# Forces and Moments acting on an entire system.

## Homework Statement

The ceiling-mounted bicycle rack (shown in "Capture" image in attachments) with dimensions p = 50 mm, q = 1000 mm and r = 150 mm for a bicycle that weighs F = 200 N.

The rack is to be made from two parts, ABC and BD, cut from a steel tube and then welded together at B.

Determine the forces and moments acting on the whole rack, ABCD.

## Homework Equations

The only equations that I can see would be relevant here are the force and moment equations:
M = (F*d)
Ʃ M = 0
Ʃ F = o

## The Attempt at a Solution

I have found M(of B) and M(of C) by doing the following:

M(of B) = 200*0.15 = 30Nm Clockwise

Therefore, 30 = 0.05*F(at A), so F(at A) = 600N

So... M(of C) = 1.05*600 = 630Nm Clockwise.

So I have found M at points B and C, and the force at A, however I am not confident that is what's required of the question. What does it mean by "the forces and moments acting on the whole rack ABCD"??

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haruspex
Homework Helper
Gold Member
There seems to be something missing in the problem statement. I gather from your attempted solution that there is a a horizontal force FA at A.
I have found M(of B) and M(of C) by doing the following:

M(of B) = 200*0.15 = 30Nm Clockwise

Therefore, 30 = 0.05*F(at A), so F(at A) = 600N
If you are taking moments about B then you must consider a contribution from the force at C. It does not necessarily act vertically. Better might be to take moments about C.

There seems to be something missing in the problem statement. I gather from your attempted solution that there is a a horizontal force FA at A.

If you are taking moments about B then you must consider a contribution from the force at C. It does not necessarily act vertically. Better might be to take moments about C.
There is no acting force on A. I just calculated that because if there is a moment at B, then having the 200N force at D would be the equivalent of having a Force of 600N at A. Am I wrong?

haruspex