Spring constant, vertical ball launch speed.

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SUMMARY

The discussion focuses on a physics problem involving a spring with a spring constant of 128 N/m that compresses 2.0 m to launch a 4.0 kg ball vertically. The potential energy of the spring is calculated to be 256 J, and the maximum height reached by the ball is determined to be 6.53 m. The key challenge addressed is calculating the ball's velocity at the equilibrium position of the spring, which is found to be 9.42 m/s using conservation of mechanical energy principles, accounting for the gravitational potential energy of the ball.

PREREQUISITES
  • Understanding of spring potential energy (Us = 1/2 kx²)
  • Knowledge of kinetic energy (KE = 1/2 mv²)
  • Familiarity with gravitational potential energy (PE = mgh)
  • Concept of conservation of mechanical energy
NEXT STEPS
  • Study the principles of conservation of mechanical energy in physics.
  • Learn how to apply the spring constant in various mechanical systems.
  • Explore the effects of air resistance on projectile motion.
  • Investigate the relationship between potential energy and kinetic energy in dynamic systems.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for practical examples of spring dynamics and energy transfer.

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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