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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

    Attached Images

    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.

    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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