Question

A package of mass 9 kg sits on an airless asteroid of mass 8.0 x 1020 kg and radius 8.3 x 105 m. 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 250 m/s. We have a large and powerful spring whose stiffness is 2.8 x 105 N/m. How much must we compress the spring? m

Answer 1

solution: imb mass of asteroid = 8 x 1040 kg radrus () = 8.3x10fm velocity of pookage for away |")= 250m/s Stiffnen in spring (K) = 2.8 * 105 N/m Energy conse Applying conservation of opy Ei= Ef 2 1 K² - Gimm = 1 m uz where x = comprension in spring m = man of pockage - 9 kg 2.8 x105 22- 667x10-11 X 8x102° x 9 1x 9X (250) 2 8.3x105

- zd sol x bed = selx bt 9 1802 sol x 1-4 x2 = 8.6 1 x = 204 78 m