Solution Found!
a) Consider a mass m in a uniform gravitational field g,
Chapter 4, Problem 4.5(choose chapter or problem)
a) Consider a mass m in a uniform gravitational field g, so that the force on m is mg, where g is a constant vector pointing vertically down. If the mass moves by an arbitrary path from point 1 to point 2, show that the work done by gravity is Wgray(1 > 2) = mgh where h is the vertical height gained between points 1 and 2. Use this result to prove that the force of gravity is conservative (at least in a region small enough so that g can be considered constant). (b) Show that, if we choose axes with y measured vertically up, the gravitational potential energy is U = mgy (if we choose U = 0 at the origin).
Questions & Answers
QUESTION:
a) Consider a mass m in a uniform gravitational field g, so that the force on m is mg, where g is a constant vector pointing vertically down. If the mass moves by an arbitrary path from point 1 to point 2, show that the work done by gravity is Wgray(1 > 2) = mgh where h is the vertical height gained between points 1 and 2. Use this result to prove that the force of gravity is conservative (at least in a region small enough so that g can be considered constant). (b) Show that, if we choose axes with y measured vertically up, the gravitational potential energy is U = mgy (if we choose U = 0 at the origin).
ANSWER:Step 1 of 3
(a)
The force acting on the mass 
Let there are two points which are at a distance 
The vertical height between points 1 and 2 is,
