Calculating work with variable force

[forester404]

Homework Statement

Hi.
I am trying to learn some physics with MIT free resources (just out of personal interest),
and this is where i got stuck:
on section 14-13, in
http://ocw.mit.edu/courses/physics/8-01-physics-i-fall-2003/lecture-notes/binder13.pdf"
I am a little puzzled on how the work is calculated in the given solution - mgh,
where h is delta y between the 2 points. if i got it right, this calculation assumes
that the net force on y direction is mg and is constant throughout the path, but it seems
to me like the tension in the string is larger than 0 in every point along the path
except the very top of the circle (where it's 0 by porblem definition), and
always has some y component, so i don't understand how the net force in y direction
is a constant mg. what am i missing here ?

Homework Equations

W = integral from a to b (Fydy)

(sorry but i couldn't handle the LaTex renderer here...)

The Attempt at a Solution

 

[Doc Al]

The tension in the string is always perpendicular to the motion, thus it does no work on the rock. Only gravity does work on the rock.

 

[forester404]

Thanks for the quick reply !