Solve Torque w/ 2 Supports & Equilibrium Problems Easily

[VelvonVeden]

1. A 6.0 m long uniform plank is balanced on two supports with are 3.7 m apart. The plank weighs 400N. If one of the supports is 0.5m fro one end of the plank, how far from the other end can a 65 kg load hang without the plank tipping over?

and

A 7.2 m long beam AB weighing 480 N has its center of gravity 2.4 m from A. A 5.0 kg mass and a 2.5 kg mass are hung from the beam at 1.2 m and 0.8 m distances from B respectively. Calculate the position where the fulcrum is placed to keep the beam in equilibrium horizontally.

2. If someone could give me tips on a method of generally approaching such problems, I would appreciate itAccording to the laws of equilibrium, the moments of the force on with either side of the fulcrum must be equal, and the force acting downward must be equal to the opposite force acting upward.

Keeping that in mind I calculated the weight of 65 kg load mg - (65)(9.8) =637. I have had this problem for a while and have tried so many different methods i can't remember them all. Calculating the weights and trying to make them equal. Calculating the moments. Adding subtraction dividing etc. my instructor refuses to help.

I am stuck, I have no idea how to attack it now simple. Please help! I have four other similar problems.

 

[haruspex]

Please post at least one attempted solution, showing all working. Keep it all symbolic, not plugging in any numbers yet.