Physics
posted by Stephanie on .
A 30lb weight is attached to one end of a 6ft uniform beam whose own weight is 20lb. Where is the balance point of the system? I know the answer is "1.2 ft from the 30lb weight" but I can't figure out how to get there. Please help. Thanks...

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 (3x)*20 ftlb 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 (3x)*20 = 30x
60  20x = 30x
60 = 50x
x = ___ 
1.2

30x20(6x)=0
30x120+20x=0
50x120=0
50x=120
x=2.4 ft
the balance point is 2.4ft from the 30lb weight.