Uniform Beam Reactions | Coplanar Forces Problem Solution

[jernobyl]

Homework Statement

A uniform beam AB of length 6m and weight 11 N rests horizontally on two supports C and D, where AC = 1m and DB = 2m. Weights of 6 N and 7 N are hung from points A and B respectively. Calculate the reactions at each support. What extra force must be applied at B in order to cause the beam to just lift off the support at C?

Homework Equations

Moments...

The Attempt at a Solution

I figure this diagram is accurate:

My problem is that I get the right answer, but I can't understand why gravity isn't factored into the answer. Let me explain.

First of all I've taken moments about A, equating the clockwise and anticlockwise:

P + 4Q = 33g + 42g
P + 4Q = 75g equation 1

And about B:

5P + 2Q = 33g + 36g
5P + 2Q = 69g equation 2

Obviously now I have two simultaneous equations, so I solve them by multiplying equation 2 by 2, then subtracting equation 1.

10P + 4Q = 138g
-(P + 4Q = 75g)

9P = 63g
P = 7g = 68.6 N

Then substituting this in equation 1:

7g + 4Q = 75g
4Q = 68g
Q = 17g = 166.6 N

HOWEVER...the answers I have are 7 N for P, and 17 N for Q. Why has gravity not been factored into these answers? I don't understand! :S

Thanks!

 

[PhanthomJay]

It already has been factored in, since the loads and beam weight are given in force units of Newtons. If the beam's mass was given instead, say in kilograms, only then would you have had to multiply the mass by g to get the proper force unit of Newtons.

 

[jernobyl]

Oh! Oh, I see. Okay, thanks! Um...I couldn't trouble you to look at my other coplanar force, could I? ;)