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

Answer 1

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 = ___

Answer 2

1.2

Answer 3

30x-20(6-x)=0
30x-120+20x=0
50x-120=0
50x=120
x=2.4 ft

the balance point is 2.4ft from the 30lb weight.