Why rocket altitude does not increase proportionally?

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SUMMARY

The discussion centers on the relationship between gravitational potential energy and elastic potential energy in the context of rocket altitude. The participant posits that the conservation of energy principle explains why rocket altitude does not increase proportionally. They conducted an analysis assuming a constant mass of 1 kg for the rocket and noted that the spring constant (k) decreases as the rubber band stretches. This indicates a non-linear relationship between the energy stored in the elastic medium and the altitude achieved by the rocket.

PREREQUISITES
  • Understanding of gravitational potential energy and elastic potential energy concepts.
  • Familiarity with the conservation of energy principle in physics.
  • Basic knowledge of mass and spring constant (k) in mechanics.
  • Experience with experimental physics and data analysis.
NEXT STEPS
  • Research the mathematical relationship between gravitational potential energy and elastic potential energy.
  • Explore the implications of varying spring constants in elastic systems.
  • Study the principles of rocket propulsion and altitude dynamics.
  • Investigate experimental setups for measuring energy conservation in elastic systems.
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Students and enthusiasts in physics, aerospace engineers, and anyone interested in the mechanics of rocket propulsion and energy conservation principles.

Starnair
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Homework Statement
1. Why rocket altitude does not increase proportionally with the amount of rubber band stretch? Provide an explanation for the lack of direct correlation.
I'm not sure that I am doing in right way, and cannot understand why k value is decreasing as rubber band stretches because I thought k value never changes.
Relevant Equations
Es=Eg
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I thought it is because of the consevation of the energy, so I used (gravitational potential energy at the top = elastic potential energy). Since the mass of the rocket never changes, I supposed mass= 1kg, and k value is unknown. As a result, I got the result that k value is decreasing as ruvber band stretches.
 

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I don't think your attachment would be legible even if you had NOT posted it sideways. You should fix both of those issues and re-post it.
 

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