Question

A package of mass 5 kg sits on an airless asteroid of mass 9.4 × 1020 kg and radius 9.0 × 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 170 m/s. We have a large and powerful spring whose stiffness is 2.8 × 105 N/m. How much must we compress the spring? m

Answer 1

Here ,

let the compression in the spring is x

using conservation of energy

initial mechanical energy = final mechanical energy

gravitational potential energy + spring potential energy = final kinetic energy

- 6.673 *10^-11 * 5 * 9.4 *10^20/(9 *10^5) + 0.50 * 2.8 *10^5 * x^2 = 0.50 * 5 * 170^2

solving for x

x = 1.734 m

the compression in the spring is 1.734 m