How High Does a Swing Reach After Pumping Stops?

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SUMMARY

The discussion centers on calculating the maximum height a swing reaches after a child stops pumping, given an initial speed of 6.7 m/s at the lowest point and gravitational acceleration of 9.8 m/s². The conservation of energy principle is applied, where the kinetic energy (KE) at the lowest point converts to potential energy (PE) at the highest point. The relevant equations are KE = 0.5mv² and PE = mgh. The user successfully resolves the problem, indicating a clear understanding of energy conservation principles.

PREREQUISITES
  • Understanding of kinetic energy (KE) and potential energy (PE)
  • Familiarity with the conservation of energy principle
  • Basic knowledge of gravitational acceleration (9.8 m/s²)
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the conservation of mechanical energy in physics
  • Learn how to derive maximum height from kinetic energy
  • Explore real-world applications of energy conservation in sports
  • Investigate the effects of mass on energy calculations
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Students studying physics, educators teaching energy conservation, and anyone interested in understanding the mechanics of swings and motion dynamics.

Snape1830
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A child on a swing pumps hard and achieves a speed of 6.7 m/s at the swing’s lowest point. She then stops pumping. How high above the lowest point does the swing reach after that?

I honestly have no idea how to go about solving this. I know the velocity is 6.7 m/s (but is it final or initial or both?). I also know gravity is 9.8 m/s. But I don't know anything else?

I know the equation for conservation of energy is PEf+KEf = PEi+KEi. I know PE= mgh and KE= .5mv2 However, I have no idea how to do this because I don't have the height or the mass, and I don't know if 6.7 m/s is the initial, final, or both. I'm just completely lost.

Please help! Thanks!
 
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