Question

A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket is given by

F(x) = - GMm /x2

where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of theearth. Take the radius of the earth to be 4000 miles, so that x > 4000 miles.

1. Find the work, W1, done against gravity when the rocket rises 900 miles.


2. Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth.

Answer 1

This question was already answered before I formulated this solution, but it was answered wrong. Please rate this post first. Thank you.

I hope the choice of wording, "work done against gravity" is you paraphrasing the question, because the only thing we have enough information to solvefor is the work done "by" gravity. The work done by the rocket propulsion is positive, but it is significantly more than the negative of the work doneby gravity (because of all the acceleration)