Finding speed using conservation of mechanical energy

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SUMMARY

The discussion centers on calculating the speed of a ball in a pinball machine after being propelled by a spring with a spring constant of 675 N/m. The ball, with a mass of 0.0585 kg, is initially at rest and compressed against the spring by 0.0650 m. The analysis employs the conservation of mechanical energy principle, leading to the conclusion that the speed of the ball at point B, which is 0.300 m higher than point A, is calculated to be 23.105 m/s. The approach and values used in the calculations are confirmed to be correct by participants in the discussion.

PREREQUISITES
  • Understanding of conservation of mechanical energy principles
  • Familiarity with spring mechanics and Hooke's Law
  • Basic knowledge of gravitational potential energy (mgh)
  • Ability to manipulate and solve algebraic equations
NEXT STEPS
  • Study the derivation of the conservation of mechanical energy equation
  • Learn about Hooke's Law and its applications in mechanical systems
  • Explore the effects of potential energy in different gravitational fields
  • Investigate real-world applications of springs in mechanical devices
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Students in physics, mechanical engineers, and anyone interested in the dynamics of spring systems and energy conservation in mechanical contexts.

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In preparation for shooting a ball in a pinball machine, a spring (k = 675 N/m) is compressed by 0.0650 m relative to its unstrained length. The ball (m = 0.0585 kg) is at rest against the spring at point A. When the spring is released, the ball slides (without rolling) to point B, which is 0.300 m higher than point A. How fast is the ball moving at B?

I drew three springs vertically each having a ball on the top. The first spring on my left, is unstrained. The second spring is compressed by 0.065 m. The third spring is the tallest, it is .3 m above the second spring. The second spring having a ball at the top is called point A. The third spring having the ball at the top is called point B. I made my h=0 at point B.
From the way I understand the problem, speed at A is zero and mgh at B is also zero. This leads me to the following equation:
(mgh at A) + (1/2)(k)(x^2 at A) = (1/2)(m)(V^2 at B) + (1/2)(k)(x^2 at B)

I don't know if this is right, but I think that h at A is -0.3. Also, x^2 at A is 0^2 - (0.065^2). My x^2 at B is (-(.065^2)) - (.235^2). Plugging everything in, I get my speed at B to be 23.105 m/s. Is this right? Am I using the right approach. Are my values right? Unfortunately, this question is an even question from my textbook, so I do not have an answer for it. If someone is certain, please help me.
 
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I don't think the spring expands all .3 meters with the ball. I think the ball leaves the spring when it expands. I think you can neglect the potential energy of the spring after it has expanded.
 
thanks, your right, the answer works that way
 

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