spent ages trying to work this out. i tried working moments out about C and about D, and using the fact that the reactions are the same but got nowhere.
Q. A uniform road AB has length 4m and weight 150N. The road rests in equilibrium in a horizantal position, smoothly supported at points C & D, where AC = 1m and AD = 2.5m, as shown in the diagram above. A particle of weight W Newtons is attached to the road at a point E where AE = x metres. The road remains in equilibrium and the magnitude of the reaction at C is now eqaul to the magnitude of the reaction at D.
a. Show that W = 150/(7-4x)
A diagram is attached to help illustrate it (altho excuse my lack of artistic ability)
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- Thread Starter
- 20-01-2010 22:56
- 20-01-2010 23:02
Well on your diagram for starters you should place an arrow going underneath at the midpoint of th beam with force 150N due to it beinf a uniform rod.
Now you should take points around one of your posts remembering that everything going in a clockwise direction = everything in a anti clockwise direction.
(This is to say the way the forces are going.)
See what you do with that as it should turn to be a simple simplyfying what you get from doing what I said.
- 21-01-2010 13:52
I'd start by resolving forces vertically. That gives you the (equal) reactions at C and D easily.
You then need to take moments about somewhere. I chose C. Moment of weight and W are balanced by moment of reaction at D. Comes out fairly easily.