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    A large log AB is 6m long. It rests in a horizontal position on two smooth supports C and D, where AC=1m and BD=1m. David needs an estimate of the weight of the log, but the log is too heavy to lift off both supports. When David applies a force of magnitude 1500N vertically upwards to the log at A, the log is about to tilt about D.

    a) State the value of the reaction on the log at C for this case.

    David intially models the log as a uniform rod. Using the model,

    b) estimate the weight of the log.

    The shape of the log convinces David that his intial modelling assumption is too simple. He removes the force at A and applies a force acting vertically upwards at B. He finds that log is about to tilt about C when this force has magnitude 1000N. David now models the log as a non-uniform rod, with the distance of the centre of mass of the log from C as x metres. Using the model, find

    c) a new estimate for the weight of the log.
    d) the value of x.

    I can do parts a) and b) with answers 0 and 3750N

    Thanks
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    (Original post by MM1234)
    A large log AB is 6m long. It rests in a horizontal position on two smooth supports C and D, where AC=1m and BD=1m. David needs an estimate of the weight of the log, but the log is too heavy to lift off both supports. When David applies a force of magnitude 1500N vertically upwards to the log at A, the log is about to tilt about D.

    a) State the value of the reaction on the log at C for this case.

    David intially models the log as a uniform rod. Using the model,

    b) estimate the weight of the log.

    The shape of the log convinces David that his intial modelling assumption is too simple. He removes the force at A and applies a force acting vertically upwards at B. He finds that log is about to tilt about C when this force has magnitude 1000N. David now models the log as a non-uniform rod, with the distance of the centre of mass of the log from C as x metres. Using the model, find

    c) a new estimate for the weight of the log.
    d) the value of x.

    I can do parts a) and b) with answers 0 and 3750N

    Thanks
    Hmm, I believe I see a way to do this, but I may be missing something simple(r). If I am I can't see it though.

    Assuming from being able to answer the previous question, you know that if it's about to tilt at C, the reaction at D = 0.

    I think you then have to take moments about C and and centre of mass (getting two equations in X). Then find C in terms of W and substitute it into these for a quadratic. Can you see how you would do that?

    Spoiler:
    Show
    Equate the forces upwards and downwards
    Spoiler:
    Show
     W = C + 1000


    I think the quadratic gives two solutions but you should be able to disregard one clearly.
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    bump. I don't actually understand how to do c) or b), even after the explanation :/

    EDIT: I've resolved to find 1000 + Rc = W, and finding the moment about C I get Wx=5000.

    Answer to C = 3125 N
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    (Original post by moonymeen)
    bump. I don't actually understand how to do c) or b), even after the explanation :/

    EDIT: I've resolved to find 1000 + Rc = W, and finding the moment about C I get Wx=5000.

    Answer to C = 3125 N
    B) is simply take moments about D, so you get 2W = 5*1500, so W=3750.

    As for c) and d) I am not too sure. We can form a few statements in terms of c, w and x, it'll just be a case of being able to substitute one into another until you can solve it.
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    (Original post by Thrug)
    B) is simply take moments about D, so you get 2W = 5*1500, so W=3750.

    As for c) and d) I am not too sure. We can form a few statements in terms of c, w and x, it'll just be a case of being able to substitute one into another until you can solve it.
    Thanks for replying. Yeah c) is really getting on my nerves. I hate having to find out 3 things :rolleyes:
 
 
 
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