Calculating Spring Compression for Escape Velocity from Spinning Asteroid

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SUMMARY

The discussion focuses on calculating the necessary compression of a spring to launch a 9 kg package from an airless asteroid with a mass of 6.1 x 10^5 kg and a radius of 36 m. The asteroid's equatorial speed is 2 m/s, and the package must achieve a final speed of 189 m/s to escape. The spring has a stiffness of 1.1 x 10^5 N/m. The energy conservation principle is applied, utilizing the equation Kp,f = Kp,i + Ui + W to relate initial and final energies, including gravitational potential energy.

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  • Understanding of energy conservation principles in physics
  • Familiarity with gravitational potential energy calculations
  • Knowledge of spring mechanics and Hooke's Law
  • Basic algebra for solving equations
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  • Study energy conservation in mechanical systems
  • Learn about gravitational potential energy and its applications
  • Explore Hooke's Law and spring potential energy calculations
  • Investigate escape velocity concepts in astrophysics
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Students in physics, particularly those studying mechanics and energy conservation, as well as educators looking for practical examples of spring dynamics and escape velocity calculations.

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Homework Statement



A package of mass 9 kg sits at the equator of an airless asteroid of mass 6.1 * 10^5 kg and radius 36 m, which is spinning so that a point on the equator is moving with speed 2 m/s. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 189 m/s. We have a large and powerful spring whose stiffness is 1.1*10^5 N/m. How much must we compress the spring?

Homework Equations



Kp,f = Kp,i + Ui + W

The Attempt at a Solution



Im kinda lost at how to attempt this problem so any help explaining me through the process would be great.
 
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Looks like an energy conversion problem. You could write
initial energy = final energy
then put in expressions for the various kinds of energy it has. Don't forget the gravitational potential energy.
 
Alright thanks imma work on this problem and see what i get as an answer
 

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