Calculating Spring Compression for Escape Velocity from Spinning Asteroid

AI Thread Summary
To calculate the spring compression needed to launch a 9 kg package from a spinning asteroid, the initial and final energy states must be considered. The problem involves converting potential energy and kinetic energy, factoring in the gravitational potential energy of the asteroid. The required final speed for the package to escape is 189 m/s, while it starts with a speed of 2 m/s due to the asteroid's rotation. The spring's stiffness of 1.1 * 10^5 N/m will play a crucial role in determining the necessary compression. Understanding energy conservation principles is essential for solving this problem effectively.
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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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