Posted by Stephanie on Friday, April 22, 2011 at 12:54am.
Let x be the distance (in feet) of the balance point from the end with the 30 lb weight.
The total moment about the balance point must be zero, if the beam is balanced. The beam's weight acts through the center of mass and exerts a moment of (3-x)*20 ft-lb about the pivot point.
This equals the moment (of opposite sign) due to the added weight, which is 30*x. The center of mass and the added weight are on opposite sides of the balance point.
Solve (3-x)*20 = 30x
60 - 20x = 30x
60 = 50x
x = ___
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