How to Calculate Mechanical Advantage of Box On a Board

[syang9]

Let's say you put a box on a board, like this. (the dot represents a fulcrum point). Let's say the center of mass is exactly halfway between the fulcrum and the edge of the board.

http://dl.getdropbox.com/u/119319/board.jpg

Now let's say you exert an upward force F in the direction of the arrow. My book tells me that the force should be reduced by a factor of 2.. which I suppose is plausible, but how can you know the exact mechanical advantage without knowing the length of the board?

 

[Doc Al]

Can you figure out the mechanical advantage if you knew the length of the board? Call the length L and see what happens.

 

[syang9]

Okay, I think I was confused because I didn't really understand the definition of a 'lever arm.' The lever arm is defined as the distance from the rotation point to where the force acts perpendicular. So the lever arm for F would be L, and the lever arm for the weight of the box would be L/2. F*L = mg(L/2), and F = mg/2. Thanks, Doc!