. Got my final tomorrow morning.
 

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