Springs, Hooke's Law, Work, and Energy

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SUMMARY

The discussion focuses on calculating the peak height of Yelena Isinbayeva's center of mass during her pole vault using principles of mechanics, specifically Hooke's Law and energy conservation. Key formulas include Potential Energy (PE = mgh), Stored Strain Energy (SSE = (1/2)K(Δx)^2), and Kinetic Energy (KE = (1/2)mV^2). Given the pole's bending stiffness of 1158 N/m and a deflection of 1.41 m, the stored strain energy is calculated to be 1151.11 J. The work done by the pole equals this energy, which, when combined with her kinetic energy of 651.52 J, allows for the determination of her peak height above the ground.

PREREQUISITES
  • Understanding of Hooke's Law and its application in mechanics
  • Familiarity with energy conservation principles in physics
  • Knowledge of the formulas for potential, kinetic, and strain energy
  • Basic skills in algebra for manipulating equations
NEXT STEPS
  • Study the derivation and application of Hooke's Law in real-world scenarios
  • Explore energy conservation in mechanical systems
  • Learn how to calculate maximum height using energy equations
  • Investigate the effects of different materials on bending stiffness in pole vaulting
USEFUL FOR

This discussion is beneficial for physics students, sports scientists, and coaches involved in pole vaulting, as well as anyone interested in the application of mechanical energy principles in athletic performance.

x2022
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Homework Statement
The above image shows Yelena Isinbayeva (69.5 kg) at a point in her vault where the pole is maximally deflected (Δx = 1.41 m). The pole has a bending stiffness of 1158 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 4.33 m/s and she is 2.92 m above the ground.

If all of the stored stain energy is transferred from the pole to the vaulter, then what will be the peak height of her center of mass (relative to the ground) during the vault?
Relevant Equations
Stored Stain energy stored in pole = 1151.11
Work done by pole = 1151.11
Force applied to pole = 1632.78
Kinetic energy in Y = 651.52
Gravitational Kinetic Energy = 1990.84
The formulas we have been given include Potential energy=mgh, Stored strain energy=(1/2)K(change in X)^2, , Kinetic energy=(1/2)mV^2, Work=F(change in d), Force=K(change in X). Not sure how exactly to answer the question.
 
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x2022 said:
Homework Statement: The above image shows Yelena Isinbayeva (69.5 kg) at a point in her vault where the pole is maximally deflected (Δx = 1.41 m). The pole has a bending stiffness of 1158 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 4.33 m/s and she is 2.92 m above the ground.

If all of the stored stain energy is transferred from the pole to the vaulter, then what will be the peak height of her center of mass (relative to the ground) during the vault?
Homework Equations: Stored Stain energy stored in pole = 1151.11
Work done by pole = 1151.11
Force applied to pole = 1632.78
Kinetic energy in Y = 651.52
Gravitational Kinetic Energy = 1990.84

The formulas we have been given include Potential energy=mgh, Stored strain energy=(1/2)K(change in X)^2, , Kinetic energy=(1/2)mV^2, Work=F(change in d), Force=K(change in X). Not sure how exactly to answer the question.
You have found all the components of her mechanical energy at the point in the (missing) diagram.
What will be the components of her mechanical energy at the peak of her trajectory?
 

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