Complicated spring stretch (compression )

[mshah3]

Homework Statement

A package of mass 8 kg sits at the equator of an airless asteroid of mass 5.8 105 kg and radius 32 m, which is spinning so that a point on the equator is moving with speed 4 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 194 m/s. We have a large and powerful spring whose stiffness is 2.8 105 N/m. How much must we compress the spring?

 

[Astronuc]

We respectfully request students to show some effort and work.

Think about the gravitational potential energy, kinetic energy, and spring energy.

The asteroid is spinning so there is already some centrifugal acceleration which counteracts the relatively small gravitational force.

If something never comes back then it must achieve escape velocity. The minimum requirement would the kinetic energy equivlent to the change in GPE at a very large distance away (where gravity would be essentially nil).

 

[mshah3]

well I figured it out to be Kf = Ui
so i did (0.5)mv^2 = (0.5)(k)(s)^2

thanks tho

 

[rubberduck]

i'm assuming that you used 8kg as the mass but what did you use for the v?