Understanding Potential Energy of Hanging Mass on Spring

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SUMMARY

The discussion focuses on calculating the potential energy of a mass attached to a hanging spring, specifically addressing the integration bounds for potential energy calculation. The user employs the principle that potential energy is the negative integral of force, leading to the equation for potential energy as -1/2 ky² + mgy. The integration bounds are debated, with the user considering whether to integrate from -y to y0 or from y0 to y, emphasizing the importance of consistency in symbols and conventions used during integration.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants (k)
  • Familiarity with basic calculus, specifically integration techniques
  • Knowledge of gravitational force (mg) and its impact on potential energy
  • Concept of oscillatory motion in spring-mass systems
NEXT STEPS
  • Study the derivation of potential energy in spring systems using Hooke's Law
  • Learn about the principles of oscillatory motion and energy conservation in mechanical systems
  • Explore advanced integration techniques in calculus, focusing on definite integrals
  • Investigate the effects of varying spring constants on potential energy calculations
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone studying dynamics of spring-mass systems who seeks a deeper understanding of potential energy calculations.

atarr3
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I'm having a little trouble understanding the concept of energy for a hanging spring. Suppose I have a system with a mass that is attached to a hanging spring and then is released, causing the mass to oscillate. I'm trying to determine the equation for potential energy, but I'm thrown off by signs.

I'm using the concept that potential is the negative integral of force.

I set my initial position of the spring to be be y0 = 0, so when the mass is attached, we're moving in the negative y direction. This leads me to believe that my bounds for integration should be from -y to y0.

[tex]\int (kx + mg)dy[/tex] from -y to y0 would give me [tex]- \frac{1}{2}ky^{2}+mgy[/tex] if I substitute in y0 = 0.

I guess my question is if I would be correct in integrating from -y to y0 in order to find potential as a function of position, or if I should integrate from y0 to y like I'm traditionally used to.
 
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it's never been a problem from which to which you'll integrate as long as you are consistent with the symbols and convention that you are using.
 
Ok that's what I thought thank you so much!
 

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