Mechanics 1 - Moments question

Apr 2010
8
1
Bristol, England
A non-uniform beam, AB, of weight 200 N and length 5m, rests horizontally on supports at C & D, where AC=1m and AD=3m. If particles of weight 5W and W are attached at A and B respectively, the beam is on the point of tilting about C. If particles of weight W and 3W are attached at A and B respectively, the beam is on the point of tilting about D.

(i) Find the distance of the centre of gravity of the beam from A.
(ii)Find the value of W.

Hope someone can help, I keep getting ridiculously small values for the distance and hence can't really solve W.
Thanks in advance.
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
A non-uniform beam, AB, of weight 200 N and length 5m, rests horizontally on supports at C & D, where AC=1m and AD=3m. If particles of weight 5W and W are attached at A and B respectively, the beam is on the point of tilting about C. If particles of weight W and 3W are attached at A and B respectively, the beam is on the point of tilting about D.

(i) Find the distance of the centre of gravity of the beam from A.
(ii)Find the value of W.

Hope someone can help, I keep getting ridiculously small values for the distance and hence can't really solve W.
Thanks in advance.
1. Draw a sketch (see attachment)

2. In the first case the beam is at equilibrium with C as pivot point. Calculate the moments of forces:

\(\displaystyle 5W \cdot 1 = 4W+200 \cdot (x-1)\)

3. In the second case the beam is at equilibrium with D as pivot point. Calculate the moments of forces:

\(\displaystyle 1W \cdot 3 + 200(3-x) = 3W \cdot 2\)

4. Solve the system of simultaneous equations.
I've got x = 1.5 m (from A) and W = 100
 

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