Simple lift calculations for pivoting load; help, please.

Hello, all. I've got a device I'd like to build which will require a small panel (maybe 3 feet tall by 2 feet wide) be pivoted. The panel will have a pivot at the narrow edge. I'd like to assist the lifting of panel by placing a hanging weight on the opposite side of the panel. I intend for the counter weight to attach to the pivoting panel at the end farthest from the pivot. I want the panel to always be heavier than the force applied by the counter weight so that it will fall due to gravity when the panel is pushed out of the way. I'm sure there is a way to calculate how much weight needs to be used as the counter weight, given the panel weight, but I've no idea what that calculation might be.

Here's the gist of it: weight----*pivot-----------------panel. Assuming the panel is uniform in weight distribution and disregarding friction in the pivot, 1) how do I calculate how much weight I need to place on the other side of the pivot and how far from the pivot does it need to be (directly related items, I'm sure)? 2) assuming the panel has the pivot at the "top" (farthest from the ground) and is leaning 60 degrees up from the ground (mostly vertical), can I use a straight arm from the pivot to the counter weight attachment point or will I need a cam/egg shaped piece to carry a cable and effectively change the amount of force applied by the counter weight by moving it farther from the pivot point? Oh, and the panel will start at a 60 degree angle like this / and be raised only to the horizontal position like this ----, so 60 degrees of rotation.

Thanks for your time and help. I'd like to make calculations ahead of time instead of trial-and-error for days.

--HC