Engineering Statics

B-13


Three stage lights are mounted on a pipe as shown. The lights at A and B weigh 4.1 lb, while the one at C weighs 3.5 lb. (a) If d = 25 in., determine the distance from D to the line of action of the resultant of the weights of the three lights. (b) Determine the value of d so that the resultant of the weights passes through the midpoint of the pipe.

The free-body diagram is easier to see when it is drawn in 2D.
The weight of the three lights are added to get a resultant in 
the y-direction.
The moment is taken about point D on the left of the pipe.
This gives a moment about D.
The moment is also equal to the distance from D time the resultant 
force.
Solving for L gives us the distance from D to the line of action 
of the resultant.

The moments for part (b) are again taken about D, but this time they are calculated in terms of d, the distance between lights B and C. The moment is also set equal to the distance to the middle of the pipe (84/2) times the total weight of the lights." >
Simplification:
Arithmetic yields the answer for d.