1. The problem statement, all variables and given/known data Imagine a thin tower 4000 miles tall; ı.e. as tall as the earth’s own radius Re, placed at the north pole of the earth. Suppose you start at rest at the base of the tower and climb to the top (wearing a spacesuit and carrying supplies you need, so that your total mass is M). How much work would you have done by the time you are at the top of the tower and at rest again? Neglect the mass of the tower compared to the mass of the earth. 2. Relevant equations These are the formulas I picked up from class and from reading the textbook: Total energy= U+K= Work by SURROUNDINGS change in U = -Work internal change in Ug= mgh 3. The attempt at a solution so, the explanation said to use "W= change in U" which I see they got from change in E= change in U + change in K = Work by surroundings (because change in K is 0 in this problem). HOWEVER, the explanation also said "if we consider the system to be you plus the earth, the gravitational potential energy is Ug(r)= ...." But, wait a second....If I and the earth are the system, then why are we using the equation that gives work done by the SURROUNDINGS. Shouldn't we use change in U = -Work internal? (in other words, change in U should have negative sign on it). I'm just confused on what to make my system, which equations to use, why E even equals work done by surroundings. Can someone please explain the concept and the reasoning behind the formulas here? Thank you so much. EXPLANATION: If we consider the system to be you plus the earth,the gravitational potential energy is Ug(r) = −G Me M / r The initial energy is Ei = Ug,i and the final energy is Ef = Ug,f. Thus the Energy Principle gives: W=∆Ug=Ug(2Re)−Ug(Re)= GMe M/2Re .