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    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)

    Cake shall be delivered if appropriate help is given as to how to solve this

    thanks
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    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.
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    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.
 
 
 
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