How to find out the range of a spring?

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SUMMARY

The discussion focuses on determining the range of a spring after calculating the spring constant using conservation of energy and projectile motion principles. The user seeks alternative methods to ascertain the necessary stretch of the spring for launching an object a specified distance. The solution involves utilizing projectile motion equations to derive the initial velocity and applying the conservation of energy formula, specifically ½ kx² = ½ mv², to find the spring stretch (x).

PREREQUISITES
  • Understanding of spring constant (k) and its calculation
  • Familiarity with conservation of energy principles
  • Knowledge of projectile motion equations
  • Basic algebra for manipulating equations
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  • Study the derivation of the spring constant (k) in detail
  • Learn about the conservation of energy in mechanical systems
  • Explore projectile motion equations and their applications
  • Investigate practical experiments to measure spring stretch and range
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Physics students, mechanical engineers, and hobbyists interested in understanding spring mechanics and projectile motion applications.

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How to find out the range of a spring??

I need to find the range of a spring after finding the spring constant. I have reduced the formula after using conservation of energy concepts and projectile motion. Is there another way to find out how much you need to stretch the spring to launch it a certain distance? Thanks
 
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Well you can use projectile motion equations such as range to get the initial velocity v and then use conservation of energy

½ kx2 = ½ mv2 to get x.
 

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